Solubility, Polymorphism, Crystallinity, Crystal Habit, and Drying Scheme of (R, S)-(±)-Sodium Ibuprofen Dihydrate

The racemic compound (R,S)-(±)-ibuprofen or (R, S)-(±)-2-(4-isobutylphenyl) propionic acid is a popular active pharmaceutical ingredient (API) in analgesic, anti-inflammatory, and antipyretic therapies (1) with abundant information about the compound provided in the literature (2–11). Ibuprofen is marketed as a racemate. The enantiomer (S)-(+)-ibuprofen is the active agent and the other enantiomer, (R)-(–)-ibuprofen, is partially converted into (S)-(+)-ibuprofen in humans. (R,S)-(±)-ibuprofen has several disadvantageous formulation properties such as poor water solubility of less than 1 mg/mL at 25 °C, a low melting point of 77 °C, and possible esterification with excipients containing a hydroxyl group (1). These problems can be easily overcome by using an (R,S)-(±)-ibuprofen salt such as the racemic compound (R,S)-(±)-sodium 2-(4-isobutyl–phenyl) propionate dihydrate or (R, S)-(±)-sodium ibuprofen dihydrate (see Figure 1), whose potential values over (R,S)-(±)-ibuprofen make the study of its solubility, polymorphism, crystallinity, crystal habit, and drying scheme meaningful (12).

Figure 1

In this study, the solubility of (R, S)-(±)-sodium ibuprofen dihydrate solids at 25 °C was determined in 23 solvents using a robust and scalable initial solvent-screening method (13). Good solvents were identified, and the solubility curves of the solids in various good solvents were constructed. Good solvents were defined as solvents in which the solubility of racemic (R, S)-(±)-sodium ibuprofen dihydrate had a solubility of < 1 mg/mL at 25 °C. All solids were produced from the supersaturated solution of the good solvents by temperature cooling from 60–25 °C.

Differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), and powder X-ray diffraction (PXRD) determined the polymorphism, crystallinity, and drying scheme of the solid samples (14). Optical microscopy (OM) and scanning electron microscopy (SEM) were used for crystal-habit imaging. The solids' solubilities and crystal habits were related to the solvent microscopic properties of dispersion forces (δ_d) polar forces (δ_p), and hydrogen bonding (δ_h) by the Hansen model adopted from the paint industry at 25 °C (15).

Solvent liquids generally are held together by van der Waals forces, which are electromagnetic interactions among molecules. The strength of van der Waals forces is directly reflected by the heat of vaporization (ΔH_v). ΔH_v can be translated into a correlation between vaporization and the solubility behavior because the types of intermolecular attractive forces needed to be overcome to vaporize a solvent liquid are the same as those that must be overcome to dissolve it. The Hildebrand numerical value (δ_t[Pa^1/2 ]) of the solvency behavior of a specific solvent was invented as a function of ΔH_v (15) in the following:

in which R is the gas constant (8.314 J/mol • K), T is the temperature (measured in K), and V_m is the molar volume (measured in m³ /mol).

Hansen parameters fine-tune the total Hildebrand value (δ_t) into three contributions: a dispersion-force component (δ_d); a polar component (δ_p); and a hydrogen-bonding component (δ_h) (15) as expressed in the following equation:

Dispersion forces are the induced attractions by the random polarities of two molecules in proximity. They are called London dispersion forces or induced dipole-induced dipole forces, and the number of temporary dipoles increases with the molecule's size. Polar forces are created when electrons are unequally shared between the individual atoms in a molecule. The charge distribution is related to the atomic composition, geometry, and size of a molecule. When polar molecules arrange themselves head-to-tail and positive-to-negative, the molecular network leads to a further increase in intermolecular interaction. These temperature-dependent dipole–dipole forces collectively create the Keesom orientation effect. A particularly strong type of polar interaction occurs when hydrogen's sole electron is drawn toward such electronegative atoms as oxygen, nitrogen, and fluorine, leaving the positively charged hydrogen nucleus exposed. The exposed positive nucleus exerts a considerable attraction on electrons in other molecules, forming a proton bridge, which is called hydrogen bonding.

