Crystallization of (±)-Modafinil in Gel - American Chemical Society

ABSTRACT: Single crystals of (()-modafinil have been grown in gel medium obtained from the hydrolysis and condensation of tetramethoxysilane (TMOS)...
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Crystallization of (()-Modafinil in Gel: Access to Form I, Form III, and Twins Pauchet,†

Morgan Thomas Ge´rard Coquerel*,†

Morelli,†

Servane

Coste,†

Jean-Jacques

Malandain,‡

and

CRYSTAL GROWTH & DESIGN 2006 VOL. 6, NO. 8 1881-1889

Unite´ de Croissance Cristalline et de Mode´ lisation Mole´ culaire (UC2M2), Sciences et Me´ thodes Se´ paratiVes (SMS), UPRES EA 3233, IRCOF, UniVersite´ de Rouen, 76821 Mont-Saint-Aignan Cedex, France, and Groupe de Physique des Mate´ riaux, UniVersite´ de Rouen, 76801 Saint-EÄ tienne du RouVray, France ReceiVed April 7, 2006; ReVised Manuscript ReceiVed June 1, 2006

ABSTRACT: Single crystals of (()-modafinil have been grown in gel medium obtained from the hydrolysis and condensation of tetramethoxysilane (TMOS). Three different crystal morphologies have been highlighted, corresponding to two modifications and a twin. The first polymorphic form was found to match with the known monoclinic form I (P21/a, Z′ ) 2, a ) 14.502 Å, b ) 9.678 Å, c ) 20.844 Å, and β ) 110.17°). The determination of the second form allowed us to validate the previously predicted form III (orthorhombic Pna21, Z′ ) 2, a ) 14.510 Å, b ) 9.710 Å, c ) 19.569 Å). The analysis of the twinned bodies and the structural similarities between form I and form III allowed us to identify the twin law: a stacking fault of (001)form I leading to a form III like interface. The analysis of the structures also suggested possible multitwinning. Introduction Single-crystal X-ray diffraction is certainly the best way to determine a crystal structure. However, the major drawback often lies in obtaining a suitable solid particle. The success of the diffraction analysis is directely linked to the quality and size of this crystal. When polymorphism arises, difficulties are multiplied by the number of varieties detected. Basically, single crystals can be obtained from solution (evaporation, cooling, solvent diffusion, in capillary), vapor (hanging drop, sitting drop, condensation of a vapor phase), or melt. Methods can be derived or combined in order to improve the results.1 Crystallization can be schematized as moving from a relevant starting domain to the domain of existence of the desired solid phase. The way it is performed (choice of the solvents, kinetics involved, ...) has a major impact on the final crystal (in terms of the nature of the polymorph and the quality and size of the crystals, for example). Whereas an enantiotropic behavior between two polymorphs may allow one to find an appropriate domain of temperature and a suitable solvent for each form, this is not the case with a variety having a monotropic character. The less stable form can only be reached out of thermodynamic equilibrium. These conditions are often inappropriate with the growth of high-quality single crystals. When such issues arise, crystallization in gels may be of interest. It is not a recent technique, since it was first used at the end of the 19th century.2 It is difficult to give an exact and accurate definition of a gel. They can, however, be described as a solid network forming pores in which a liquid phase is confined. Using gels confers several advantages over conventional crystallization in solution3 by acting at different levels of the usual process (supersaturation, nucleation, and growth). First, the size and connectivity of the pores will influence the nucleation process. The number of nuclei can be dramatically reduced by limiting the size of the pores. Acting on the pore size and connectivity is also a good way to prevent unwanted * To whom correspondence should be addressed. E-mail: [email protected]. † Unite ´ de Croissance Cristalline et de Mode´lisation Mole´culaire (UC2M2), Universite´ de Rouen. ‡ Groupe de Physique des Mate ´ riaux, Universite´ de Rouen.

