Inversion of the Relative Stability between Two Polymorphic Forms of

CRYSTAL GROWTH & DESIGN

Inversion of the Relative Stability between Two Polymorphic Forms of (() Modafinil under Dry High-Energy Milling: Comparisons with Results Obtained under Wet High-Energy Milling

2007 VOL. 7, NO. 9 1608-1611

Julie Linol, Thomas Morelli, Marie-Noe¨lle Petit, and Ge´rard Coquerel* Unite´ de Croissance Cristalline et de Mode´ lisation Mole´ culaire, SMS, UPRES EA3233 -IRCOF, UniVersite´ de Rouen, F-76821 Mont Saint Aignan Cedex, France ReceiVed January 23, 2007; ReVised Manuscript ReceiVed March 29, 2007

ABSTRACT: Among the seven different forms of (() modafinil, form I is the most stable variety (at whatever the temperature, T), and form III is very close to form I in terms of lattice energy. Under high-energy milling (HEM), every modification converts into a defective form III. The inversion of “stability” between form I and form III is then evidenced when a high-powered mechanical flux of energy is applied. When 3% mass/mass of watersa very poor solvent for this racemic compoundsis introduced in the vials, the same types of experiments lead to defective form I. This study tends to show that whatever the number of polymorphic forms in the temperature, pressure (T, P) space, a single variety exists as a steady state for a given set of HEM parameters. Introduction High-energy milling (HEM) is known to often cause crystalline powders to be far from their equilibrium.1 As organic compounds show a great propensity to adopt several packing arrangements (i.e., numerous cases of polymorphism have been detected so far2), we see special interest in answering the following questions. Do the polymorphic forms of the title compound exhibit the same behavior under high-energy milling? In other words, does the hierarchy in terms of relative stability among the different varieties remain unchanged with or without HEM?3-5 In case of polymorphic transformation induced by HEM, is there any possible reversibility when milling is applied with medium or low intensity of milling? With regard to the two questions above, is there any significant difference in the behavior of a given molecular component undergoing dry and wet milling? After an introduction on “the theory of forced phases” and the presentation of polymorphism of the molecular compound chosen for this study, the comparison between the nature of the stable thermodynamic form (at pressure P ) 1 atm and at whatever the temperature, T) and the nature of the dynamic form (obtained under high-energy milling) will be established and the nature of the reversibility will be examined under dry and wet conditions of milling. Dynamic Approach: The Theory of Forced Phases. The concept of driven alloys was introduced by Martin’s group.6-8 Various experiments have shown that a new configuration of alloys (i.e., composition, amorphization...) could be obtained under external forcing (i.e., strong irradiation or high-energy milling). The steady-state obtained under a high-powered mechanical flux depends on the usual physical variables: temperature and pressure but also on the external forcing intensity. Moreover, sometimes the nature of the steady state depends on environmental conditions applied during the milling9 (e.g., wet or dry milling as exemplified by this work). Under high-energy milling, a dynamic equilibrium exists between damage and recovery. After a sufficient period of time, * To whom correspondence [email protected].

should

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this equilibrium is reached, and a given steady state is obtained. The nature of this steady state depends on the following three parameters: (i) the mean milling temperature (in the case of amorphization: Tmilling < Tg) (ii) the addition of solvent (in the case of “wet” milling) (iii) the milling intensity The milling intensity is defined as the momentum transferred by a ball to the unit mass of powder per unit time. The formula for milling intensity is simply:

I ) (MbVb f )/Mp

(1)

where Mb is the total mass of the balls, Vb is the maximum velocity of balls, f is the impact frequency, and Mp is the mass of the powder submitted to HEM. According to the literature,10 in the case of planetary milling, the impact velocity and the shock frequency depend on the disk radius and the milling couple (Ω,ω). If these parameters are constant, the milling intensity depends on the ball-to-powderweight ratio R ) Mb /Mp

I ) (RVb f )

(2)

Some controversies have appeared on the relevance of I, as defined above, on the physical and kinetic aspects of HEM. Additional parameters have been proposed such as the volume of the powder trapped between two balls or between a ball and the vial wall, the maximum contact pressure, the stress contact life, the nature of the grinding materials, etc. (ref 11 and references therein). Indeed, the intensity parameter (i.e., the transfer of momentum) considered here increases monotonically with the ball velocity and is proportional to R. That is to say, it is inversely proportional to the mass of the entire powder. A correction factor taking into account the momentum transferred to the trapped powder only also could have been considered. Moreover, up to now these concepts have been tested on metals or “hard” inorganic materials. Their pertinence has not been proven yet with “soft” organic compounds. So far, five different elementary behaviors have been observed when HEM is applied to molecular phases:

