Intricate Phase Behavior and Crystal Structure Features of Chiral para

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Intricate phase behavior and crystal structure features of chiral paramethoxyphenyl glycerol ether forming continuous and partial solid solutions Robert R. Fayzullin, Dmitry V. Zakharychev, Aidar T. Gubaidullin, Olga A. Antonovich, Dmitry B. Krivolapov, Zemfira A. Bredikhina, and Alexander A Bredikhin Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.6b01522 • Publication Date (Web): 29 Nov 2016 Downloaded from http://pubs.acs.org on December 1, 2016

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Crystal Growth & Design

Intricate phase behavior and crystal structure features of chiral para-methoxyphenyl glycerol ether forming continuous and partial solid solutions Robert R. Fayzullin,*‡ Dmitry V. Zakharychev,‡ Aidar T. Gubaidullin, Olga A. Antonovich, Dmitry B. Krivolapov, Zemfira A. Bredikhina, Alexander A. Bredikhin A.E. Arbuzov Institute of Organic and Physical Chemistry, Kazan Scientific Center, Russian Academy of Sciences, Arbuzov street, 8, Kazan, 420088, Russian Federation KEYWORDS Solid solution of enantiomers, mixed crystals, pseudoracemate, racemic compound, phase transitions, polymorphism, multiple molecules in asymmetric unit, disorder, DSC, X-ray analysis.

ABSTRACT

Heterogeneous equilibria, crystallization, and polymorphism of chiral para-methoxyphenyl glycerol ether 1 have been inspected and, as a result, the binary phase diagram and the Gibbs free energy vs. temperature plot were constructed and analyzed. This enantiomeric system forms a stable racemic compound, which turns into an almost ideal continuous solution of the

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enantiomers in the crystalline phase at elevated temperatures. At room temperature the system represents a stoichiometric racemic compound and two symmetrical eutectoid invariants with partial solid solutions based on the enantiomers. Crystal structures of the true racemate, the pseudoracemate, and the pure enantiomer were investigated by single crystal X-ray diffraction. The true racemate crystallizes in the Pc space group with Z' = 2. The pseudoracemate was solved in the Pbcn group with the only independent molecule equally disordered into two mirror-related positions. The enantiomeric crystals belong to the P21212 group and are characterized by six symmetry independent molecules (Z' = 6), two of which undergo disordering. We also discussed possible connection between the phase behavior features and the details of the crystal structure, in particular, bilayer supramolecular organization, pseudosymmetry, high Z', and disordered packing. General considerations about the crystalline nature of solid solutions of enantiomers were also made.

INTRODUCTION Heterogeneous equilibria and crystallization of chiral compounds govern many processes of isolation and purification of nonracemic chemicals.1-4 The great interest in these issues, in our opinion, is explained not only by the possibility of commercializing research results, but also by comprehension of false simplicity of the common model of phase behavior of organic compounds in the condensed state. So, examples of rare types of crystalline racemates and cases with complicated phase behavior appear in the literature.5-8 Thus, more thorough understanding of the interrelation between phase behavior of a chiral substance and its molecular and crystal structures is a problem on the cutting edge of the present-day scientific research. Crystallization of an enantiomer mixture is determined by combination of thermodynamic and kinetic factors.9 The result of crystallization under equilibrium conditions must be the formation


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of the most thermodynamically favored phase. In the vast majority of cases, such a phase happens to be a crystalline molecular compound with the equimolar composition, i.e., a racemic compound (the examples of compounds with a non-equimolar composition are also known, but rare). In those cases, when the energetically favored molecular compound is absent, the crystallization of individual enantiomers (in other words, a racemic conglomerate) is expected. In any case, the crystallization is accompanied by the decrease in entropy of the system, and the driving force of the process is enthalpy factor, namely, taking an advantageous conformation and the formation of energetically favorable intermolecular contacts in the ordered system. Nonetheless, the entropy could play a decisive role, especially at elevated temperatures. It is evident that the entropy of a real crystal at non-zero temperatures is invariably positive: thermal vibrations of atoms, dynamic and static disorder of molecular fragments and whole molecules are always presented. In the case of chiral compounds, the disorder caused by the possibility of enantiomers occupy the same site of crystal lattice can be further expected. If this does not lead to a significant loss in the enthalpy, the entropy factor could make a significant contribution to the free energy of crystal formation, and even provides thermodynamic preference of the structure with high disordering. Most obviously the above-described effect is manifested in the cases of exotic and poorly studied continuous10-16 and partial17-22 mixed crystals, or, in other words, solid solutions. Behavior of a solid solution could be additionally complicated owing to transition into ordered phase (phase layering) at low temperatures. Based on the difference in the melting points of a racemic phase and an enantiomer, three types of continuous solid solutions are traditionally distinguished: ideal and with positive or negative deviation from ideality.23 4-Methoxyphenyl glycerol ether 1 (Chart 1) has been proposed as a convenient backbone in lipid synthesis.24 During our initial attempts to obtain this compound with high enantiomeric


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purity, we discovered that it was not possible using simple recrystallization methods.25 Preliminary thermoanalytical studies suggested that diol 1 forms a solid solution phase.6 Recently we have synthesized the homologous series of para-alkoxyphenyl glycerol ethers. The melting behavior of the first seven representatives studied by hot-stage microscopy reveals the proximity of the fusion temperatures for the “racemate-enantiomer” pairs. At the same time, we did not observe the eutectic melting of the samples of intermediate composition. Thus, we presumed that the members of the whole family of the explored glycerol derivatives, from paramethoxy- to para-n-heptyloxyphenyl glycerol ether, forms a solution of enantiomers in crystalline state.26 Interestingly, another notable group of glycerol ethers, which shows so-called preferential enrichment phenomenon, falls into a solid solution class as well.27 Chart 1. The structural formula and the partial numbering of diol 1.

In this work, we set out to investigate in depth the nature of the racemic substance, the features of phase behavior, and the crystal structure of para-methoxyphenyl glycerol ether 1, the simplest representative of the above mentioned homologous series. EXPERIMENTAL The synthesis of the racemic and enantiopure samples of diol 126 and the procedure of solubility experiments28,29 were described in detail in our previous work. The thermograms were measured on a Netzsch DSC 204 F1 Phoenix differential scanning calorimeter (τ-sensor). The X-ray powder diffraction data (XRPD) were collected on a Bruker D8 Advance X-ray diffractometer (CuKα1 radiation) in the Bragg-Brentano geometry.


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The single crystal XRD experiments were performed using a Bruker Smart Apex II CCD diffractometer (MoKα radiation) at 20 °C. The structures were solved by intrinsic phasing methods using SHELXT-2014/5 and refined by the full matrix least-squares on F2 using SHELXL-2014/7.30 Non-hydrogen atoms were refined anisotropically. The position of the hydrogen atoms H1 and H2 (Chart 1) of α-phase rac-1 was determined on the basis of the electronic density distribution, and these atoms were refined isotropically. The other hydrogen atoms of diol 1 in all three cases were inserted at the calculated positions and refined as riding atoms. Unfortunately, the crystals of β-phase rac-1 diffracted poorly due to solid solution nature and bad quality of crystals, nonetheless the obtained model proved to be appropriate. The crystal data, data collection and structure refinement details for the three investigated phases are summarized in Table S1. Crystallographic data for the investigated structures have been deposited in the Cambridge Crystallographic Data Centre as supplementary publication numbers CCDC 1510171, 1510172, and 1510173 for α-phase rac-1, α-phase (R)-1, and β-phases rac-1, respectively. RESULTS & DISCUSSION Polymorphism inspection. Scalemic diol (R)-1 crystallizes from its solution or melt as platelike crystals (α-phase (R)-1) that do not change with time. While heating the dry sample of (R)-1, no changes in the appearance of the crystals were observed up to the melting at 78-78.5 °С. In the case of racemate, diol rac-1 exhibits more complex behavior: crystallization from the hot saturated solution or the melt leads to the formation of thin micaceous crystals (β-phase rac-1) resembling the scalemic one (Fig. S1). But unlike the latter, ripening of the β-phase rac-1 crystals in the mother liquor for a few hours leads to recrystallization of a new phase (α-phase rac-1). According to XRPD and IR spectroscopy data, the grinded crystals of β-phase rac-1


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convert into the α-phase in the absence of a solvent in a few days. The study of the α- and βphases of rac-1 with the help of hot-stage microscopy did not show any significant differences: both samples melt in the interval of 79-80 °С. This result is consistent with study of the crystal morphology by using SEM. The smooth surface of the crystals of freshly crystallized β-phase rac-1 (Fig. 1a) is turning spoilt after the phase transformation into the α-modification in a mother solution media (Figs. 1b, c). Moreover, Fig. 1c illustrates that the transformation occurs particularly on the edges of the plates. We believe that the nuclei of the β-phase (stable or metastable, but preferred for kinetic reasons) are formed and grown during the crystallization from the hot solution. Under metastable equilibrium of the β-phase in the mother liquor at 20 °С, the molecules located mainly on energy-rich edges or surfaces undergo multiple adsorption and desorption events, which leads finally to nucleation and growth of the stable α-phase.