particles such as dust from interfering with the growth (which can lead to the incorporation of impurities and appearance of defects). Whereas heterogeneous nucleation should be present anyway, homogeneous nucleation seems to be predominant in gels, as shown by the experiment related by Henisch et al.4 In addition, higher degrees of supersaturation without instantaneous nucleation can be reached with crystallization in gels, which is why gels may allow one to obtain single crystals of metastable phases. The transport of material is achieved only by diffusion between the pores of the gel. Convection movements are therefore suppressed, and molecules are delivered continuously to the growing faces (the depletion zone which surrounds a growing crystal is not disturbed by convection eddies). The growth of the crystals is therefore more regular. The gel also acts as a “soft” matrix which holds the crystal and reduces direct interactions (e.g. walls, other crystals). Three-dimensional single crystals with defined faces can therefore be obtained. Their morphologies may be dissimilar from those observed in solution, since the growth is not physically hindered.5,6 Techniques to bring about crystallization in gels are not so different from those used in solution. In the case of a crystal resulting from the reaction of two compounds, each of them may be allowed to diffuse inside the gel. Should a single compound be involved, crystals can be obtained by having a solution and an antisolvent diffusing at each end of the gel (e.g. in a U-tube). When appropriate supersaturation is reached, crystallization occurs. An alternative which does not use the diffusion of solution consists of doping the gel with the compound before the gelation. The driving force can then be increased by cooling or by diffusion of an antisolvent, once the gel is set. However, crystallization in gels is essentially applied to inorganic materials or macromolecules such as proteins. Cases of crystallizations involving the use of agarose or silica to form aqueous gels are numerous, though some cases have been reported of crystallization in nonaqueous gels.7 Crystallization of organic compounds in gels is less common.8 In this paper, we will describe the application of the crystallization in gels to (()-2-((diphenylmethyl)sulfinyl)-N-

10.1021/cg060203k CCC: $33.50 © 2006 American Chemical Society Published on Web 06/30/2006

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Figure 1. Developed formula of (()-modafinil.

Figure 2. Tetramethoxysilane molecule (TMOS): Si(OCH3)4.

acetamide (marketed under the name modafinil; see Figure 1). Among its different polymorphic forms,9 a concomitant crystallization is observed between the stable racemic form I and the metastable racemic form III. Up to now, the latter has never been obtained as a single crystal of sufficient size: the crystallization in solution close to the thermodynamic equilibrium always leads to single crystals of form I, the most stable phase. Pure form III can be obtained as a powder by crystallization far from equilibrium (precipitation). A transition from form III toward form I systematically occurs when a suspension is slurried for a long period of time or when it is seeded by form I. These data give evidence of the metastability of form III with respect to form I. In a previous paper the structure of form III has been proposed, following the analysis of a conventional XRPD pattern and the use of the derived crystal packing (DCP) model.10 This work highlighted the putative small energy gap as well as structural analogies between them. The use of gels was thus expected to promote the growth of the “less stable” form in order to validate the predicted crystalline structure. This paper is divided into two parts. In the first part, the crystallization experiments are described. In the second part, the three kinds of crystals obtained, namely form I, twinned form I, and form III, are analyzed and their structural relationships are detailed. Experimental Section Gel and Method Used. In this study, the gel is formed from tetramethoxysilane (hereafter TMOS; see Figure 2) from ACROS, 99%. This gel was found to be very convenient for crystallizing the compound: its formation involves water and methanol, which are respectively an antisolvent and a good solvent for (()-modafinil. Therefore, these properties can be used to change the solubility inside

