Solubility-Hardness Correlation in Molecular Crystals: Curcumin and

Article pubs.acs.org/crystal

Solubility-Hardness Correlation in Molecular Crystals: Curcumin and Sulfathiazole Polymorphs Manish Kumar Mishra,† Palash Sanphui,† Upadrasta Ramamurty,*,‡,⊥ and Gautam R. Desiraju*,† †

Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560 012, India Department of Materials Engineering, Indian Institute of Science, Bangalore 560 012, India ⊥ Center of Excellence for Advanced Materials Research, King Abdulaziz University, Jeddah 21589, Saudi Arabia ‡

S Supporting Information *

ABSTRACT: Curcumin and sulfathiazole exist as three and five polymorphs, respectively. We correlate solubility and mechanical properties in these polymorphic systems. It is seen that hardness (H) is inversely proportional to the solubility of a polymorph. H of the polymorphs is explained on the basis of slip planes in the crystal structure, the Schmid factor (m), and the relative orientation of molecules with respect to the nanoindenter direction. Effectively, H is a useful parameter (compared to melting point, Tm, and density, ρ) that correlates well with the solubility of a polymorph. Such a correlation is helpful in systems like curcumin and sulfathiazole in which the Gibbs free energy of the polymorphs are close to one another. To summarize, a softer polymorph is more soluble.

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INTRODUCTION Polymorphism in molecular crystals has direct implications on physical properties such as melting point (Tm), density (ρ), elastic modulus (E), and hardness (H).1 In the pharmaceutical context, the differences in crystal packing of polymorphs can lead to variations in solubility, grindability, and tabletability, which, in turn, affect the processes adopted for industrial scale manufacture of drugs as well as methods for their formulation. Stress-induced phase transformations2 from one crystalline form to another during milling and tableting are generally undesirable. Consequently, the most stable form of a solid drug is preferably marketed so as to avoid any phase transformation in subsequent stages. Similarly, the solubility of an active pharmaceutical ingredient (API) is an important parameter that often determines how it is administered.3 For APIs that have several polymorphs, it may be possible to select the form that exhibits the highest solubility. In trying to understand solubility, attempts have been made to correlate it with other physical properties such as Tm, stability, and bioavailability. These studies show that the solubility of a compound correlates inversely with its Tm and stability and directly with its bioavailability. Recently, nanoindentation has been successfully employed by us and others to study the mechanical properties of a wide variety of molecular crystals, with emphasis on crystal structure−property correlations.4 In α,ω-alkanedicarboxylic acids, for example, a one-to-one correspondence between Tm, which shows the well-known odd−even effect, and E was established.4c Another example is that of the shear instability of form II of aspirin as compared to that of form I.4d Continuing © XXXX American Chemical Society

with this theme, we seek to answer the question here as to whether any correlation exists between H and solubility of molecular crystals. To date, no experimental study has been conducted to examine if such a correlation exists. If indeed there is a one-to-one correspondence, it would pave the way for the tuning of solubility through crystal engineering principles by changing H, whose dependence on the crystal structure is reasonably well established by now. Curcumin5 and sulfathiazole6 were selected for this study because they exhibit multiple polymorphic forms (three and five, respectively). The close structural similarity and the small differences in Tm between polymorphs of each of these APIs allows us to directly compare the measured H with the solubility, without the influence of other factors like entropy in the system or homologous temperatures of solvation experiments. Curcumin7 (Scheme 1), or diferuloylmethane, is the most bioactive component of the popular Indian spice turmeric (Curcuma longa) with a wide variety of medicinal benefits. Yet, curcumin is not available as a commercial drug because of its poor aqueous solubility (8.7 mg/L). The compound is not soluble in acidic medium and decomposes within 30 min in the physiological pH (7.4). Curcumin exists in the keto form in acidic and neutral pH media and in the enol form in alkaline pH medium. A stable crystal form of curcumin is long known in the literature.5a Recently, two new metastable polymorphs (enol form) of curcumin were reported that exhibit improved Received: March 3, 2014 Revised: April 21, 2014

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dx.doi.org/10.1021/cg500305n | Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