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Figure 1. The SEM photographs of the non-conditioned crystalline samples of diol rac-1. Freshly crystallized β-phase rac-1 (a) and the same sample after the contact with the mother liquor for more than 2 hours (b, c). To further elaborate on this point, we utilized a solution-mediated phase transformation procedure as a reliable and easy method for obtaining a stable at a given temperature crystalline phase (with intermediate enantiomeric composition as well). It is obvious that an equilibrium crystalline phase can be obtained after intensive stirring of a suspension of a solid substance and a solvent for about two or three hours. This procedure employs repeated recrystallization of a solid material, which takes place mainly on the surfaces of fine crystallites and is catalyzed by a solvent. The driving force of the process is a higher solubility of metastable phases as compared to the stable one. The events leading up to an initial solid sample do not play a significant role; a solvent should be chosen so that the solubility of a compound is about 0.05 g L-1 and no solvate formation happens. According to the suspension experiment for diol rac-1 in cyclohexane, the αphase is under equilibrium with solution at the temperature region of 20 to 72 °С (which was documented by solid state IR spectroscopy and XRPD), but the β-phase is already stable at temperatures higher than 73 °С. Therefore, both α- and β-phases of diol rac-1 are thermodynamically stable in the certain temperature ranges, while the β-phase is metastable in standard conditions. Testing the nature of racemate types. The IR spectra of polycrystalline samples of β-phase rac-1, α-phase (R)-1, and α-phase rac-1 are presented in Fig. 2a, respectively. Fig. 2b clearly shows that the vibrational spectra of β-phase rac-1 and α-phase (R)-1 are very similar: the correlation trajectory28 close to a diagonal line. The analysis of the observed loops (Fig. S2) on the trajectory points to the differences between the spectra in the areas from 730 to 772 cm-1 and from 881 to 895 cm-1. All this may indicate a similarity in the molecular microenvironment and thereby the isostructural nature of crystals of the compared phases. As discussed in the


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introduction, we did not observe the eutectic melting for the samples with intermediate enantiomeric compositions of diol 1,26 which is not typical for conglomerate or racemic compound forming systems. Basing on this, we hypothesize that diol 1 forms an almost ideal solid solution of the enantiomers (β-phase rac-1) that is stable at high temperatures. The fact that the melting points of the racemic and enantiomeric samples are very close is also consistent with this assumption.

Figure 2. The IR spectra (a) of the polycrystalline samples of β-phase rac-1 (red), α-phase (R)-1 (blue), and α-phase rac-1 (green) recorded at 20 °С in potassium bromide matrix and the graphical representation of correlations between β-phase rac-1 and α-phase (R)-1 (b) and between α-phase rac-1 and α-phase (R)-1 (c). On the contrary, there is a marked dissimilarity between the IR spectra of α-phase (R)-1 and αphase rac-1 and simultaneously between the spectra of the two modifications of racemate. Fig. 2с demonstrates the correlation diagram with a sophisticated pattern, which leaves no doubt about a significant discrepancy between these spectra, notwithstanding the moderately high value of the Pearson correlation coefficient r = 0.951. The principal difference between the pairs of spectra under consideration relates to the first absorption bands in the interval ν = 3120-3550 cm1

corresponding to stretching vibrations of H-bonded hydroxyl group. In accordance with the

spectrum of α-phase rac-1, at least three types of hydrogen bonding can be identified: strong


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with a red shifted band ν = 3227 cm-1, “usual” ν = 3406 cm-1, and rather weak with a narrow blue shifted band ν = 3454 cm-1, whereas one characteristic broad band with a maximum at ν = 3346 cm-1 is recorded for α-phase (R)-1 and β-phase rac-1. Extra sets of absorption bands responsible for the difference at low-frequency parts of the spectra relate to stretching vibrations of C–O(H) fragments and bending vibrations of O–H groups. The spectral difference for a pair of α-phase (R)-1 and α-phase rac-1 implies the formation of the molecular compounds in the case of the latter.

Figure 3. The IR spectra of racemic (a-d) and enantiomeric (e-h) samples of diol 1 in potassium bromide pellets recorded at 20 °С (a, d, e, h), 65 °С (b, f), 85 °С (c, g). The spectra of different phases are depicted in green (α-phase rac-1), red (β-phase rac-1), blue (α-phase (R)-1), cyan (βphase (R)-1), and black (isotropic melt) colors, respectively. The spectra d and h correspond to the samples crystallized from the melt. Heating of the polycrystalline samples of α-phase rac-1 and α-phase (R)-1 results in broadening of the spectral bands up to the melting point (the curves b and f in Fig. 3). Unfortunately, this experiment did not allow to clearly observe the transformation of the α-phase rac-1 into the β-phase. As the curves c and d in Fig. 3 show, the solid solution β-phase rac-1 is spectrally similar to its isotropic melt. This fact could be interpreted as the similarity of microenvironment in the named phases. Further, the spectra of racemic and scalemic melts are very similar, which argues that the racemic melt is close to an ideal solution. Characteristically,


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heating of α-phase (R)-1 leads mainly to the significant weakening of H-bonds, observed from blue shifting of hydroxyl vibrations from 3346 to 3388 cm-1 at ca. 65 °C (the curve f). Most probably, such behavior is linked to the solid-state phase transition of α-phase (R)-1 into previously unnoticed β-phase (R)-1. Crystal phase characterization. Three pairs of powder diffractograms are compiled in Fig. 4: the colored curves are experimental patterns, while the black curves, which are placed slightly lower than the experimental one, correspond to reference patterns calculated according to the structural models based on single crystal diffraction data.

Figure 4. The experimental and theoretical (black) XRPD patterns of β-phase rac-1 (red), αphase (R)-1 (blue), and α-phase rac-1 (green). The patterns are partially cut off on top for clarity. Selected reflections are marked under the calculated curves. Taking into account an expected increase of reflection intensity due to preferential orientation of the crystallites, the experimental diffraction patterns are in good agreement with the calculated ones, which indicates the correctness of the molecular packing models. The texturing affects mainly the group of reflections with h00 indexes in the case of the α-phase rac-1 and β-phase rac-1 patterns and the analogous group of reflections with 0k0 in the case of α-phase (R)-1,


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which is common for plate crystals. The comparison of the experimental curves enables to note the coincidence of some peaks and resemblance between the patterns of β-phase rac-1 and αphase (R)-1, which can be caused by the proximity or multiplicity of the cell parameters. Thus, this is another sign to the formation of the solid solution of the enantiomers within the crystals of β-phase rac-1. The experimental diffractogram of α-phase (R)-1 (the P21212 group), as expected for the system with fewer translation symmetry elements, is more detailed than for β-phase rac-1 (the Pbcn group). The presence of low-intensity and often slightly broad peaks in the regions of 2Θ < 19° and 23° < 2Θ < 28° characterize α-phase (R)-1. These peaks correspond to 0kl, h0l, and hk0 reflections, the analogues of which are systematically absent in case of β-phase rac-1, and additionally hkl reflections. Solubility experiments. For the identification of racemate type of diol 1 at a room temperature, we have employed the original test, which is supposed to determine the enantiomeric composition of the eutectic in presence of an achiral solvent.28 The test is based on the fact that the enantiomeric composition of the eutectic point is identical to the enantiomeric composition of solution that is in equilibrium with the phases forming this eutectic.28,29,31 In our case, the experiment was carried out for three samples with different enantiomeric compositions in cyclohexane as a solvent at 20 °С. For the samples with x = 0.6 and x = 0.75 mole fractions (m.f.) of R-enantiomer in the initial solid phase the ratio of the enantiomers in saturated solution did not depend on the composition of the solid phase and was equal to х = 0.82(1) m.f. This result confirms the above assumption that α-phase rac-1 is a racemic compound and indicates the formation of the eutectic by an enantioenriched phase and the mentioned racemic compound. Nevertheless, for the third sample with x = 0.9 m.f. the enantiomeric composition of the equilibrium liquid phase was close to the composition of initial


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solid phase x = 0.89(1) m.f. Inasmuch as the variation of composition of an equilibrium solution, when changing the ratio of components in the solid, are typical of solid solutions, the observed discrepancy can be explained by the fact that the solid phase starting with a particular composition (no less than 0.75 m.f.) is represented as partial mixed crystals. With the smaller values of enantiomeric excess, the eutectic is actually formed and composed of the racemic compound and the saturated partial solid solution. The absolute solubilities of the α-phases of rac-1 and (R)-1 in cyclohexane at 20 °С were determined by means of suspension isothermal experiments29,32 in order to quantitatively compare their free energies. The following values were obtained: the concentrations of the -1 ࢙ࢇ࢚ saturated solutions of the enantiomer ࢉ࡭ࢻ = 0.15(1) g L-1 and racemate ࢉ࢙ࢇ࢚ ࡾࢻ = 0.086(6) g L .