10.1021/cg0700723 CCC: $37.00 © 2007 American Chemical Society Published on Web 06/01/2007

Relative Stability of Polymorphs of (() Modafinil

Crystal Growth & Design, Vol. 7, No. 9, 2007 1609

Figure 2. Structure of modafinil, namely, (2-(diphenylmethyl)sulfinyl)N-acetamide or 2-benzhydrylsulfinylethanamide. Table 2. Dry Milling of (() Modafinil Forms I, III, IV, V, and VI

Figure 1. (a) The dynamic form and the thermodynamic form are identical (except that because of the drop in crystallinity, the adjective “defective” is associated with the dynamic form). (s) Stable form (thermodynamic), (---) metastable form (thermodynamic), (---) “stable” dynamic form. (b) The defective dynamic form and the thermodynamic form are different. (s) Stable form (thermodynamic), (---) metastable form (thermodynamic), (---) “stable” dynamic form. Table 1. Crystallographic Data of Modafinil Form I and Form III

form I form III

space group

Z′

a (Å)

b (Å)

c (Å)

β (°)

F

P21/a Pna21

2 2

14.517 14.517

9.71 9.71

20.875 19.763

110.14 90

1.314 1.3035

(i) The nature of the initial solid phase remains unchanged under the milling conditions applied (milling intensity, mean temperature). Only an anisotropic drop in crystallinity is observed, resulting from the introduction of numerous defects in the crystal lattice (e.g., saccharine). (ii) Amorphization: when milling is carried out below the glass transition, a glassy state is usually obtained. Therefore, the control of the mean milling temperature is critical.12 For a constant Mb, the greater the number of balls the higher the mean temperature due to the friction effect. To avoid an excessive mean temperature, it could be necessary to apply an intermittent HEM. (iii) A new solid phase, which could only be obtained only under HEM13 (iv) Access to a polymorph, which could also be obtained by adjustment of conventional variables: temperature, pressure, nature of the solvent (or mixture of solvents), cooling ramp, etc. Two cases are known: (a) The dynamic form (steady state) and the stable thermodynamic form are the same, at whatever the milling intensity (for example, this is the case of (()5-methyl-5-(4′-methylphenyl)hydantoin)14 (Figure 1a) (b) Inversion of stability of two polymorphic forms according to milling intensity15 and this work (Figure 1b) Some studies have reported that several of these elementary behaviors can occur simultaneously.16 Polymorphism of (() Modafinil. So far, no less than seven polymorphic forms of (() modafinil (I, II, III, IV, V, VI, and VII17) have been reported. The structures of form I and form III have been determined by using single-crystal X-ray diffraction18,19 (Table 1). They display a high degree of similarity and consistently are close in energy. Without particular precaution, forms I and III are concomitant polymorphs.20 At P ) 1 atm, and at whatever the temperature, form I is the stable form and form III is the second best in terms of stability. The behaviors of the polymorphic forms I, III, IV, V, and VI of (() modafinil, under dry and wet HEM, have been studied. The study was not extended to the metastable forms II and VII.

starting form

mass of powder (g)

no. of balls

ratio r

milling duration (h)

form VI form V form IV form III form I form I

1.5 1.5 1 2.5 2.5 21

3 3 2 5 5 1 (Ø ) 3 cm)

15 15 15 15 15 13

10 10 10 5 5 10

steady state

defective form III

Experimental Section The planetary mill used in this study is the Pulverisette 4 (P4) from Fritsch (Oberstein, Germany). This mill is composed of two vials (80 mL, r ) 4.5 cm) attached to a horizontal disk; the vial rotation speed and the disk rotation speed are independent. The vials and the balls are made of tungsten carbide (d ) 14.7, ball diameter: 1 cm, mass ca. 7.5 g except for the last experiment listed in Table 2, in which the ball was 3 cm in diameter, mass ca. 210 g). Following parameters were kept constant throughout this study (dry and wet milling): (i) Milling couple (Ω,ω). The couple (Ω,ω) determines the milling mode: when Ω and ω have the same sign, the friction mode is favored, and when Ω and ω have opposite signs, the shock mode (or impact mode) is predominant. Because of the overlapping of milling vials and supporting disc, the material to be ground and the balls execute motions inside the vials whose effects on the powder depend on the ratio between the rotation velocities of the vials (ω) and the disc (Ω). On the one hand, the faster the rotation of the vials the more the friction mode is favored. On the other hand, the faster the rotation of the planetary disc the more the impact mode is favored. In this series of experiments, the same velocities have been used for the vials (ω) and for the disc (Ω) with opposite signs. (ii) R ) Mb/Mp. This ratio has been determined by different preliminary experiments so that a compromise could be reached between the following: (a) The kinetics of transformations are fast enough. (b) The crystallinity of the resulting materials is always sufficient for an unambiguous identification of the solid phase. (c) The mean milling temperature is kept at (25 ( 2) °C. It is worth noting that this series of fixed parameters have imposed a constant ratio between the impact mode and the shearing mode in every experiment leading to fair comparisons among the experiments. For these experiments, lot no. P980906 (() modafinil (supplier: Cephalon France) was used. The nature of the powder after milling was checked by X-ray diffraction (D5005, Siemens).