Pauchet et al. the gel and to control the drowning out of modafinil (addition of water drastically reduces the solubility of (()-modafinil in methanol). The formation of TMOS gel is carried out in two steps. In the first step, TMOS is hydrolyzed by addition of water and methanol is released. Large amounts of water are used (if a stoichiometric amount is used, the hydrolysis is incomplete11). Since TMOS and water are not miscible, methanol is added so as to obtain a single liquid phase (it is called the sol and contains between 5% and 20% volume of TMOS). It is usually accepted that the reaction involves in this first step the formation of silicic acid, instantaneously polymerized by condensation in a second step to form branched -Si-O-Si- chains to yield a three-dimensional structure which is the solid network of the gel (see Figure 3). Water molecules are released during this part of the process. The reaction is thermally activated. Therefore, the sol is heated to gelation. The pores, partially connected, contain the liquid phase of the gel, consisting of water and methanol (and possibly unreacted TMOS). Crystals studied in this paper have been obtained by the gel-doping method: when the gel is set, the pores already contain the compound to be crystallized. To achieve this, (()-modafinil is placed in the initial sol so as to obtain a saturated solution at ambient temperature. The system is then heated to allow (()-modafinil to dissolve and the gelation reaction to occur. Once the gel is set, the system is cooled to ambient temperature and nucleation arises. Preliminary studies were performed on the gel itself to determine the most appropriate conditions for its setting. Since the gelation reaction is thermally activated, it was studied with respect to temperature (from ambient temperature to 70 °C). A temperature of 50 °C was found to be suitable to work with: the gel does not set immediately so that the compound can dissolve before that point. Such a temperature also allows us to limit the effect of solvent evaporation. The initial concentration in TMOS (limiting reactant) determines the final density of the gel: the higher the concentration, the denser the gel. This is also related to the size of the pores: the higher the concentration, the smaller the pores.12 Whereas nucleation can hence be drastically restricted, increasing the density of the gel may totally prevent the crystals from growing. It is also worth noting that the inclusion of a compound in the sol strongly affects the formation of the gel. The compound may interfere with silica and lead to precipitation or may even completely inhibit the gelation. Therefore, it is difficult to predict the time needed for gelation for a given compound. One must also keep in mind that, even if the gel is set, every silanol (Si-OH) group has not yet condensed. If the gel is allowed to expel the liquid phase from its pores, the polycondensation goes on, resulting in gel shrinking (a process known as syneresis13). Preparation of the Gel. The (()-modafinil was placed in a glass tube of 2 cm inner diameter and 15 cm in length (pure (()-modafinil provided by Cephalon Inc. was used without further purification). Volumes of 2 mL of TMOS and 8 mL of MeOH were added, and the tube was placed in a thermostated bath at 50 °C. Agitation was performed by a magnetic stirrer. The top of the tube was stopped with a plastic cork. Depending on the initial mass of (()-modafinil, dissolution occurred at once or within a few minutes. Water containing 2 drops of a NaOH solution at 0.5 M (so as to catalyze the reaction) was then poured into the tube. The agitation was maintained for 15 min, and then the magnetic rod was removed from the sol. The tube was sealed with several layers of Parafilm and kept in the bath for 30 min before being placed in an oven at 40 °C. The gel was allowed to

Figure 3. Hydrolysis and condensation of TMOS. The chains aggregate to form pores of different sizes and connectivities.

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Figure 4. (()-Modafinil single crystals grown in TMOS gels. The TMOS/water/methanol ratios are as follows, from left to right: 2/9/5, 2/8/6, 2/7/7, 2/6/8, and 2/5/9. The initial mass of (()-modafinil is 0.3 g, and the initial volume of TMOS is 2 mL. The tube on the far left-hand side shows hundreds of small crystals that could be taken at first glance as precipitation inside the gel, whereas the tube on the far right-hand side yielded no crystals.

Figure 5. Indexation of the faces for a crystal of form I. set overnight. So as to be able to directly compare the results of different experiments, the very same duration for stirring/bath/oven standing was observed. The tube was finally cooled to ambient temperature to let nucleation and crystal growth occur. It is important for the gel to be set before any nucleation takes place; otherwise, the advantages brought by the gel would be jeopardized. Gels should remain uniformly transparent without any cracking. Several experiments were carried out under the same conditions of temperature and volumes of TMOS, methanol, and water, while varying only the initial mass in (()-modafinil from 0.05 to 0.6 g (i.e. from 3.125 g/L to 56.25 g/L or 1.14 × 10-2 mol/L to 20.58 × 10-2 mol/L). After a few hours to a few days, crystals can be observed in some tubes: great numbers of them for the high initial concentrations in (()modafinil (crystals appear very quickly but are small and not well formed) and fewer to none for the lower concentrations. A compromise between the number of crystals (the lower the better) and the time needed to grow them was found, and a mass of (()-modafinil of 0.30 g was found to reproducibly give crystals with suitable sizes for singlecrystal X-ray diffraction and well-defined faces for observation with an optical micoscope. The crystals were evenly distributed inside the gel (i.e. no top, bottom, or wall effect). A majority of crystals corresponding to form I was obtained. Twinned crystals of form I grew in a lower amount, and form III crystals were only observed sporadically (two crystals among several dozens of tubes). The gel was recovered by cutting the bottom of the tube and sliding it out (with gentle air pressure when needed). Crystals were then “mechanically” extracted (they separate easily from the gel).