Since the concentrations of diol 1 in cyclohexane are small, the ratio of the equilibrium concentrations is equal to the ratio of the thermodynamic activity of the components. Because of the equality of partial molar free energies of components under equilibrium, the difference between the chemical potentials of the enantiomer and the racemic compound in the crystalline state can be found as ૙ ∆ࣆ࡭ࢻ/ࡾࢻ = ࡾࢀ૙ ‫ܖܔ‬

૙.૞ࢉ࢙ࢇ࢚ ࡾࢻ ࢙ࢇ࢚ ࢉ࡭ࢻ

.

The obtained value can be interpreted as the difference between the free energies of formation ૙ ૙ of the crystal lattices of the corresponding phases ∆∆ࡳ࡭ࢻ/ࡾࢻ = ∆ࣆ࡭ࢻ/ࡾࢻ . Its numerical value is

equal to –3.0(2) kJ mole-1, which means that the crystals of α-phase rac-1 are energetically more preferable than α-phase (R)-1. Heterogeneous transitions by DSC. Differential scanning calorimetry was employed for the qualitative and quantitative description of phase behavior in the binary system of diol 1. Selected DSC thermograms are shown in Fig. 5.


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Figure 5. The normalized DSC curves of diol 1 with different enantiomeric and phase compositions. Heating rate is 2 °С min-1. The blue curve shows melting behavior of pure enantiomer. The sets of red and green curves correspond to the heating of solid solution phases and solids containing α-phase rac-1 and partial mixed crystals saturated at 20 °С, respectively. Baselines of the individual curves are shifted in proportion to enantiomeric composition. There is one sharp melting peak on the DSC curves of the enantiomer (blue one) and samples with different composition prepared by fast evaporation of solutions (red). While changing enantiomeric excess, the area of the peak is almost constant, but its position on the temperature scale changes slightly and uniformly. No eutectic melting is observed for the samples with intermediate enantiomeric composition, which is typical of a continuous solid solution phase. The green curves in Fig. 5 correspond to a series of samples equilibrated at 20 °С and prepared by the solution-mediated phase transformation procedure. In these cases, the contour of the melting peak is significantly different from the series of red curves and complicated by the additional heat flow. Two pronounced peaks can be identified on the thermogram of the


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equilibrated racemic sample. The contour of the second peak corresponds to the melting process of the solid solution of the racemic composition. According to the results of the suspension experiments described above, β-phase rac-1 becomes thermodynamically favored at 73 °C, which is considerably lower than the temperature of the first endothermic event on the curve. Hence the first peak could be ascribed to a combination of metastable equilibrium processes of melting of superheated α-phase rac-1 and crystallization of stable β-phase rac-1 from the just obtained melt. Indeed, decrease of heating rate up to 0.3 °C min-1 allows to observe these processes separately (Fig. 6). The onset of the resolved peak corresponds to the melting temperature of the α-phase rac-1. The complex shape of the contour of the resulting process could be explained by the presumption that on the first stage the crystallization of β-phase rac-1 from the melt lags as compared to the melting process α-phase rac-1 for kinetic reasons, but because of spontaneous nucleation and rapid growth of β-phase rac-1 (the second stage), the process of crystallization catches up with the melting, which affects the contour by the presence of a sharp hollow of the heat flow. Then the recrystallization proceeds in a stationary mode feeding on the residue of the melt.

Figure 6. The DSC curve of racemic diol 1 equilibrated at 20 °С. Heating rate is 0.3 °С min-1.


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The equilibrated samples with an intermediate enantiomeric composition exhibit different phase behavior: at x = 0.63 and 0.75 m.f. the extended endothermic process precedes cooperative melting (Fig. 5). We attribute this to the change in the mechanism of transformation of the racemic compound into the solid solution owing to the presence of the surplus enantiomer. As pointed out above, even at 20 °С the excess the enantiomer in equilibrium mixture exists as partial mixed crystals. The boundary of this phase on a constitutional diagram of the system is extending upon increasing the temperature, which leads to the absorption of the racemate, if present, by partial solid solution in crystalline state so as to reach the limit of saturation.

Figure 7. The dependence of the enthalpy of fusion for the samples with a different phase composition on mole fraction of the R-enantiomer of diol 1. The blue, green, and red colors correspond to the pure enantiomer, the phases equilibrated at 20 °С, and the phases crystallized from hot solution, respectively. Fig. 7 depicts the dependence of the enthalpy of fusion on enantiomeric composition of the samples. The linear regressions for two sets of points are plotted by dash lines in the graph. It is evident that the overshoot of the melting enthalpy for equilibrated samples as compared to those freshly crystallized from hot solution is caused by the energy contribution of the phase transition of the racemic compound into the solid solution. This contribution must be proportional to the amount of α-phase rac-1. Therefore, the graph in Fig. 7 can be considered as a Tamman plot, and consequently the intersection point of the regression lines corresponds to the saturation limit of


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the partial solid solution. From this it follows that the composition of the partial solid solution saturated at the temperature of preparation of the samples (20 °C) is equal to x ≈ 0.9 m.f., which is in agreement with our solubility experiments.

Figure 8. The normalized DSC curves of scalemic diol 1 with х = 0.98 and 1.00 m.f. of Renantiomer by heating and subsequent cooling. Heating rate is 2 °С min-1. Melting and crystallization traces are omitted. Nuances of thermochemical behavior in the system are not limited to the conversion of the racemic compound into the solid solution phase. The DSC curves of the scalemic samples with high enantiomeric excess (x > 0.96 m.f.) shown in Fig. 8 provide evidence of the enantiotropic polymorphism for (R)-1. For enantiopure sample at ca. 51 °C there is a fairly broad and reversible peak corresponding to a solid-solid transition. The shape and position of the peak do not almost depend on the heating rate. The particular feature of this transition is a sharp decrease of the temperature and the peak area while adding a small amount of the minor enantiomer in the system; even at x = 0.96 m.f. this process becomes unobserved. The presence of solid phase transition at a relatively low temperature along with rather low energy and high reversibility seems anomalous: the nature of this process will be discussed below. Table 1 summarizes the thermodynamic characteristics of the phase transitions. The information on the values of thermodynamic functions of phase transitions allowed us to


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estimate the stability regions for each phase and the energy correlation between them at different temperatures. As a result, the thermodynamic cycles of changes in enthalpy and entropy in the system were constructed (Fig. S3). On the basis of the cycles the difference of the Gibbs free energies of the α-phases of (R)-1 and rac-1 can be calculated. If we neglect the difference in heat capacities of the phases and assume that mixing of the enantiomers in the liquid phase leads to an ࢓ࢋ࢒࢚ ideal solution, i.e. ∆ࡴ࢓ࢋ࢒࢚ ࢓࢏࢞ = 0 and ∆ࡿ࢓࢏࢞ = ࡾࢀ ‫ ܖܔ‬૛, the required difference of the free energies

is ࢀ૙

ࢌࡾࢻ

૙ ∆∆ࡳ࡭ࢻ/ࡾࢻ = ቀ૚ − ࢀࢌࡾࢻ ቁ ∆ࡴࢀࢌࡾࢻ − ቀ૚ −

ࢀ૙

ࢌ࡭ࢼ

ࢀ

ࢌ࡭ࢼ

ቁ ∆ࡴࢀࢌ࡭ࢼ + ࡾࢀ ‫ ܖܔ‬૛

,

and amounts to –3.8 kJ mole-1 that is different from the value obtained from solubility data (– 3.0 kJ mole-1). The obvious reason for this discrepancy could be a meaningful contribution of the difference of heat capacities of components to their thermodynamic functions in the considered temperature range. Table 1. The DSC measured temperatures (ࢀ), enthalpies (ࢤࡴ), and entropies (ࢤࡿ) of fusion (ࢌ) and solid state transition (࢙࢙) of racemic (subscript R) and enantiopure (subscript A) diol 1. Phase transition