Results and Discussion Every experiment conducted during this study failed to bring about the appearance of any detectable amount of side product (NMR 1H analysis). Dry HEM. For this set of experiments, the milling couple was (400, -400) rpm, and the value of the ratio R (Mb/Mp) was 15 (except for the last experiment carried out with a ball 3 cm in diameter, R ) 13). To keep this ratio constant, the number of balls has then been adjusted according to the mass of powder loaded in the vial. As shown in Table 2 and Figure 3, all polymorphic forms converge into a defective form III. The duration of milling for a complete conversion of forms I, IV, V, and VI into the defective form III was determined

1610 Crystal Growth & Design, Vol. 7, No. 9, 2007

Linol et al.

Figure 3. XRPD patterns of milled forms I, III, IV, V of (() modafinil.

Figure 4. XRPD patterns of “wet” milled (() modafinil forms I, III, and IV.

by X-ray powder diffraction (XRPD) analyses of the powder at regular intervals. The last experiment tends to show that the definition of the milling intensity (eq 1) is appropriate in this study, and there is no need for considering the mass of powder trapped between the ball and the wall of the vial. Therefore, the nature of the stable thermodynamic form (i.e., form I at P ) 1 atm, and at whatever T < Tmelting) and that of the stable dynamic form under these specific milling conditions differ. By contrast to normal T, P space with a lot of local minima (i.e., polymorphs), this study tends to show that in T, P, I space, a single defective form only can stand a high intensity of mechanical stress.

Reversibility. To test the reversibility of these transformations driven by high mechanical stress, a series of experiments has been carried out with defective form III as the starting material (Table 3). At whatever the “soft” milling conditions imposed to the defective form III (R < 15, milling couple < (400, -400) rpm), no return to form I has been observed. Consistently, defective form III stored at room temperature for more than 1 year showed no sign of evolution toward form I. “Wet” Milling. The same fixed scheme of experiments has been applied to the different polymorphs of (() modafinil, i.e., 2.5 g of solute with five balls of 1 cm in diameter were loaded in each vial (R ) 15) and were submitted to the milling couple

Relative Stability of Polymorphs of (() Modafinil

Crystal Growth & Design, Vol. 7, No. 9, 2007 1611

Conclusion

Figure 5. Alternate crystallization of forms I and III under consecutive dry and wet HEM. Table 3. Series of Experiments to Test the Reversibility under HEM mass of powder of defective form III (g)

no. of balls

ratio Ra

milling duration (h)

(Ω,ω) rpm

4 3 2.7 2.4 2.5

5 3 2 5 5

9 7.5 5 16 15

15 10 10 40 40

(400, -400) (400, -400) (400, -400) (300, -300) (100, -100)

a

steady state defective form III

Ratio R ) mballs/mpowder. Table 4. Experimental Data in the Case of “Wet” Milling

b

starting form

mass of powder (g)

milling duration (h)a

nature of solvent/(%)

steady state

form I form I form I form III form IV form V form VI

2.5 2.5 2.5 2.5 2.5 2.5 2.5

10 10 10 10 10 10 10

methanolb/11.2 methanolb/2.8 water/3.2 water/3.2 water/3.2 water/3.2 water/3.2

form I form I defective form I defective form I defective form I defective form I defective form I

a Duration has not been optimized in this series of experiments. Solubility of (() modafinil in methanol is about 7.6% at 20 °C.