Materials and methods

Solvents. Table I lists the 23 solvents from five different classes in the ascending order of Hildebrand parameters (13). Two other solvents n-propanol (CH₃(CH₂)₂OH, ACS grade, 99.98%, boiling point of 97 °C, molecular weight of 60.1 g/mole, Lot 909065 Tedia Company, Fairfield, NJ) and cyclohexane (C₆H₁₂, ACS grade, 99.9%, boiling point of 80.7 °C, molecular weight of 84.16 g/mol, Lot k24470166, Merck KGaA, Darmstadt, Germany) were used to verify the solubility sphere in the three-dimensional (3-D) Hansen plot.

Table I: Total Hildebrand value and Hansen parameters for solvents at 25 8C.

Active pharmaceutical ingredient. Ibuprofen sodium salt (C₁₃H₁₇NaO₂, molecular weight of 228.29 g/mol, batch number 015K0586) purchased from Sigma-Aldrich Corporation (St. Louis, MO) was a dihydrate of racemic (R, S)-(±)-sodium 2-(4-isobutylphenyl) propionate with a molecular formula of C₁₃H₁₇NaO₂•2H₂O and a molecular weight of 264.29 g/mol. The amount of the stoichiometric water was determined by the thermogravimetric-use test showing about 13% water loss by weight near the boiling point of water (see Figure 2).

Figure 2

Solubility studies. Because of the expensive nature of (R, S)-(±)-sodium ibuprofen dihydrate, its solubility was determined by the gravimetric titration method that required a relatively small amount of material (13). Although the gravimetric titration method had an inherent error of about ± 20% because the solvent volume used was assumed to be the same as the solution volume (13) and was less accurate than the well-known UV-visible spectroscopic technique (16) and the evaporation-weighing technique (17), it was rapid, robust, and more suited for the initial screening. Unlike the other two techniques, the gravimetric titration method did not require establishing time-consuming calibration curves of (R, S)-(±)-sodium ibuprofen dihydrate concentration in every solvent and did not produce any unforeseen solvates that could interfere with the true mass of the dihydrate solids after removal of the solvents.

Solvent-miscibility studies. The miscibility tests were performed by mixing two solvents from the 23 solvents in a 20-mL scintillation vial (13). The number of miscible and immiscible solvent pairs from the miscibility investigations and the API solubility in the 23 single solvents from the Solubility Studies Section (13) were combined to deduce a form space. The form space is defined as the total number of solid-generation experiments in pure-solvent, cosolvent and antisolvent systems (13).

Polymorph, crystallinity, and crystal-habit studies. Solids were produced in the good solvents ferreted out by the Solubility Studies Section (13). The polymorphism, crystallinity, and crystal habit of the solids were determined by DSC, TGA, PXRD, OM, and SEM, respectively.

Scanning electron microscopy. Solids of racemic (R, S)-(±)-sodium ibuprofen dihydrate compound grown from water were filtered, rinsed with acetone, and vacuumed-dried at 40 °C or 4 h. The anhydrous (R, S)-(±)-sodium ibuprofen solids were mounted on an aluminum stub by a double-sided carbon conductive adhesive tape (Product number 16073, Ted Pella Inc., Redding, CA). The solid sample was sputter-coated with a 6-nm thick gold film in an Hitachi E-1010 Auto Sputter Coater (Hitachi Ltd., Tokyo, Japan).

SEM was carried out using an Hitachi S-3500N (Hitachi Ltd., Tokyo, Japan) instrument equipped with a tungsten filament cathode source. Gold-coated samples were examined with beam energies of 15 kV with a chamber pressure of 10^-5 Pa (resolution ~3Å at these voltages).

Drying-scheme studies. Filtered solids of the racemic (R, S)-(±)-sodium ibuprofen dihydrate compound were dried by three various modes in a DOV-40 oven (Dengyng Instrument Co., Ltd., Taiepi, Taiwan) at 40 °C for 4 h in air, at 40 °C for 4 h under vacuum, and 90 °C for 2 h under vacuum. A vacuum of 6.7 × 10^-2 Pa was generated by the GVD-050A vacuum pump (Ulvac Kiko Inc., Yokohama, Japan).