Whereas these crystals allowed the validation of the predicted structure of form III, their infrequent occurrence did not permit us to make a link between the crystallization in gels and the growth of this form. So as to eliminate the suspicion of a fortuitous crystallization, further experiments were carried out, aimed at the promotion of the form III nucleation. A new protocol similar to the former one was set up. The density of the gel was left unchanged (i.e., the total volume and the concentration of TMOS were kept constant), and several water/ methanol ratios were tested. The water concentration was still in large excess so as to optimize the hydrolysis of TMOS. Moreover, the density of the final gel was kept constant (if it is considered that the loss of solvent by evaporation during heating can be neglected) and the size of the pores unaffected. With this approach, it can be surmised that we investigated directly the initial supersaturation inside the gel. If we consider that the pores of the gel were filled only with water and methanol (which may not be true, since TMOS may not have been entirely hydrolyzed) and that the mass of (()-modafinil is kept constant between the growth experiments, varying the water/methanol ratio will directly reflect the variation of the supersaturation inside the gel.14 TMOS/water/methanol ratios from 2/5/9 to 2/9/5 (mL) were examined, and the procedures remained identical with those of the previous experiment. The results are presented in Figure 4. As expected, variations in the water/methanol ratios strongly affected the crystallization of (()-modafinil inside the gel. When high degrees of supersaturation were involved (high water/methanol ratio), the crystallization occurred at 40 °C and yielded numerous small crystals (e.g., the tube on the left side of Figure 4). The number of crystals then decreases with the degree of supersaturation involved (from left to right in Figure 4). Crystals grown in tubes with a 2/7/7 ratio were found to be mainly of form III, thus validating the role of the crystallization in gels. It is worth noting that the pores of a single gel may differ by their size and connectivity. The supersaturation can therefore take different values at different locations in the gel. This may explain why form III was never obtained alone. Moreover, since the gel still evolved during the crystallization (and consequently the composition of the sol in the pores), it was difficult to ascertain the supersaturation in the gel.

Figure 6. Comparison with the calculated morphologies for (()-modafinil form I. From left to right: Bravais-Friedel-Donnay-Harker morphology, Cerius2 growth morphology, and experimental morphology.

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Pauchet et al. Table 1. Resolution of the Crystal Structure of the Twinned Form I: Addition of the Twin Law without the twin law with the twin law

Figure 7. Schematic representations of a crystal of form I (left) and a twinned crystal of form I (right).

goodness of fit on F2 final R indices (I > 2σ(I)) R1 wR2 R indices (all data) R1 wR2 largest diff peak and hole, e Å-3 twin fraction, %

1.137

1.052

0.1742 0.4414

0.0416 0.1138

0.1770 0.4423 1.753 and -0.756

0.0437 0.1151 0.263 and -0.399 ∼32

Table 2. Data and Data Collection and Refinement Details for (()-Modafinil Form III and Form I

Figure 8. Indexation of the faces of the twinned crystal. The twin law is denoted by a double arrow.

Results: Study of the Crystals The morphology of the crystals was observed with an optical microscope. Among them, three different typical morphologies were identified, each one having a different occurrence. While different morphologies do not necessarily mean different polymorphic forms, they could at least be expected, especially when the crystals are grown under the same conditions. This method, if undertaken with care, was found to be useful in this case and was accurate in discriminating between particles of different nature. Then single-crystal X-ray diffraction was used to determine the corresponding structures. Analyses were performed on a Bruker SMART APEX diffractometer with a CCD area detector and a three-circle goniometer. The cell parameters and the orientation matrix were determined by using SMART software.15 The space group determination and the refinement were performed with the SHELXTL package.16 Form I. Form I is found to be the most widespread form among the crystals obtained from the protocol defined by m(()-modafinil ) 0.30 g and 2/8/6 TMOS/MeOH/H2O (vol). The space group is P21/a (monoclinic), and the crystallographic parameters are

a ) 14.502 Å, b ) 9.678 Å, c ) 20.844 Å, and β ) 110.17° The faces of the crystal were then indexed using the “face option” of SMART software, and the apparent symmetry was found to correlate with the theoretical point group 2/m. The morphology of these crystals (see Figure 5) was compared to those obtained by computational techniques. The results obtained by the BFDH technique (only spacings between lattice planes have been taken into account17,18) and by the Hartman-Perdok method (calculation of attachment energies after generation of connected nets19-21) are significantly different from those of the experimental crystals (see Figure 6; these morphologies have been computed by using Cerius2,22 and MOPAC charges using the AM1 approximation method have been assigned). Although the solvent effect has been disre-

cryst syst space group a (Å) b (Å) c (Å) β (deg) cell vol (Å3) calcd density (g/cm3) Z Z′ µ(Mo KR) no. of unique rflns (>2σ(I)) Rall (%) (Rgt (%)) final diff electr dens max/min (e Å-3)

form III

predicted form III

orthorhombic Pna21 14.510(4) 9.710(3) 19.569(5)

orthorhombic Pna21 14.50 9.68 19.76

2757.1(12) 1.3171 8 2 0.71073 5677 (5023)