(400, -400) rpm. The nature and the amount of solvent together with the resulting phases are collected in Table 4 and illustrated in Figure 4. All polymorphic forms converge into a defective form I. Therefore, the nature of the stable thermodynamic phase remains unchanged under wet milling conditions. It is important to note that the solubility of the racemic compound (form I) is ca. 0.02% in water at room temperature. Thus, it is difficult to imagine that the solubility increases by such a factor that the solid-solid transition to defective form III occurs and the very small amount of solute dissolved in the “aqueous solution” drives back the solid to form I. In our opinion, it is more the genuine combination of shock and friction effects that is modified. The contrasting results obtained by using “dry” and “wet” millings prompted us to design a cyclic process schematized in Figure 5. The first step of this cycle consisted of milling 2.5 g of form I with five balls without solvent: the defective form III was obtained (XRPD analysis). In the same vial (containing the defective form III and five balls), 3.2% of water was added. After 10 h of milling, the defective form I was unambiguously characterized. Reversibility between defective form I and defective form III can thus be obtained by alternating dry and wet HEM.

At P ) 1 atm at whatever the temperature and without any milling energy, form I is the stable form. Therefore, the other polymorphic forms (III, IV, V, and VI) are of monotropic character. Under HEM (in Fritsch P 4 setup) defined by the following intensity parameters (i) the ratio of total mass of balls/mass of powder equals 15, (ii) (Ω,ω) ) (400, -400) rpm, all forms (I, III, IV, V, and VI) converge toward a defective form III. Thus, in the space P ) 1 atm, T and I, the dynamic form corresponding to a steady state, is the defective form III. An apparent inversion of dynamic stability between forms I and III is therefore evidenced. So far, the reversibility of the polymorphic transition under high-energy milling in dry conditions has not been established. Nevertheless, when adding a small amount of water it is possible to observe the “return” from defective form III to defective form I. In contrast to a “rich” landscape in T; P space with a lot of local minima (i.e., polymorphs), this study tends to show that in T, P, I space (with a specific value of I and a defined context: “dry” or “wet” milling) only a single defective form can stand the flux of mechanical energy. Acknowledgment. The authors are thankful to Cephalon Inc. (West Chester, PA) for the continuous support during this study. References (1) Boldyreva, E.; Boldyrev, V. ReactiVity of Molecular Solids; John Wiley & sons, Ltd: Chichester, 1999. (2) Hilfiker R. Polymorphism in the Pharmaceutical Industry; WileyVCH: Weinheim, 2006. (3) Bakker, H.; Zhou, G. F.; Yang, H. Prog. Mater. Sci. 1995, 39, 159. (4) Huang, J. Y.; Wu, Y. K.; Ye, H. Q. Appl. Phys. Lett. 1995, 66, 308. (5) Pochet, P.; Tominez, E.; Chaffron, L.; Martin, G. Phys. ReV. B 1995, 52, 4006. (6) Chen, Y.; Bibole, M.; Le Hazif, R.; Martin, G. Phys. ReV. B 1993, 48, 14-21. (7) Martin, G.; Bellon, P. Solid State Phys. 1997, 50, 189-331. (8) Suryanarayana, C. Prog. Mater. Sci. 2001, 46. (9) Boldyrev, V. V. Russ. Chem. ReV. 2006, 75, 203-216. (10) Abdellaoui, M.; Gaffet, E. Acta Metall. Mater. 1995, 43, 10871098. (11) Begin-Colin, S.; Girot, T.; Le Cae¨r, G.; Mocellin, A. J. Solid State Chem. 2000, 149, 41-48. (12) Willart, J. F.; Caron, V.; Lefort, R.; Dane`de, F.; Pre´vost, D.; Descamps, M. Solid State Commun. 2004, 132, 693-696. (13) Coquerel, G.; Linol, J.; Souvie, J.-C. FR Patent 03/08/05 No. 0508278. (14) Linol, J.; Coquerel, G. J. Therm. Anal. Calorim. 2007, submitted. (15) Willart, J. F.; Lefebvre, J.; Dane`de, F.; Comini, S.; Looten, P.; Descamps, M. Solid State Commun. 2005, 135, 519. (16) Shakhtshneider, T. P.; Boldyrev, V. V. Mechanochemical Synthesis and Mechanical Activation of Drugs; In ReactiVity of Molecular Solids; Boldyreva, E. V., Boldyrev, V. V., Eds.; Wiley: New York, 1999; pp 271-311. (17) Broquaire, M.; Courvoisier, L.; Mallet, F.; Coquerel, G.; Frydmann, A. US patent, WO/014846 AI, 2004. (18) Pauchet, M.; Gervais, C.; Courvoisier, L.; Coquerel, G. Cryst. Growth Des. 2004, 4, 1143-1151. (19) Pauchet, M.; Morelli, T.; Coste, S.; Malandain, J. J.; Coquerel, G. Cryst. Growth Des. 2006, 6, 1881-1889. (20) Bernstein, J.; Davey, R. J.; Henck, J. O. Angew. Chem. Int. Ed. 1999, 38, 3440.

CG0700723