ࢀ (°С)

ࢤࡴ (kJ mole-1)

ࢤࡿ (kJ mole-1 K-1)

ࢌࡾࢻ

78.61

38.62

109.8

ࢌࡾࢼ

80.9

27.5

77.8

࢙࢙ࡾࢻ/ࢼ

73.03

11.13

32.03

ࢌ࡭ࢼ

78.7

25.8

73.4

1

– the value was determined as the onset of the first endothermic peak on the thermogram of the equilibrated racemic sample; 2 – the value was determined as a total area of the endothermic effects on the thermogram of the equilibrated racemic sample; 3 – the values were calculated via the thermodynamic cycle. To take into consideration this contribution, additional DSC experiments with a larger mass of samples (≈ 10 mg) were carried out. In these cases, the baseline correction was fulfilled taking


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into account the asymmetry of the calorimeter cell and thermal capacities of crucibles. The thermograms recorded in this way are shown in Fig. 9.

Figure 9. The DSC curves presenting the effective heat capacity of α-phase rac-1 (green), βphase rac-1 (red), and pure enantiomer (blue curve). Heating rate is 5 °С min-1. The dashed lines show an extrapolation of the heat capacity in the temperature areas corresponding to the phase transitions. The appearance of the curves marks the nearness of β-phase rac-1 and the enantiomer and a considerable divergence of α- and β-phases rac-1 in the course of heat capacity, which may be the consequence of the structural similarity with the former pair. The thermal capacity of the enantiomeric and racemic melts is unified because of closeness of a liquid mixture of enantiomers to the ideal solution. As illustrated in Fig. 9, the solid-state transition of α-phase (R)-1 into β-phase (R)-1 at 50.5 °C is accompanied by a significant jump in the heat capacity (69 J mole-1 K-1). This jump together with low latent heat of transition (0.72 kJ mole-1) in assumption of the first-order phase transition model would lead to the dome-shaped dependence of the Gibbs free energy on temperature for (R)-1 (Fig. S4a). Such behavior was thoroughly investigated for the processes of thermal denaturation of proteins.33 In such case, the region of thermodynamic stability of the α-phase would have both high and low temperature limits: not only at 50.5 °C, but also at lower temperature (31.8 °C). If the α-phase (R)-1 would be stable inside of the mentioned region, an


18

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additional endothermic peak for the “β-phase–α-phase” transition should be observed at ca. 32 °C (Fig. S4b), but this is contrary to our observations. Thus, the process in the region of 5060 °C might be considered as a λ-anomaly of the heat capacity, which is characteristic for second-order phase transitions. Small observed temperature hysteresis, which is not typical for continuous phase transitions, can be due to temperature inhomogeneity of the sample during scanning and the relaxation time of the crystal structure of organic matter. Hence, the transformation is accompanied with the rather small correlated changes on the micro-level of the crystals, but not associated with their significant structural reorganization. Although the thermoanalytical data do not provide direct information about the nature of the transition, it may be assumed that the process corresponds to the cooperative release of the additional conformational degrees of freedom for flexible molecular fragments. For each phase the difference of the thermodynamic functions by heating a crystalline sample from the initial temperature ࢀ૙ to the fusion temperature ࢀࢌ and further to the final temperature of a melt ࢀ૚ can be represented as: ࢀࢌ

ࢀ૚

࢒ࢗ

ሺࢀሻࢊࢀ + ∆ࡴࢌ + ‫ ࢖࡯ ࢌࢀ׬‬ሺࢀሻࢊࢀ, ∆ࡴࢀ૙/ࢀ૚ = ‫ࢀ׬‬૙ ࡯࢙࢕࢒࢏ࢊ ࢖ ࢀࢌ ࡯࢙࢕࢒࢏ࢊ ࢖

∆ࡿࢀ૙/ࢀ૚ = ‫ࢀ׬‬૙

ࢀ

ሺࢀሻࢊࢀ +

∆ࡴࢌ ࢀࢌ

࢒ࢗ

ࢀ૚ ࡯࢖

+ ‫ࢌࢀ׬‬

ࢀ

ሺࢀሻࢊࢀ,

∆ࡳࢀ૙/ࢀ૚ = ∆ࡴࢀ૙/ࢀ૚ − ࢀ૚ ∙ ∆ࡿࢀ૙/ࢀ૚ . We calculated the changes in the enthalpy, the entropy, and the Gibbs free energy of the considered phases as functions of temperature according to these equations, using the data given in Table 1 and the temperature dependences of the heat capacities of the phases, and assuming that the liquid phases of the racemic and enantiopure composition differ only in the value of the entropy of mixing ∆ࡿ࢓ࢋ࢒࢚ ࢓࢏࢞ = ࡾࢀ ‫ ܖܔ‬૛. In the absence of absolute values for standard thermodynamic potentials, the enthalpy and the entropy of α-phase of rac-1 at 20 °С were taken


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as conventional zero. Obtained relationships are graphically illustrated in Figs. 10 and 11. The graphs presented in Fig. 10 indicate closeness of thermodynamic functions of the enantiopure substance and the racemic solid solution (β-phase rac-1). At the same time, it emphasizes an essentially different nature of the racemic compound (α-phase rac-1).

Figure 10. The dependences of the relative enthalpies (a) or entropies (b) of α-phase rac-1 (green), β-phase rac-1 (red), and pure enantiomer (blue) on temperature.

Figure 11. The dependences of the relative Gibbs free energies on temperature for α-phase rac-1 (green), β-phase rac-1 (red), pure enantiomer (blue), and racemic (chlorine) and enantiopure (cyan curves) melts. The solid lines indicate thermodynamically stable forms and dashed lines – metastable. Filled and unfilled circles represent stable and metastable equilibriums, respectively. Referring to Fig. 11, we see that the racemic compound is on ca. 1.2 kJ mole-1 more energetically favorable than the solid solution at 20 °С. The relative position of the curves indicates that the solid solution becomes more thermodynamically stable at ࢀ࢙࢙ࡾࢻ/ࢼ ≈ 73.0 °C


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(which is in full compliance with the transition temperature according to the suspension experiments). In spite of that, both racemic modifications exist as metastable forms up to their melting points. Further inspection of the graph discloses the difference of free energies of the ૙ racemic and enantiopure phases under equilibrium at 20 °C. This value ∆∆ࡳ࡭ࢻ/ࡾࢻ ≈–

3.1 kJ mole-1 is in remarkable accordance with the above result calculated from the solubilities of ૙ the racemic and enantiopure samples (∆∆ࡳ࡭ࢻ/ࡾࢻ ≈ –3.0 kJ mole-1).

Figure 12. The binary constitutional diagram of the diol 1 enantiomeric system. Only stable phase equilibria are indicated. The solidus of the mixed crystal phase is marked by the red color; the green and blue lines denote the upper bounds of existence of the racemic compound (α-phase rac-1) and α-phase scal-1, respectively. Filled circles represent the direct results of the DSC measurements, unfilled – calculated data. Fig. 12 shows a phase diagram of the binary enantiomeric system under consideration, mostly based on the DSC data. Narrow melting peaks of mixed crystals in the whole concentration range did not allow us to distinguish between the solidus and liquidus temperatures, consequently, there is only a line built according to the onsets of the peaks. The solvus line and the upper bound of existence of α-phase scal-1 are plotted on the diagram as well. The minimal curvature of solidus line confirms that the solid solution is almost ideal at least near the melting temperature. Thus, diol 1 forms a stable racemic compound, which turns into an almost ideal continuous solution of the enantiomers in the crystalline phase at elevated temperatures. At room


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temperature the system represents a stoichiometric racemic compound and two symmetrical eutectoid invariants with partial solid solutions for high enantiomeric composition. Unfortunately, basing on thermal analysis, it is impossible to confidently assert that the β-phase rac-1 is precisely a pseudoracemate, but not a racemic compound forming mixed crystal phase. The solution to this problem can be found with the help of direct structures analysis. Crystal structure of α-phase rac-1. As indicated earlier, α-phase rac-1 crystallizes from a racemic material under equilibrium at a room temperature. Basing on the spectral data and nonracemic composition of the eutectic point, we have assumed that α-phase rac-1 is a racemic compound. According to the single crystal X-ray analysis, the mentioned phase belongs to the acentric space group Pc of the monoclinic crystal system. The asymmetric part of the cell includes two molecules A and B of diol 1 with the same configuration of the chiral center С2. The equimolar composition of the whole unit cell is provided by a glide symmetry operation on its homochiral asymmetric part. Fig. 13 shows the probability ellipsoid plot and the geometry of the symmetry independent molecules in crystals. The analysis of the anisotropic displacement parameters and the difference electron density map confirm the absence of the disorder of molecules A and B. To summarize, α-phase rac-1 is indeed a true racemic compound.