2773.5 1.308 8 2

3.41 (3.02) 0.229/-0.237

form I monoclinic P21/a 14.5022(1) 9.6875(8) 20.8445(2) 110.1700(1) 2748.85(4) 1.3210 8 2 0.71073 5621 (5018) 3.95 (3.59) 0.218/-0.278

garded, these simulated morphologies are closer than those observed in solution. This shows that the crystal growth is drastically changed when it is performed in gels. Twinned Form I. The second kind of morphology differs from form I and does not match with a 2/m but rather to an mm2 point group. The rarer occurrence of these crystals could be the expression of a less stable polymorphic form (metastable form III belongs to the Pna21 space group and, thus, theoretically exhibits an apparent mm2 symmetry). However, several indications also prompted the hypothesis of a twin. First of all, the morphology is similar to that of form I: half of the crystals seem to be in common (see Figure 7) (microscopy with polarized light did not allow any further observation). From the indexation of the faces of a form I crystal, a twin plane (001) was expected, with the twin law being either a mirror in this plane or a 2-fold screw axis along [100]. The first attempt to solve the structure gave a poor reliability factor (the final R value for the reflections with I > 2σ(I) is 17.43%). A total of 54 systematic absence violations inconsistent with any known space group were noticed. K ) σFo2/σFc2 was found to be systematically high for reflections with low intensities and Fo was greater than Fc for the “most disagreeable” reflections.23 These are characteristics of a twinned crystal. Thanks to the size and the quality of the crystals, additional analyses allowed us to highlight the twinning. The beam of the diffractometer was focused on only half of the crystal. The experiment was then repeated with the other part of the crystal so as to analyze each of them independently. The orientation matrices of the unit cell corresponding to each half (respectively M1 and M2) were obtained (crystallographic parameters of the unit cells are those of form I). They allowed the computation of the twin law matrix M (details are available in the Supporting Information):

M ) M1-1‚M2

(1)

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Crystal Growth & Design, Vol. 6, No. 8, 2006 1885

Figure 9. SEM pictures of the edge between (111) and (11-1) faces of a form I single crystal (left) and at the boundary between the two bodies of a twinned form I (right). The areas in white rectangles of the top pictures are magnified in the bottom pictures. Scale bars are shown for the respective pictures.

Figure 10. Comparison between the conformations of the two independent molecules of the asymmetric unit of form III.

which yields

M≈

[

1 0 0 0 -1 0 -1 0 -1

]

This matrix corresponds to a rotation around a 2-fold axis along [100] in the monoclinic structure. The respective faces of the twin were then indexed as shown in Figure 8. The off-diagonal term equals (2c cos β)/a, and its almost rational value reflects the quasi-perfect match between the two reciprocal spaces of both halves.24 The twin law linking the hkl values of each domain of the twin was then used during the refinement of the first analysis (where the two bodies of the twin are indeed taken into account at the same time). The reliability factor drastically decreased to suitable values (see Table 1).

Figure 11. Packing of the (004) slices in the structure of form III starting from form I. Matching slices with the structure of form I are in gray and nonmatching slices in white. The respective unit cells are given within dashed lines.

Scanning electron microscopy allowed investigation of the boundary between the two bodies of the twin edge of the crystals where the twinning occurs (Figure 9). Whereas form I shows “sharp edges” between the (111) and (11-1) faces (or their equivalents), a reentrant corner in the domain boundaries is observed in twins. This is not unusual for twins, but this may

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Figure 12. Symmetry relationships in (()-modafinil form III. The prime is used to make a distinction between the first and second molecules of the asymmetric unit.