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Scheme 1. Chemical Structures of Enol (left)−Keto (right) Tautomers of Curcumin

solubility compared to the stable form.5c The other system we examine in this work, sulfathiazole (Scheme 2), is a well-known

three-sided pyramidal Berkovich diamond indenter with a tip radius of ∼100 nm was used. The loading and unloading rates were 0.6 mN/s, and the hold time at the peak load of 6 mN was 30 s. Five to six crystals of each form were examined and a minimum of 15 indentations were performed on each crystal to obtain reproducible data. The P−h curves obtained were analyzed using the standard Oliver−Pharr (O−P) method10 to determine H of the crystal in that orientation. Solubility studies on curcumin polymorphs were conducted in 40% EtOH−water medium for 24 h, according to the procedure described in the literature.5c The final concentration of curcumin in the aqueous extract was measured by the UV−vis spectrophotometer at 430 nm. The final residue was examined with the aid of PXRD to confirm that there were no phase transformations during the solubility experiments. Dissolution studies on the sulfathiazole polymorphs were conducted in EtOH using an 8-station dissolution tester (TDT-08L model, Electrolab, Mumbai, India). Each of the polymorphs weighing 200 mg were ground and filtered through a 200 μm sieve to ensure similar particle size for dissolution experiments. All the polymorphs were dipped in a 500 mL EtOH medium at 310 K with the paddle rotating at 100 rpm. Ten milliliters of the dissolution medium was withdrawn at different intervals for spectrophotometric concentration assay (PANalytical UV−vis spectrometer at 289 nm). The withdrawn medium is immediately replaced by an equal volume of fresh EtOH to maintain a constant volume. The solubility of the each polymorph was measured at different time intervals.

Scheme 2. Chemical Structures of Sulfathiazole Tautomers

sulfonamide-containing antibacterial drug, which exhibits five polymorphs.6 The stabilities of these forms have been examined extensively, with different authors reporting different stability ranks. Like curcumin, sulfathiazole can exist as tautomeric polymorphs (A and B). However, in all the five reported polymorphs, sulfathiazole exists as tautomer B. (Scheme 2).

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EXPERIMENTAL SECTION

Commercially available curcumin and sulfathiazole (Sigma-Aldrich) were used for crystallization. Large single crystals (1.5 × 0.5 × 0.5 mm3) of curcumin polymorphs were grown in conical flasks by slow evaporation of a saturated solution of different solvents at room temperature. Crystals of forms 1 (with platelet morphology) and 2 (with rod morphology) were obtained from saturated solution of EtOH and MeOH, respectively, following the procedure outlined in the literature.5b−d Form 3 crystals (with square-plate morphology) were obtained, while attempting cocrystallization with artemisinin in MeOH. The bulk phase purity of each form was confirmed by comparison with the calculated powder X-ray patterns (see Figures S1 and S2 of the Supporting Information). Form 1 crystals of sulfathiazole were grown in plate morphology by slow evaporation from a 3:2 mixture of acetone and chloroform, whereas forms 2 and 4 were obtained concomitantly in block morphology from a saturated solution in MeCN. Hexagonal-shaped form 3 crystals were harvested from a saturated solution in MeOH. The crystalline polymorphs of curcumin and sulfathiazole were confirmed by checking the cell parameters and comparison with the reported polymorphs in the CSD.8 X-ray diffraction was carried out on a Rigaku Mercury 375R/M CCD (XtaLAB mini) diffractometer using graphite monochromatic Mo Kα radiation. Face indexing of good quality single crystals was performed with Crystal Clear,9 and the major faces were assigned. BFDH morphology using Mercury also supports the major face indicated by Crystal Clear; see Figures S3 and S4 of the Supporting Information for details. Large (approximately 1.5 × 1.0 mm2 in cross section and 0.30 mm in thickness), well-shaped and defect-free dried single crystals of curcumin and sulfathiazole polymorphs were selected, after viewing them through an optical microscope supported by a rotatable polarizing stage, for nanoindentation experiments. The crystals were first washed with paraffin oil to remove any small crystals that might have been attached to the surface during crystallization. Then, each crystal was firmly mounted on a metallic stud using a thin layer of cyanoacrylate glue, and indentations were performed on the major faces on both polymorphs (see Figures S3 and S4 of the Supporting Information). Nanoindentation was performed using the Triboindenter (Hysitron, Minneapolis, MN) with an in situ imaging capability. During the experiment, load (P), vs displacement (h), of the indenter was recorded with resolutions of 1 nN and 0.2 nm, respectively. A