Figure 13. The ORTEP diagram showing 50 % probability anisotropic displacement ellipsoids of non-hydrogen atoms for both molecules of the symmetry independent part of the unit cell in the α-phase rac-1 crystals. As illustrated in Fig. 14 and suggested in Table S2, the independent molecules A and B in crystals show close absolute values of torsion angles except for τ22 (O2–C2–C3–O3) and


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resemble a pair of enantiomers. This feature together with a crystallographic glide plane c leads to “(S)-A and (R)-B” and “(S)-B and (R)-A” pairs, which are partially related by noncrystallographic inversion symmetry. Thus, the space group P21/c with higher symmetry may be wrongly assigned for α-phase rac-1 during data examination. If this were the case, one independent molecule which had undergone mirror disordering would be presented in the asymmetric part of the cell.

Figure 14. The conditional superposition (without inversion) of two symmetry independent molecules A (green) and B (magenta) of the α-phase rac-1 crystals.

Figure 15. The fragment of the molecular packing in the α-phase rac-1 crystals. The bilayer formed by classic hydrogen bonds viewed along the 0b. Molecules A and B are shown in green and magenta, respectively. H-bonds are marked in dotted lines: blue for strong contacts, green for “intermediate”, and red for weak. The crystal structure of the racemic compound of diol 1 has not occurred among previously studied glycerol ethers. Fig. 15 illustrates a fragment of the molecular packing in the α-phase rac-1 crystals. The crystal formative motif presents a bilayer parallel to the plane 0bc. The primary framework of this 2D bilayer appears to be 1D helical sequences of hydrogen bonds extended along the shortest axis 0b and joined together by covalent spacers (the glycerol moiety of molecules B) and additional lateral hydrogen bonds.


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Figure 16. Two projections of the 2D supramolecular primary motif in the α-phase rac-1 crystals viewed along the 0c (a) and 0a axes (b). Molecules A and B are shown in green and magenta, respectively. The atoms involved in the continuous helical sequence are singled out by the spacefill style. Different types of classical H-bonds are marked with dotted lines in different colors. The above described distinction between the conformations of the independent molecules A and B is directly related to their different roles in the formation of the bilayer motif. A full turn of the helix is defined with the pitch equal to the parameter b = 5.8283(12) Å and consists of three molecules of diol 1: one A and two B. The configuration of the helixes alternates within the bilayer: the right-handed P-helixes consist of the sequence of (S)-A, (S)-B, (R)-B molecules, while the left-handed M-helixes – of the opposite sequence (R)-A, (R)-B, (S)-B. Molecules B provide the helix construction with both primary and secondary hydroxyls, whereas the molecules A provide only primary hydroxyls О1–Н1. So, the convolution of the helix is described by the recurring sequence of three H-bonds: О1A–Н1A···О1B–Н1B···О1B'– Н1B'···{О1A'–Н1A'···}. In Fig. 16 the spiral is assigned a spacefill style. Table S3 brings out the parameters of H-bonds in the α-phase rac-1 crystals. According to geometry, the interactions could be conditionally divided into three groups: strong (O2B–H2B···O1A), usual (O1B– H1B···O2B), and weak (O1A–H1A···O1B and O2A–H2A···O1B), which agrees with the shape of absorption bands of the IR spectrum in the interval ν = 3120-3550 cm-1. The 3D crystal parking is arranged by the association of the 2D bilayers via dispersion interactions of the peripheral fragments. The packing index of the racemic compound of diol 1 is equal to 68.9 %.


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Crystal structure of α-phase (R)-1. Enantiopure diol (R)-1 crystallizes in the Sohncke space group P21212 of the orthorhombic crystal system. Table S1 suggests that the volume of the unit cell of the α-phase (R)-1 crystals is equal to 6067(5) Å3 that is six times larger than that of αphase rac-1 (1002.8(4) Å3). Therefore, the unit cell is able to contain 24 molecules, and its asymmetric part – 6 molecules, which is rare enough for real molecular crystals.34,35

Figure 17. The ORTEP diagram showing 40 % probability anisotropic displacement ellipsoids for six symmetry independent molecules in the α-phase (R)-1 crystals. The atoms of the disordered glycerol fragments of molecules E and F are labelled; the minor components are marked with EE and FF. The hydrogen atoms are omitted for clarity. Indeed, as shows Fig. 17, the crystals of α-phase are formed by six molecules A-E in the general position with R-configuration of the chiral center C2 and appreciably different conformations. Additionally, two independent molecules E and F undergo static positional disorder of the glycerol moiety without alternation of the configuration of the asymmetric atom. In the case of molecule E, the disorder affects only the atoms of the primary hydroxyl group that leads to the major conformer E with occupation of 0.741(10) and the synclinal torsion angle τ1 (O1–C1–C2–C3) = 52.4(10)° and the minor conformer EE with the antiperiplanar angle τ1 = 177.3(12)°, whereas molecule F is characterized by disordering of the whole glycol


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fragment into two positions: the conformer F with occupation of 0.516(7), τ1 = –69.4(15)°, and τ22 = 47.9(15)° and the conformer FF with τ1 = 179.9(14)° and τ22 = –145.6(13)°. The differences between the independent molecules A-F as well as the conformations of EE/E and F/FF are illustrated in Fig. 18.

Figure 18. The conditional superposition (without inversion) of six symmetry independent molecules of α-phase (R)-1 crystals: A (green), B (blue), C (red), D (yellow), E (magenta), F (cyan). The minor components EE and FF of the disordered glycerol fragments of molecules E and F are shown in wireframe styles. The hydrogen atoms are neglected for clarity. As obvious from Fig. 18 and Table S2, there are no symmetry independent molecules of (R)-1 with identical geometry in the lattice cell, nevertheless two groups of conformations can be distinguished: (i) B, D, E/EE, and FF with negative torsion angle τ22 and (ii) A, C, and F with positive synclinal angle τ22. It is worth noting that the molecules of one group imitate conformations which would be expected for enantiomers of the second group. Thereby the crystal structure of α-phase (R)-1 exemplifies the pseudosymmetry. This feature can be considered as a consequence of the structural preorganization of α-phase (R)-1 for introduction of the molecules with opposite handedness without dramatic rearrangement. In turn, such a preorganization of enantiomeric crystals is essential for the formation of partial and/or continuous solid solutions on the basis of the structure of enantiomeric crystals. Furthermore, the presence of several independent molecules per unit cell leads to difficulties in implementation of crystallographic translation, but provides more flexibility to accommodate the packing. So, disorder and high Z' are apparently the other consequences of the “substitutional ability” of the molecule packing of α-phase (R)-1. Incidentally, α-phase (R)-1, characterized by ૙ ≈ –3.1 kJ mole-1), the appreciably greater free energy than α-phase rac-1 (∆∆ࡳ࡭ࢻ/ࡾࢻ


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demonstrates the greater number of symmetry independent molecules (six vs. two). We believe that this fact is not just a sheer coincidence. Although the number of symmetry independent molecules does not relate to enthalpy or entropy of a crystalline phase directly, in our opinion, a high value of Z' in an enantiomer crystal can be considered as one of the structural features of the packing disadvantage of this phase in a “racemate-enantiomer” pair. Consequently, if enantiomer crystals demonstrate high Z', we expect that crystallization of a racemic mixture will more likely lead to a racemic compound with a lower Z' value or a solid solution phase (but not to a conglomerate). The primary supramolecular motif in the α-phase (R)-1 crystals again appears to be a 2D bilayer oriented parallel to the a0c plane. The motif partly resembles that of α-phase rac-1. Within the unit cell, a layer in the bilayer includes all six independent molecules. The bilayer is formed by a sophisticated framework of classical intermolecular hydrogen bonds concentrated in its central part. Due to the dispersion interactions of peripheral fragments, the bilayers connect to each other and form 3D crystal packing with the sufficiently high Kitajgorodskij index (68.6 %). It is of interest that both disordered sites and their symmetry equivalents are located around every second twofold proper rotation axis (Fig. 19), hence 1D regions of disorder, which are parallel to 0c axis, can be observed within the bilayers. The fact of disordering of the glycerol fragments, which are involved in the formation of hydrogen bond system, allows potential “flexibility”, or numerous variations of the contacts forming the bilayers. As mentioned above, α-phase (R)-1 turns into β-phase (R)-1 by heating. This transformation is characterized by the reversibility and quite significant jump in heat capacity under quite a small change of enthalpy (Fig. 8). The position and intensity of the reflections in the powder diffraction pattern obtained for enantiomeric sample at 65 °C (i.e., for β-phase (R)-1) are similar


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to the one recorded at a room temperature (α-phase (R)-1). The foregoing data together with the similarity of IR spectra of the enantiomer at 20 °C and 65 °C (Fig. 3) indicate the resemblance of the (R)-1 molecule packing in α- and β-phases. Thereby this transformation cannot be accompanied by a significant change in the positions of the molecules and is most probably attributed to dynamic disordering of the glycerol fragments while the rigid bilayers and their relative orientation in the lattice cell are fixed.