Figure 13. Relationships between the molecules of the unit cells of form I (left) and form III (right). Crystallographic symmetries are depicted by solid lines and pseudo-symmetries by dashed lines, and the relationship involved in the formation of the twin is shown by dotted lines. Pseudo operators are shown in gray.

be a useful characteristic to identify putative polysynthetic twinning. It will be discussed in the next part. Form III. The third morphology was repeatedly obtained in the tubes with m(()-modafinil ) 0.30 g and a 2/7/7 TMOS/MeOH/ H2O (vol) ratio. Single-crystal X-ray diffraction revealed the form III. This structure can thus be compared with the theoretical structure predicted in a previous paper.10 Form III is confirmed to belong to the space group Pna21 with the parameters

molecules (this issue was already put forward in a previous paper10). The poor quality of the XRPD pattern of form III available at the time the structure was derived did not allow a Rietveld refinement. Therefore, the c parameter was manually adjusted so that simulated and experimental XRPD values could match.

a ) 14.5104 Å, b ) 9.7103 Å, c ) 19.5695 Å

Earlier, we mentioned strong similarities between form I and form III. We highlighted that, instead of the expected (002) layer used in the reconstruction (i.e. two consecutive (004) layers), four consecutive (004) layers were found to match between both structures. Then the next four (004) layers in form III differ by a shift of half of the a parameter (Figure 11). This “stacking fault” is periodically repeated every d001 (i.e. four d004) to obtain form III from form I. We have highlighted the existence of a pseudo-2-fold screw axis in the structure of form III at 1/8 and 5/8 (corresponding indeed to the 2-fold screw axis of the monoclinic form I (Figure 12), 1 f 3′; a pseudo inversion center is also found at 3/8 and 7/ (Figure 12), 1 f 4′). Since this pseudo axis does not intersect 8

This result is in good agreement with the predicted structure (see Table 2). The second independent molecule of the asymmetric unit does not differ significantly from the first (the difference is even less pronounced than the two conformations observed in the structure of form I; see Figure 10). The experimental structure is, however, slightly denser than the predicted one (the parameter c is 19.569 Å compared to 19.76 Å, and the difference in density is 0.30%). Such a difference can be explained by the failure of the force field to reproduce the exact structure of (()-modafinil form I or III: it does not transcribe perfectly the existing interactions between the

Discussion: The Twin and Form III

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Figure 14. Packing at the interface of the twinned bodies of form I. The red and blue lines depict the unit cell corresponding to a packing of form III for each body.

the crystallographic 2-fold screw axis of the form III (1 f 4 in Figure 12), it is compulsory that another pseudo-2-fold screw axis linking these two molecules exists in the structure (3′ f 4 in Figure 12). A comparison between the superimposable slices of form I and form III is presented in Figure 13. The possibility of twinning was suggested;10 however, no twin law was proposed. It is likely that this pseudo symmetry is involved in the twinning: the plane and the direction are in agreement with the results found in the resolution of the twin law. Moreover, the (004) slice which contains the pseudo-2fold axis corresponds to the location of the “stacking fault” observed in form III and is parallel to the twin plane experimentally observed. As reported by Aminoff and Broome´,25 “The atomic coordination in the transition layer is either identical with that in the crystal structure or closely related to it. In the latter case, the transition structure is that of a possible polymorphic modification of the structure, or else that of a modification which could be plausible for that substance”. The twin of (()-modafinil form I seems to match this statement (see Figure 14). Whereas the experimental data are in agreement with the hypothesis of a 2-fold axis as the twin law, a pseudo glide plane also exists in the plane identified as the composition plane (3′ f 3 or 4′ f 4 in Figure 12). Therefore, a second kind of twin may be expected in which the twin law would be a mirror plane. The interaction energies between the molecules in both bodies would remain unchanged. It is likely that this new twin should have the same “probability” of occurrence as the experimentally observed one. There would, however, be no impact on the morphology of the twin, which would make it hard to differentiate between them. Investigations on other possibilities of twinning in the different (004) planes did not yield any results (favorable interactions only lead toward a form I or form III like packing). Whereas the “stacking fault” is only observed once in the twinned form, it is periodically repeated in form III. Owing to the weak energy difference between both forms, we could thus imagined an infinite number of intermediate cases where several

Figure 15. Stacking of (001) slices in form I, twinned form I, and form III. The unit cells are shown respectively by red and blue dotted lines for form I and form III. A plausible intermediate case with several stacking faults is represented in the middle.