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RESULTS AND DISCUSSION Crystal Structures. The crystal structures of various polymorphs examined in this work have already been reported in the literature.5,6 Hence, only a brief summary of the necessary crystallographic information is provided here. Form 1 of curcumin crystallizes in the monoclinic system, while forms 2 and 3 are orthorhombic (see Table S1 of the Supporting Information for the unit cell parameters). While form 1 (P2/n, Z′ = 1) is stable, forms 2 (Pca21, Z′ = 2) and 3 (Pbca, Z′ = 1) are metastable. A common feature in all the three polymorphs is the intramolecular hydrogen bond between enolic OH with the carbonyl group and interaction of the phenolic O−H group with the carbonyl acceptor via O−H···O hydrogen bonds. Because of the twisted conformation in form 1, four curcumin molecules assemble through intermolecular O−H···O hydrogen bonds between phenols and the enolic carbonyls to make a macrocylic ring (Figure S5 of the Supporting Information). Auxiliary C−H···O interactions also play an important role in the overall molecular stability. There is a bifurcated C−H···O hydrogen bond in form 1, involving a phenyl C−H group and an alkenic C−H group with the phenolic O−H group (Figure 1). The molecular packing of form 1 is different from that in forms 2 and 3 because of the angular structure in the former. However, forms 2 and 3 are similar in their crystal packing, such as the presence of a common ring because of bifurcated C−H···O hydrogen bonds between olefinic C−H and phenolic O−H, but differ in the number of molecules in the asymmetric units (Z′). Further, the relative orientation of keto−enol group in neighboring molecules is different for form 3. Both forms have a common O−H···O hydrogen bond motif between the phenol O−H group and the methoxy oxygen (Figure 2, panels B



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a and b). The major difference between forms 2 and 3 is that the methoxy methyl hydrogen forms C−H···O interactions with the carbonyl group in form 2, whereas in form 3, these interactions are with the enolic O−H. The conformation is slightly twisted in form 1 compared to the linear one in forms 2 and 3. The molecular overlay diagram of the three curcumin polymorphs suggests that molecules in the stable form 1 deviate from the mean plane more than in forms 2 and 3 (Figure S6 of the Supporting Information). The crystal structures of the five polymorphs of sulfathiazole are reported in the literature,6 and the crystallographic parameters of each form are summarized in Table S2 of the Supporting Information. Forms 1 through 4 belong to the monoclinic space group P21/c or P21/n. The molecular packing in form 1 is different from those of the others forms. In form 1, the two independent molecules are connected through a N− H···N hydrogen-bonded amine−imino dimer, which is referred to as α6f (Figure 3a). Forms 2, 3, and 4 are constructed by the dimer growth unit referred to as β, which is built from sulfato oxygen to aniline hydrogen and aniline nitrogen to amino hydrogen contacts (Figure 3b). This β dimer is assembled into sheets, and the variation of assembly results in the difference between forms. The molecular packing of forms 2 and 4 are similar, which results in epitaxial growth in these two forms.6e Nanoindentation and solubility studies were conducted only on these four forms as sufficiently large crystals of form 5 required for nanoindentation could not be produced. Nanoindentation Responses. Curcumin. Representative P−h curves obtained on the major faces (001) of form 1, (100) of form 2, and (001) of form 3 of curcumin are displayed in Figure 4. The loading part of the P−h curves obtained on forms 2 and 3 are smooth, indicating a homogeneous plastic deformation. In contrast, the loading segment of the P−h curve on form 1 shows discrete displacement bursts, which are also referred to as pop-ins in the literature.11 Such discrete events point to intermittent plasticity instead of a continuous change. The magnitudes of the displacement burst, hpop‑in, were found to be either ∼10 nm or integer multiples of it. Since the distance between the bilayers [i.e., interplanar d-spacing (001)] in form 1 is 0.99 nm, the pop-ins can be construed as collective sliding of multiple (001) planes during indentation. The large residual depths upon complete unloading indicate significant plastic deformation during nanoindentation of all the three polymorphs. Form 1 showed the least indentation depth as

Figure 1. C−H···O interactions between curcumin molecules complete the packing of tape structure in form 1.