Figure 19. The lattice cell in the α-phase (R)-1 crystals viewed along the 0c. Symmetry elements are illustrated as black symbols. The symmetry independent molecules are painted in different colors. The atoms of the minor components EE and FF of the disordered glycerol fragments are shown as balls. Insofar as crystals of a pseudoracemate and a corresponding enantiomer are postulated to be isostructural,11,36 uniformly arranged lattices with similar parameters and volumes of the unit cells are expected for racemic and enantiopure β-phases. Referring to Table S1, the volume (2008.1(14) Å3) and one of the parameters (с = 6.379(3) Å) of the unit cell of β-phase rac-1 is about three times less than α-phase (R)-1 (6066(5) Å3; a = 18.878(9) Å). Consequently, we suppose that transition of enantiomeric α-phase into β-phase is accompanied by a threefold collapse of the unit cell triggered by temperature-induced merging of (R)-1 conformations. Crystal structure of β-phase rac-1. Let us speculate about the consecutive substitution of molecules of one enantiomer by the other in the crystal. In case of such substitution, a possible


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energy loss must be compensated by a gain in entropy so as to prevent the segregation of a solid solution phase. From the structural point of view, a continuous solid solution of enantiomers can be implemented only in two ways: on the basis of the crystal structure of (i) an enantiomer and a molecular compound or (ii) a pair of enantiomers. In the former case the existence of two sites in a lattice cell of an enantiomer crystal is assumed. Furthermore, the molecules of one site are supposed to have geometry similar to an antipode of molecules from the other site. Only the molecules located on the particular strained site (in practice they show chiral mimicry described above and conformational disorder15,16,36) are substituted, while the molecules of the other site are not affected. Such substitution results in a molecular compound. A solid solution phase is hence arranged on the crystal structures of the molecular (racemic) compound and the enantiomer. On the contrary, the sequential non-preferential and stochastic substitution eventually results in the crystal of the other enantiomer, and no ordered molecular compound in crystalline phase is observed. The crystalline nature of mixed crystal with racemic composition, or, in other words, a true pseudoracemate, does not differ from the nature of any other phases of intermediate compositions. The pseudoracemate retains virtually the cell parameters of the enantiomers. So, the chiral molecules in the crystals of the pseudoracemate are supposed to be disordered on two mirror-related positions with the site occupancy equal to the mole fraction of the enantiomer (i.e., 0.5 m.f.). Observed inversion and translational symmetry has an averaged character and cannot be fully satisfied: knowing the configuration of the molecule occupying a reference site, it is impossible to predict the chirality of the neighboring molecule. The high-temperature β-phase of racemate, in contrast to the enantiomer, was available for single crystal XRD analysis, because it is easily obtained by rapid crystallization from hot


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solution. The preliminary structure solution and refinement allowed us to describe the crystal structure of β-phase rac-1 in several groups of the monoclinic and orthorhombic crystallographic systems, for instance, P21/n, Pbcn, Pna21, or P21212. In all cases the structures are accompanied by chiral disordering. The highest diffraction symmetry with reasonable R(int) value and compatible with the original unconstrained cell metrics is mmm corresponding to the orthorhombic crystal system. Basing on the model described above, it can be assumed that a pseudoracemate has to be described in the same space group, wherein an enantiomer crystallized, or in its supergroup. As a result, the choice of the space group is ambiguous and varied, and cannot be defined only according to the convergence of data refinement. However, the adherence to the first way leads to the insuperable disadvantage: refinement of racemic sample in an enantiomorphic space group is fraught with the “missing symmetry”, which is often interpreted as the incorrect assignment of the space group and implies refinement problems.37,38 The systematic absences of the original set of reflections correspond with the presence of the translational symmetry elements specific to the space group Pbcn with the highest possible symmetry. The solution and refinement of the structure in the indicated space group leads to the model with the only molecule in general position, whose glycerol moiety is disordered on left and right subsites with occupancy of 0.519(8). Therefore, β-phase rac-1 is a true pseudoracemate, namely, a substitutional solid solution based on the crystal structure of the individual enantiomers (β-phase (R)-1 and β-phase (S)-1). Fig. 20 exhibits probability ellipsoid plots of the symmetry independent molecule in the β-phase rac-1 crystals. High anisotropic displacement parameters of the atoms of the glycerol fragments and some problems with intramolecular bond distances are anticipated because of the expected additional dynamic disordering of each subsite.


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Figure 20. The ORTEP diagram showing 30 % probability anisotropic displacement ellipsoids for the disordered molecule in the β-phase rac-1 crystals. The subsites A and B contain S and Renantiomers, respectively. The hydrogen atoms are omitted for clarity; other atoms are labelled.

Figure 21. The fragment of the molecular packing in the β-phase rac-1 crystals viewed along the 0b. Symmetry elements are illustrated as black symbols. The symmetry independent molecules are painted in different colors. R- and S-isomers are shown in red and blue colors, in the order mentioned. The atoms of the second components of the disordered glycerol fragments are shown as spots. The β-phase rac-1 crystals are formed by bilayers along the shortest axes 0b and 0c, which is the same manner as in the α-phase (R)-1 crystals, but with the cyclical permutation of the cell axes taken into account. In this case 2D regions of disorder are concentrated in the centers of bilayers and shielded from the external contacts. In general, the molecular packing in the crystal is sufficiently dense and characterized by the same packing index as for α-phase (R)-1 (68.6 %). Fig. 21 demonstrates the fragment of the molecular packing of the pseudoracemate in the analogues orientation as shown in Fig. 19 for the enantiomer. Interestingly, significant similarity of the molecular packing of β-phase rac-1 and α-phase (R)1 is obvious while comparing Figs. 19 and 21. Perhaps, the auxiliary role of the secondary


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hydroxyl in the formation of crystal formative motif and “internal insulation” of chiral glycerol fragments inside the bilayers, which is observed in the above-described crystal structures of diol 1, are essential requirements for the existence of the system as a solution of enantiomers in the crystalline phase. Nonetheless, the formation of a continuous solid solution of enantiomers by a substance, wherein a chiral center is directly bonded to the functional group potentially participating in primary motif, seems to be hardly conceivable. SUMMARY Heterogeneous equilibria and transitions in the condensed phase of chiral para-methoxyphenyl glycerol ether 1 were investigated by the DSC, IR spectroscopy, solubility measurements, and other methods. The binary phase diagram and the dependence of Gibbs free energy on temperature emphasize the polymorphism and peculiar heterogeneous equilibria of the chiral system under consideration. The equimolar mixture of enantiomers of diol 1 forms a stable racemic compound (α-phase) at a room temperature that belongs to the Pc space group with two molecules per the asymmetric cell. At elevated temperatures close to the melting the crystalline nature of diol 1 changes dramatically: the system forms a continuous and almost ideal solid solution phase in all concentration ranges based on its enantiomers. The racemic phase of the solid solution (β-phase) was refined in the Pbcn group with the molecule equally disordered into two mirror-related positions. No clear evidence of the existence of a racemic compound directly participating in the formation of the mixed crystal phase was found. Hence the racemic β-phase of diol 1 relates to a true pseudoracemate. The mentioned phase transformation is under the thermodynamic control: at 20 °С the racemic compound is on 1.2 kJ mole-1 more energetically favorable than the solid solution; but due to the combination of the entropic factor and significant