“stacking faults” would arise inside the crystal (i.e. polysynthetic twinning). This is shown schematically in Figure 15. This kind of twinning has already been reported for trinitrotoluene. It exhibits two polymorphic forms which share the same structural similarities as observed for (()-modafinil form I/form III.26 The polymorphic forms of trinitrotoluene have also been related by means of the DCP model.27 Extensive twinning is systematically observed during the crystallization of the monoclinic form. The examination by optical microscopy of crystals of (()-modafinil form I did not allow us to observe any evidence of such a feature. Since twinning could affect only thin domains in the crystal and therefore might not be seen macroscopically, some crystals were observed by means of a scanning electron microscope. Single crystals grown in gels exhibit flat faces exempt from any defect. Identical results were obtained for crystals grown in solution, except in some cases where growth disruptions arise (parallel to the (001) plane if it is considered that in solution (001) faces are the most developed ones; see Figure 16). This could be the expression of the repetition of the aforementioned stacking fault.

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Figure 16. Crystals of (()-modafinil form I grown in methanolic solution.

Figure 17. Representation of the interactions between (004) layers in (a) form I and (b) form III. Interactions between two consecutive slices are represented by crosses: red for a-a, green for b-b, and black for a-b. Since some slices are identical or matching between the two structures, b-b and a-a interactions in form I are identical with a-b interactions in form III. Energetic differences arise from interactions at a longer range: i.e., between two nonconsecutive (004) slices (represented by red brackets on the left-hand side of the figure).

More than 50 years ago, Jeffrey depicted in a paper the behavior of wollastonite which exhibits stacking faults along [100].28 Depending on these stacking faults, a triclinic or a monoclinic form is obtained (the crystallographic parameters in the (100) layer are almost identical, and the third parameter of the monoclinic form is twice that of the triclinic form). Some considerations about interaction energies related in this paper can be applied to (()-modafinil. Given the structural similarities between form I and form III, the interaction energies between two consecutive (004) layers (i.e. inside a (002)A or (002)B layer) should be identical in both unit cells. This is depicted in Figure 17, where the interactions between the two different (004) slices (namely a and b; each one containing one molecule of the asymmetric unit) are depicted by crosses. Three interactions can be distinguished: a-b, a-a, and b-b. In the structural study it was shown that some slices were matching; i.e., the b-b interactions in form I (Figure 17, on the left) are identical with the a-b interactions in form III (Figure 17, on the right). Therefore, the differences in lattice energy arise from interactions at a longer range (at least between two nonconsecutive (004) layers), represented by red brackets in Figure 17. This explains the close lattice energies computed for the two structures (by using the Dreiding force field 2.21 with MOPAC charges, the lattice energy difference is 0.93 kJ mol-1). Conclusion Whereas single crystals of (()-modafinil form III have not been obtained by crystallization in solution, crystallization in

gels was found to occur. Suitable parameters for the density of the gel and the different concentrations in compound and solvents allowed us to promote its nucleation. The X-ray analysis confirmed the predicted structure previously proposed by using the derived crystal packing model on the structure of form I. However, crystallization in gels is not straightforward and numerous parameters need to be determined before obtaining satisfactory results. Interactions between the compound to crystallize and the gel, though not expected, are unavoidable and play an important role during the formation of the gel and should not be overlooked. Twinning was expected because of the structural similarities between the two polymorphic forms and their propensity to crystallize concomitantly in solution. Crystal growth in gels allows us to confirm the twinning of form I (in almost onethird of the crystals). The twin law has been determined. The interface of form I twinning exhibits a part of the form III packing. Therefore, the Aminoff and Broome´ statement25 could be reversed. When two structures differ only by an interplay of a common slice, it is likely that twinning, multitwinning, polytypism, or even an incommensurable phase can be observed. The isoenergetic character of the two polymorphs and their concomitant appearance are additional features which increase the likeliness of the twinning phenomenon. Between form I and form III an infinite number of stackings can be envisaged, just as in SiC, C60, or CdI2. Conceptually, a stacking fault on the one side of this gradient (close to form I) becomes the “rule” on the other side (form III) (see Figure 15). Further work will be devoted to the study of this phenomenon during the crystallization of (()-modafinil. Acknowledgment. We thank Cephalon Inc. for their support during this study. Supporting Information Available: Text and a figure giving details of the twinning in form I and a CIF file giving crystal data for form III. This material is available free of charge via the Internet at http:// pubs.acs.org. In addition, CCDC 284321 contains crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, by e-mail to data_request@ ccdc.cam.ac.uk, or by contacting The Cambridge Crystallographic Data Centre, 12, Union Road, Cambridge CB2 1EZ, U.K. (fax: +44 1223 336033).

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