Figure 2. (a) O−H···O and C−H···O hydrogen bonds in form 2 (Z′ = 2). Different color shades of carbon atom are used to differentiate between two asymmetric molecules. (b) O−H···O and C−H···O hydrogen bonds in form 3 (Z′ = 1). See the differences in the molecular orientation in forms 2 and 3.

Figure 3. Sulfathiazole form 1 dimer illustrating (a) α ring and forms 2, 3, and 4 dimers illustrating (b) β ring. α ring consists of centrosymmetric N−H···N dimer of R22(8) ring. β ring consists of noncentrosymmetric dimer of R22(18) ring assembled through N−H···N and N−H···O H bonds. C



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Figure 4. Representative load (P) vs displacement (h) curves obtained on the major faces of the curcumin polymorphs. Arrows indicate discrete displacement bursts or pop-ins in the P−h curves obtained in form 1 crystal, whereas the P−h curves obtained on forms 2 and 3 are smooth.

compared to forms 2 and 3, a result of its high H. The AFM topographic images of the indents show material pile-up along the edges of the indenter impressions on form 1 crystal, whereas no such pile-up is seen in forms 2 and 3 (Figure S7 of the Supporting Information). The average values of E and H extracted from the P−h curves are listed in Table 1. Form 1 is much stiffer and harder, with its Table 1. Elastic Modulus (E), Hardness (H) of Curcumin Polymorphs curcumin polymorphs

indented face

hardness, H (GPa)

elastic modulus, E (GPa)

slip plane, slip direction

form 1 form 2 form 3

(001) (100) (001)

0.432 ± 0.015 0.341 ± 0.017 0.333 ± 0.018

11.15 ± 0.20 5.68 ± 0.25 5.60 ± 0.29

(010) [110] (010) [111] (010) [111]

E being twice that of the other two forms, which have similar values. Likewise, forms 2 and 3 also have similar H, which are only about 20% smaller than that of form 1. In molecular crystals, plastic deformation occurs due to shearing of planes along specific crystallographic planes and directions. The slip planes are typically those for which the attachment energy (Eatt) is the lowest, whereas the slip directions are those along which molecular shuffling from one energy minimum to another is the shortest. Eatt for the major crystal faces of curcumin were estimated using the Compass 27 force field in Materials Studio 6.012 (see Table S5 of the Supporting Information). This leads us to identify the possible slip systems of curcumin which are summarized in Table 1 (see the Supporting Information for Eatt values). The macrocylic ring (Figure S5 of the Supporting Information) with two intermolecular and strong O−H···O interactions (D, d, θ: 2.90 Å, 2.28 Å, 119.8°; 2.80 Å, 1.89 Å, 150.1°, see Table S3 of the Supporting Information) and several auxiliary C−H···O interactions (3.54 Å, 2.58 Å, 149.6°; 3.53 Å, 2.54 Å, 154.5°; 3.49 Å, 2.46 Å, 157.3°; and 3.45 Å, 2.38 Å, 166.9°) have to shear during indentation on the (001) face of form 1. These strong and numerous interactions are the cause for a higher E value measured on the (001) face of form 1. The twisted conformation of the molecules of form 1 (Figure S6 of the Supporting Information) resists the easy-glide of the crystallographic planes past each other, see Figure 5a and

Figure 5. (a) Layer structure of form 1. Corrugated sheets of curcumin molecules in forms (b) 2 and (c) 3, viewed down the c and a axis, respectively, and (d) possible structural change in forms 2 and 3 during indentation.

Figure S8 of the Supporting Information. Consequently, plastic deformation through shearing of the molecular layers occurs intermittently as it requires a greater load. This explains the observation of the serrations in the measured P−h responses during loading as well as the high H value of form 1. In form 2, only one O−H···O (2.63 Å, 1.71 Å, 154.0°) interaction is normal to the (100) plane. Auxiliary C−H···O interactions (3.47 Å, 2.43 Å, 159°; 3.29 Å, 2.44 Å, 135°; 3.29 Å, 2.32 Å, 147.8°; and 3.03 Å, 2.38 Å, 116.6°) are inclined oblique to the (100) plane. While the molecular packing on the (001) plane of form 3 is the same as that of form 2, the interactions are different and less in number. In form 3, one O−H···O interaction (2.67 Å, 1.69 Å, 167.9°) is normal and another (2.98 Å, 2.17 Å, 137.8°) is skew to the plane of indentation (001). One weak C−H···O interaction (3.19 Å, 2.41 Å, 127.6°) D