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difference of the heat capacities of the phases, the solid solution becomes thermodynamically preferred at 73.0 °С. Enantiomeric crystals existing at a room temperature (α-phase) transform reversibly to β-phase accompanied by a significant jump in heat capacity under quite small peak area. The enantiopure α-phase belongs to the P21212 group with six symmetry independent molecules (!), two of which undergo disordering. It is remarkable that the crystal lattice of α-phase (R)-1 loses 3.1 kJ mole-1 at 20 °С as compared to α-phase rac-1. In our opinion, a high value of Z' in enantiomer crystals can be considered as one of the structural features of the packing disadvantage of this phase in a “racemate-enantiomer” pair. We believe that the specified temperature-related transition is accompanied by the partial merger of the independent molecules and triple reducing of the lattice cell within the same space group, which leads to the postulated isostructurality of the pseudoracemate and the enantiomer phase. Furthermore, the formation of a partial solid solution, based on the enantiomer crystals, was explored even at 20 °С. Then, the eutectic of the system under consideration is actually composed of the racemic compound and the saturated partial solid solution. When heated, the borderline of the saturation is moving towards the racemic composition until a partial solid solution turns into continuous. A bilayer motif in crystals is common for all three cases and meets the requirement in low sensitivity of molecular parking to chirality effects. Apparently, localization of donors and acceptors of hydrogens bonds and their isolation within the bilayers create conditions for the possibility of multiple binding. The relatively small energy difference between the phases, owing to their structural similarity and the significant contribution of the entropy term to this difference, allows of changing the energy relationship between the phases by means of temperature. At the same time the uniformity of the crystal formative motif of these phases provides relatively small


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kinetic barriers between these phases, which makes the solid-state transitions possible. All these factors ensure nontrivial phase behavior of the given system, namely, the transition of the stable racemic compound, complicated by the partial solid solution, into the continuous and almost ideal solid solution by means of heating. ASSOCIATED CONTENT Supporting Information. Crystallographic information, descriptions of some experimental procedures, energy diagrams for enthalpy and entropy: This information is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author * Phone/fax: +7 843 2319167 / +7 843 2731872; e-mail: [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ‡These authors contributed equally. ACKNOWLEDGMENTS The authors thank Dr Aida I. Samigullina and Dr Irina I. Vandyukova for technical support. REFERENCES (1) Jacques, J.; Collet, A.; Wilen, S. H., Enantiomers, Racemates, and Resolutions; Krieger Publishing Company: Malabar, FL, 1994. (2) Coquerel, G. Top. Curr. Chem. 2007, 269, 1–51.


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(3) Levilain, G; Coquerel, G. CrystEngComm 2010, 12, 1983–1992. (4) Lorenz, H.; Seidel-Morgenstern, A. Angew. Chem. Int. Ed. 2014, 53, 1218–1250. (5) Coquerel, G. Enantiomer 2000, 5, 481–498. (6) Bredikhin, A. A.; Bredikhina, Z. A.; Zakharychev, D. V. Mendeleev Commun. 2012, 22, 171–180. (7) Viedma, C.; Coquerel, G.; Cintas, P. In Handbook of Crystal Growth; Nishinaga, T., Ed.; Elsevier: Boston, 2015; Chapter 22, pp 951–1002. (8) Coquerel, G; Tamura, R. In Disordered Pharmaceutical Materials; Descamps, M., Ed.; Wiley-VCH Verlag GmbH & Co. KGaA: Weinheim, 2016; Chapter 5, pp 135–160. (9) Brock, C. P.; Schweizer, W. B.; Dunitz, J. D. J. Am. Chem. Soc. 1991, 113, 9811–9820. (10) Baert, F.; Fouret R.; Oonk, H. A. J.; Kroon, J. Acta Cryst. 1978, B34, 222–226. (11) Chion, B.; Lajzerowicz, J.; Bordeaux, D.; Collet, A.; Jacques, J. J. Phys. Chem. 1978, 82, 2682–2688. (12) Rollinger, J. M.; Burger A. J. Pharm. Sci. 2001, 90, 949–959. (13) Vogt, F. G.; Copley, R. C. B.; Mueller, R. L.; Spoors, G. P.; Cacchio, T. N.; Carlton, R. A.; Katrincic, L. M.; Kennady, J. M.; Parsons, S.; Chetina, O. V. Cryst. Growth Des. 2010, 10, 2713–2733. (14) Lopez de Diego, H.; Bond, A. D.; Dancer, R. J. Chirality 2011, 23, 408–416.


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(15) Bredikhin, A. A.; Bredikhina, Z. A.; Zakharychev, D. V.; Gubaidullin, A. T.; Fayzullin, R. R. CrystEngComm 2012, 14, 648–655. (16) Bredikhin, A. A.; Gubaidullin, A. T.; Bredikhina, Z. A.; Fayzullin, R. R. J. Mol. Struct. 2013, 1032, 176–184. (17) Lajzerowicz-Bonneteau, J.; Lajzerowicz, J.; Bordeaux, D. Phys. Rev. B 1986, 34, 6453– 6463. (18) Gallis, H. E.; van Ekeren, P. J.; van Miltenburg, J. C.; Oonk, H. A. J. Thermochim. Acta 1999, 326, 83–90. (19) Wermester, N.; Aubin, E.; Pauchet, M.; Coste S.; Coquerel G. Tetrahedron: Asymmetry 2007, 18, 821–831. (20) Renou, L.; Morelli, T.; Coste, S.; Petit, M.-N.; Berton, B., Malandain, J.-J.; Coquerel, G. Cryst. Growth Des. 2007, 7, 1599–1607. (21) Taratin, N. V.; Lorenz, H.; Kotelnikova, E. N.; Glikin, A. E.; Galland, A.; Dupray, V.; Coquerel, G.; Seidel-Morgenstern, A. Cryst. Growth Des. 2012, 12, 5882–5888. (22) Bredikhin, A. A.; Zakharychev, D. V.; Gubaidullin, A. T.; Fayzullin, R. R.; Pashagin, A. V.; Bredikhina, Z. A. Cryst. Growth Des. 2014, 14, 1676–1683. (23) Roozeboom, H. W. B. Z. Phys. Chem. 1899, 28, 494–517. (24) Vilchèze, C.; Bittman, R. J. Lipid Res. 1994, 35, 734–738. (25) Bredikhina, Z. A.; Novikova, V. G.; Efremov, Y. Y.; Sharafutdinova, D. R.; Bredikhin, A. A., Russ. Chem. Bull., Int. Ed. 2008, 57, 2320–2323.


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(26) Fayzullin, R. R.; Antonovich, O. A.; Zakharychev, D. V.; Bredikhina, Z. A.; Kurenkov, A. V.; Bredikhin, A. A. Russ. J. Org. Chem. 2015, 51, 202–209. (27) Tamura, R.; Takahashi,·H.; Fujimoto, D.; Ushio T. Top. Curr. Chem. 2007, 269, 53–82. (28) Bredikhin, A. A.; Zakharychev, D. V.; Fayzullin, R. R.; Antonovich, O. A.; Pashagin, A. V.; Bredikhina, Z. A. Tetrahedron: Asymmetry 2013, 24, 807–816. (29) Bredikhin, A. A.; Zakharychev, D. V.; Fayzullin, R. R.; Bredikhina, Z. A.; Gubaidullin, A. T. J. Mol. Struct. 2015, 1088, 111–117. (30) Sheldrick, G. M. Acta Crystallogr. 2008, A64, 112–122. (31) Klussmann, M.; White, A. J. P.; Armstrong, A.; Blackmond, D. G. Angew. Chem. Int. Ed. 2006, 45, 7985–7989. (32) Fayzullin, R. R.; Lorenz, H.; Bredikhina, Z. A.; Bredikhin, A. A.; Seidel-Morgenstern, A. J. Pharm. Sci. 2014, 103, 3176–3182. (33) Privalov, P. L. Crit. Rev. Biochem. Mol. 1990, 25, 281–306. (34) Brock, C. P. Acta Cryst. 2002, B58, 1025–1031. (35) Steed, K. M.; Steed, J. W. Chem. Rev. 2015, 115, 2895–2933. (36) Brandel, C.; Petit, S.; Cartigny, Y.; Coquerel, G. Curr. Pharm. Des. 2016, 22, 4929–4941. (37) Marsh, R. E. Acta Cryst. 1995, B51, 897–907. (38) Watkin, D. Acta Cryst. 1994, A50, 411–437.