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1 and (101)̅ of form 4 showed a relatively smaller pile-up (Figure S9 of the Supporting Information). Estimated values of E and H are summarized in Table 2. It can be seen from it that form 1 is the least stiff and hard among the four forms examined, whereas form 2 is the stiffest and also the hardest. To rationalize the variations in mechanical properties of sulfathiazole in terms of the underlying crystal structures, the packing along the indentation direction on the major faces of the different polymorphs needs to be understood. In the major face (100) of form 1, the orientations of the molecular layers are around 145.3° to the indentation direction, whereas in polymorphs 2, 3, and 4, they are at 92.2°, 95.1°, and 92.5°. The molecular layers of form 1 are interlinked with weak N−H···O interactions (2.951 Å, 2.21 Å, 129°, see Table S4 of the Supporting Information), which are parallel to the indentation direction, whereas in form 2 they are attached with strong N− H···O interactions (3.011 Å, 2.02 Å, 168°) that are normal to the indentation direction (Figure S10 of the Supporting Information). The molecular layers are interconnected in form 3 with N−H···O and N−H···N hydrogen bonds (3.181 Å, 2.23 Å, 157° and 3.005 Å, 2.01 Å, 169°) in an alternate pattern. In form 4, only N−H···N interactions (3.181 Å, 2.23 Å, 157°) exist and are at an oblique angle to the indentation direction. These crystal structures and interactions in them suggest that layers of form 1 can offer less resistance to shear sliding as compared to the other polymorphs because of the higher oblique angle (Figure 7). Consequently, (100) face of form 1 is soft vis-à-vis with the others. Krishna et al.,13a who examined H variations in the mechanochromic luminescence of difluoroboron avobenzone polymorphs, rationalize them on the basis of the critical resolved shear stress (CRSS), which is a measure of the shear stress acting on the slip system and, hence, is given by the relative orientation of the sliding planes. The higher the CRSS, the lower will be the stress required to initiate plastic deformation and hence the lower will be H. CRSS can be gauged through the Schmid factor (m).13b,c The Schmid factor, m, is directly proportional to the product of cos ϕ cos λ, where ϕ is the angle between the normal to the slip plane and the indentation axis and λ is the angle between slip direction with the indentation axis. Estimated values of m for the major faces of sulfathiazole polymorphs are summarized in Table 2, which shows an inverse correlation between H and m (Figure S11 of the Supporting Information). The molecular layer arrangement with respect to major face of forms 2, 3, and 4 are almost normal to the indentation direction. Therefore, several pop-ins were observed on the unloading curve of these three polymorphs, whereas form 1 is soft and the plastic flow is smooth because of the higher inclination angle (145.3°) between the molecular layers and indenter direction. Solubility and Dissolution Studies. Results of the solubility experiments on curcumin polymorphs are displayed in Figure 8. The PXRD data confirm that neither of the metastable forms 2 and 3 undergoes phase transformation to the stable form 1

is also normal along [001] in form 3. The smaller numbers of interactions are the reason for low E values of forms 2 and 3, smooth P−h responses and also low H values. With regard to lower H of form 3 vis-à-vis form 2, the following is a possible reason. In the asymmetric unit of form 2, two molecules (Z′ = 2) are present in which one is in a slightly twisted conformation (similar to that in form 1) and the other molecule is nearly aligned in the mean plane. In form 3, in contrast, the molecule (Z′ = 1) in the asymmetric unit is planar (Figure S6 of the Supporting Information). The twisted conformation of one of the molecules in form 2 provides a slightly higher friction for shear sliding, which in turn results in slightly higher hardness as compared to that of form 3. Similarity in H values of forms 2 and 3 is possibly due to comparable molecular packing as corrugated sheets, when viewed down the crystallographic c and a axis, respectively (Figure 5, panels b and c). The structural model depicted in Figure 5d explains the possible mechanism of molecular layer movement in forms 2 and 3 during indentation. This model also explains the absence of the materials pile-up on the crystal surfaces in these two forms. Sulfathiazole. Representative P−h curves obtained on the major faces of the sulfathiazole polymorphs are shown in Figure 6. The loading curve of form 1 is relatively smooth with large

Figure 6. Representative load (P) vs displacement (h) curves obtained on the major faces of the four sulfathiazole polymorphs. Arrows indicate discrete displacement bursts or pop-ins in the P−h curves obtained in forms 2, 3, and 4, whereas the P−h curves obtained on the form 1 crystal is smooth.

residual depth upon unloading in comparison to the other three polymorphs, indicating that form 1 is much softer. In contrast, the P−h responses recorded on the other three polymorphs show pop-ins. The average values of hpop‑in are ∼0.80 nm in form 2, ∼ 0.9 nm in form 3, and ∼0.77 nm in form 4. These correspond to integer multiples of interplanar d spacing, dhkl of (100) for forms 2 and 3 and (101̅) for form 4, see Table S6 of the Supporting Information. The indenter impressions on major faces (100) of form 2 and (100) of form 3 showed significant pile-up, whereas on the major faces of (100) of form

Table 2. Hardness (H), Elastic Modulus (E) and Schmid Factor (m) of Sulfathiazole Polymorphs sulfathiazole polymorphs form form form form

1 2 3 4

major face

slip direction

Schmid factor, m

(100) (100) (100) (101̅)

[102̅] [102]̅ [001] [001]

0.468 0.039 0.089 0.043

elastic modulus, E (GPa) 10.01 20.44 16.42 17.31

± ± ± ±

0.19 0.25 0.30 0.21

hardness, H (GPa)

angle (deg) between the trace of the molecular layer and the indentation direction

± ± ± ±

145.3 92.3 95.1 92.5

0.356 1.080 0.704 0.881 E

0.010 0.015 0.018 0.012



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Figure 7. Packing diagram differences between four polymorphs of sulfathiazole, in which indentation direction is perpendicular to the (100) plane for forms 1, 2, 3 and (101̅) plane for form 4.

displayed in Figure 9 indicate that the rate of dissolution is the highest for form 1. Form 3 also exhibits a similar behavior,

Figure 8. Solubilities of curcumin polymorphs in 40% EtOH−water medium.

during dissolution. While the solubility of form 1 is as low at 1.2 g/L, as already mentioned in the literature,5c the solubilities of forms 2 and 3 are more than twice that of form 1. The poor aqueous solubility of curcumin, in general, may be due to its high molecular weight (368.4 g/mol) and the presence of π conjugation in the alkene chain between the two phenol fragments, which increases lipophilicity.7a The relatively low solubility of form 1 is possibly due to the presence of the O− H···O hydrogen-bonded tetramer formed by four curcumin molecules because of its twist conformation, which may hinder solvent−solute interactions. In the metastable forms of curcumin, such supramolecular rings do not form, perhaps owing to the more planar conformation of the molecule. Hence, they are perhaps more soluble. Further, all the strong donor−acceptor atoms are satisfied with stronger O−H···O hydrogen bonds in form 1, whereas in forms 2 and 3, not all (such as one of the keto−enol carbonyls) are involved in strong hydrogen bonds. This suggests that form 1 has stronger interactions between curcumin molecules than the other two forms and hence comparatively less solvent−solute interactions, which results in low solubility. The sulfathiazole polymorphs exhibit a high tendency to transform from one form to another during dissolution. Hence, we have carried out powder dissolution experiments of sulfathiazole polymorphs so that the phase transformations6f during dissolution, if any, can be monitored. The results

Figure 9. Powder dissolution rates of sulfathiazole polymorphs in EtOH.

including the saturation values. Form 4 has a lower dissolution rate than forms 1 and 3 and increases slowly after 40 min. Form 2 exhibits the least dissolution rate among all four polymorphs examined, with solubility saturating at ∼35 min before getting converted to form 3. Close examination of the dissolution plots of forms 1 and 3 suggests that there is a possibility of phase transformation from higher soluble form 1 to 3. However, all the polymorphs transform to form 3 after completion of the dissolution test (PXRD comparison). Assuming similar particle size ( 3 > 4 > 2. In this context, we note that Munro et al.6f reported that forms 2, 3, and 4 have identical solubilities in ethanol due to the similarity in their crystal structure packing, whereas form 3 was slightly more soluble. The reported results closely support the dissolution behavior of sulfathiazole polymorphs. Hardness−Solubility Correlations. Both H and solubility depend broadly on the same factors, namely crystal structure and the intermolecular interactions.4a This is illustrated with the H vs solubility plots for curcumin and sulfathiazole in Figure 10 (panels a and b), respectively. In both cases, an F