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For Table of Contents Use Only Intricate phase behavior and crystal structure features of chiral para-methoxyphenyl glycerol ether forming continuous and partial solid solutions Robert R. Fayzullin,*‡ Dmitry V. Zakharychev,‡ Aidar T. Gubaidullin, Olga A. Antonovich, Dmitry B. Krivolapov, Zemfira A. Bredikhina, Alexander A. Bredikhin

para-Methoxyphenyl glycerol ether demonstrates nontrivial phase behavior, namely, the transition of the stable racemic compound, complicated by the partial solid solution, which is based on the enantiomer crystals, into the continuous and almost ideal solid solution by means of heating.


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Figure 1. The SEM photographs of the non-conditioned crystalline samples of diol rac-1. Freshly crystallized β-phase rac-1 (a) and the same sample after the contact with the mother liquor for more than 2 hours (b, c). 68x56mm (300 x 300 DPI)



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Figure 2. The IR spectra (a) of the polycrystalline samples of β-phase rac-1 (red), α-phase (R)-1 (blue), and α-phase rac-1 (green) recorded at 20 °С in potassium bromide matrix and the graphical representation of correlations between β-phase rac-1 and α-phase (R)-1 (b) and between α-phase rac-1 and α-phase (R)-1 (c). 160x85mm (300 x 300 DPI)


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Figure 3. The IR spectra of racemic (a-d) and enantiomeric (e-h) samples of diol 1 in potassium bromide pellets recorded at 20 °С (a, d, e, h), 65 °С (b, f), 85 °С (c, g). The spectra of different phases are depicted in green (α-phase rac-1), red (β-phase rac-1), blue (α-phase (R)-1), cyan (β-phase (R)-1), and black (isotropic melt) colors, respectively. The spectra d and h correspond to the samples crystallized from the melt. 129x80mm (300 x 300 DPI)



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Figure 4. The experimental and theoretical (black) XRPD patterns of β-phase rac-1 (red), α-phase (R)-1 (blue), and α-phase rac-1 (green). The patterns are partially cut off on top for clarity. Selected reflections are marked under the calculated curves. 177x109mm (300 x 300 DPI)


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Figure 5. The normalized DSC curves of diol 1 with different enantiomeric and phase composition. Heating rate is 2 °С min-1. The blue curve shows melting behavior of pure enantiomer. The sets of red and green curves correspond to the heating of solid solution phases and solids containing α-phase rac-1 and partial mixed crystals saturated at 20 °С, respectively. Baselines of the individual curves are shifted in proportion to enantiomeric composition. 80x149mm (300 x 300 DPI)



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Figure 6. The DSC curve of racemic diol 1 equilibrated at 20 °С. Heating rate is 0.3 °С min-1. 80x80mm (300 x 300 DPI)


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Figure 7. The dependence of the enthalpy of fusion for the samples with a different phase composition on mole fraction of the R-enantiomer of diol 1. The blue, green, and red colors correspond to the pure enantiomer, the phases equilibrated at 20 °С, and the phases crystallized from hot solution, respectively. 80x80mm (300 x 300 DPI)



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Figure 8. The normalized DSC curves of scalemic diol 1 with х = 0.98 and 1.00 m.f. of R-enantiomer by heating and subsequent cooling. Heating rate is 2 °С min-1. Melting and crystallization are omitted. 80x80mm (300 x 300 DPI)


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Figure 9. The DSC curves presenting the effective heat capacity of α-phase rac-1 (green), β-phase rac-1 (red), and pure enantiomer (blue curve). Heating rate is 5 °С min-1. The dashed lines show an extrapolation of the heat capacity in the temperature areas corresponding to the phase transitions. 80x80mm (300 x 300 DPI)



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Figure 10. The dependences of the relative enthalpies (a) or entropies (b) of α-phase rac-1 (green), βphase rac-1 (red), and pure enantiomer (blue) on temperature. 80x80mm (300 x 300 DPI)


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Figure 10. The dependences of the relative enthalpies (a) or entropies (b) of α-phase rac-1 (green), βphase rac-1 (red), and pure enantiomer (blue) on temperature. 80x80mm (300 x 300 DPI)



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Figure 11. The dependences of the relative Gibbs free energies on temperature for α-phase rac-1 (green), β-phase rac-1 (red), pure enantiomer (blue), and racemic (chlorine) and enantiopure (cyan curves) melts. The solid lines indicate thermodynamically stable forms and dashed lines – metastable. Filled and unfilled circles represent stable and metastable equilibriums, respectively. 80x80mm (300 x 300 DPI)


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Figure 12. The binary constitutional diagram of the diol 1 enantiomeric system. The solidus of the mixed crystal phase is marked by the red color; the green and blue lines denote the upper bounds of existence of the racemic compound (α-phase rac-1) and α-phase scal-1, respectively. Filled circles represent the direct results of the DSC measurements, unfilled – calculated data. 80x80mm (300 x 300 DPI)



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Figure 13. The ORTEP diagram showing 50 % probability anisotropic displacement ellipsoids of nonhydrogen atoms for both molecules of the symmetrically independent part of the unit cell in the α-phase rac-1 crystals. 84x33mm (300 x 300 DPI)


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Figure 14. The conditional superposition (without inversion) of two symmetrically independent molecules A (green) and B (magenta) of the α-phase rac-1 crystals. 84x30mm (300 x 300 DPI)



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Figure 15. The fragment of the molecular packing in the α-phase rac-1 crystals. The bilayer formed by classic hydrogen bonds viewed along the 0b. Molecules A and B are shown in green and magenta, respectively. H-bonds are marked in dotted lines: blue for strong contacts, green for “intermediate”, and red for weak. 84x46mm (300 x 300 DPI)


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Figure 16. Two projections of the 2D supramolecular primary motif in the α-phase rac-1 crystals viewed along the 0c (a) and 0a axes (b). Molecules A and B are shown in green and magenta, respectively. The atoms involved in the continuous helical sequence are singled out by the spacefill style. Different types of classical H-bonds are marked with dotted lines in different colors. 84x45mm (300 x 300 DPI)



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Figure 16. Two projections of the 2D supramolecular primary motif in the α-phase rac-1 crystals viewed along the 0c (a) and 0a axes (b). Molecules A and B are shown in green and magenta, respectively. The atoms involved in the continuous helical sequence are singled out by the spacefill style. Different types of classical H-bonds are marked with dotted lines in different colors. 84x45mm (300 x 300 DPI)


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Figure 17. The ORTEP diagram showing 40 % probability anisotropic displacement ellipsoids for six symmetrically independent molecules in the α-phase (R)-1 crystals. The atoms of the disordered glycerol fragments of molecules E and F are labelled; the minor components are marked with EE and FF. The hydrogen atoms are omitted for clarity. 84x91mm (300 x 300 DPI)



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Figure 18. The conditional superposition (without inversion) of six symmetrically independent molecules of α-phase (R)-1 crystals: A (green), B (blue), C (red), D (yellow), E (magenta), F (cyan). The minor components EE and FF of the disordered glycerol fragments of molecules E and F are shown in wireframe styles. The hydrogen atoms are neglected for clarity. 84x27mm (300 x 300 DPI)


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Figure 19. The lattice cell in the α-phase (R)-1 crystals viewed along the 0c. Symmetry elements are illustrated as black symbols. The symmetrically independent molecules are painted in different colors. The atoms of the minor components EE and FF of the disordered glycerol fragments are shown as balls. 121x66mm (300 x 300 DPI)



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Figure 20. The ORTEP diagram showing 30 % probability anisotropic displacement ellipsoids for the disordered molecule in the β-phase rac-1 crystals. The subsites A and B contain S and R-enantiomers, respectively. The hydrogen atoms are omitted for clarity; other atoms are labelled. 84x29mm (300 x 300 DPI)


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Figure 21. The fragment of the molecular packing in the β-phase rac-1 crystals viewed along the 0b. Symmetry elements are illustrated as black symbols. The symmetrically independent molecules are painted in different colors. R- and S-isomers are shown in red and blue colors, in the order mentioned. The atoms of the second components of the disordered glycerol fragments are shown as spots. 121x60mm (300 x 300 DPI)



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para-Methoxyphenyl glycerol ether demonstrates nontrivial phase behavior, namely, the transition of the stable racemic compound, complicated by the partial solid solution, which is based on the enantiomer crystals, into the continuous and almost ideal solid solution by means of heating. 83x34mm (300 x 300 DPI)


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Intricate Phase Behavior and Crystal Structure Features of Chiral para

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