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Figure 10. Inverse correlation of hardness and solubility in (a) curcumin and (b) sulfathiazole polymorphs.

inverse linear correlation (i.e., the higher the H, the lower the solubility), is seen. Further, the relationship between the inverse of H and solubility appears to be linear except in the case of form 1 of sulfathiazole. The exception is because of the soft nature of form 1, which is due to the difference between its crystal structure and those of the other polymorphs as explained earlier. One might pose two further questions: (i) Why does one not attempt to correlate solubility with E instead of H? (ii) Why is H a better metric than say stability or Tm in terms of correlation with the solubility? To answer the first question, it is important to note the fundamental difference between E and H. E is a measure of the stiffness of the material and indicates the resistance offered by it to elastic deformation, whereas and in contrast, H is a measure of the resistance to plastic (or permanent deformation).14 E depends on the crystal structure in terms of the packing efficiency, number of intermolecular interactions and most importantly the curvature of the potential energy curve of the interaction at the equilibrium separation. H, on the other hand, depends on the presence of slip planes as already alluded, and the relative ease with which the molecular layers can slide past each other. Note that this process requires breaking and re-establishment of the intermolecular interactions. All else being the same, if the interactions between two molecular layers can be broken more easily, shear sliding of layers will require less stress and, hence, H will be low. The solubility of an organic solid also depends on the ease with which the intermolecular interactions can be broken; in this case, it would be the solvent that does this job as against the stress in the case of H. Nevertheless, this is precisely the reason that H and solubility may be correlated and the results of our experiments show that it is indeed the case. With regards to the appropriateness of H of an organic crystal as a metric to gauge its solubility, it is important to keep in mind that H, as a standalone property in itself, is important for APIs from the manufacturing point-of-view due to its critical role in processes such as comminution and tableting. Our results also show that H is a better a gauge of solubility than stability and Tm. In curcumin and sulfathiazole, the stability order of the polymorphic forms are 1 > 2 > 3 and 2 > 4 > 3 > 1, respectively. Since H is also ranked in exactly the same way, prima facie one may construe that H and stability are correlated. However, forms 2 and 4 of sulfathiazole have nearly identical stability, whereas their H and solubilities are distinctly different (as seen from Figure 10b). With respect to the Tm,

those of the curcumin polymorphs are in the same order as the H values. However, the Tm are quite close to each other (177, 171, and 168 °C for forms 1, 2, and 3, respectively), whereas the H values are significantly different. In the case of sulfathiazole, such a correlation does not even exist. While our observations do confirm that H can be a useful physical property that can be utilized for gauging the solubility of a crystal, we would like to caution here that H in this study is that of the single crystal and not of the polycrystalline aggregate, although some connections may exist.

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CONCLUSIONS Nanoindentation provides useful information on the mechanical properties of polymorphic drugs, which in turn allows for developing an understanding of their stability in the solid state. Higher hardness, H, and elastic modulus, E, of curcumin form 1 is explained on the basis of its twisted molecular conformation in the crystal structure compared to other metastable forms 2 and 3. The close cell parameters and planar structure (packing) of forms 2 and 3 support the differences in H and E values. Further, form 1 of sulfathiazole showed smallest H and E values compared to the other three forms because of the higher inclination angle between the molecular layers and the indenter direction with respect to the different intermolecular interactions. The inverse correlation between solubility and H for both the polymorphs indirectly suggests the order of that H could be utilized as a parameter to gauge the solubility order in close energy-related polymorphic systems such as sulfathiazole and curcumin.

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ASSOCIATED CONTENT

S Supporting Information *

Details of nanoindentation experiment, attachment energy calculations, PXRD patterns of polymorphs, crystallographic and hydrogen-bonding parameters, face indexing, and AFM images of nanoindentation indents for both polymorphic systems. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest. G



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ACKNOWLEDGMENTS M.K.M. thanks CSIR for a Senior Research Fellowship. P.S. thanks Dr. D. S. Kothari fellowship. G.R.D. thanks the Department of Science and Technology for a J. C. Bose Fellowship. We thank Dr. P. Kumaradhas for providing us suitable single crystals of curcumin form 2.

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