Results and discussion

(R, S)-(±)-sodium ibuprofen dihydrate dissolved well in nine good solvents in Classes 4 and 5: tetrahydrofuran (THF), n-butyl alcohol, isopropyl alcohol (IPA), benzyl alcohol, N,N-dimethylformamide (DMF), ethanol, dimethyl sulfoxide (DSMO), methanol, and water. The compound only slightly dissolved in n-heptane, xylene, p-xylene, ethyl acetate, toluene, methyl-tert-butyl ether, benzene, methyl ethyl ketone, chloroform, N,N-dimethylaniline, acetone, 1,4-dioxane, nitrobenzene, and acetonitrile with a solubility of <1 mg/mL at 25 °C, giving 14 bad solvents in Classes 1, 2, and 3. Only nine solubility curves of (R, S)-(±)-sodium ibuprofen dihydrate in nine good solvents at 15, 25, 40, and 60 °C were constructed and grouped by their similar solubility ranges for ease of comparison (see Figure 3).

Figure 3

If the solute and the solvent formed an ideal solution, a straight line should result when ln x was plotted against 1/T according to the van't Hoff equation (13):

in which x is the mole fraction of (R,S)-(±)-sodium ibuprofen dihydrate in the solution at a given temperature (T) measured in K, converted from the solubility curves in Figure 3, and R_g was the ideal gas enthalpy constant (8.314 J/mol • K). Any deviation from the ideal solution behavior would be reflected from the correlation coefficient (R) of the linear fit in Figure 4. The relatively high correlation coefficients with values > 0.97 of the solvent systems, except for the one of DMSO, indicated that the solubility measurements by gravimetric titration were quite accurate, and the deviation of the solution from ideality was negligible. The enthalpy of dissolution (ΔH_d)and the entropy of dissolution (ΔS_d) were estimated from the slope and the y-intercept of the straight lines in Figure 4, respectively.

Figure 4

The values of (ΔH_d) and (ΔS_d) for (R, S)-(±)-sodium ibuprofen dihydrate are summarized in Table II for qualitative comparisons. The positive values of ΔH_d in Table II indicate that the energy of attraction of (R, S)-(±)-sodium ibuprofen dihydrate with each other, and the energy of attraction of the solvent molecules with each other were lower than the energy of attraction of (R, S)-(±)-sodium ibuprofen dihydrate and the solvent molecules in the solution. Heat was absorbed to make (R, S)-(±)-sodium ibuprofen dihydrate dissolve in the solvent. The solubility of (R, S)-(±)-sodium ibuprofen dihydrate increased with temperature. The positive values of (ΔS_d) in Table II show that (R, S)-(±)-sodium ibuprofen dihydrate-solvent systems became less ordered as (R, S)-(±)-sodium ibuprofen dihydrate dissolved into the solution. The entropy gain of the whole system was the main driving force for dissolution.

Table II: Total Hildebrand values for solvents at 25 8C versus enthalpies and entropies of solution of (R, S)-(6)-sodium ibuprofen dihydrate.

Because of the symmetrical nature of the solvent miscibility table (see Table III), the number of boxes was divided by 2, except for the diagonal boxes (13). Based on the solvent miscibility studies of the solvent pairs of the 23 solvents, 36 gray boxes were divided by 2 to give 18 immiscible pairs in total (see Table III). The form space (i.e,. a possible location for discovering a new polymorph) of the pure-solvent systems for the initial solvent-screening was limited to the number of good pure solvents (repesented by the yellow boxes). The form space for (R, S)-(±)-sodium ibuprofen dihydrate was 9. However, if the good cosolvent systems (i.e., binary miscible mixtures of good solvents) were taken into account, the form space would be extended to the total number of blue boxes in the solvent miscibility table divided by 2 (see Table III), which was equal to 36. In addition, if the antisolvent systems (i.e., binary miscible mixtures of a good and a bad solvent) also were considered, the form space of the antisolvent systems was calculated as the number of green boxes in the solvent miscibility table divided by 2 (see Table III); this value was 109.

Table III. Solvent miscibility table, cosolvent, and antisolvent systems of (R,S)-(6)-sodium ibuprofen dihydrate.

Consequently, the total form space should then be at least equal to 9 + 36 + 109 =154. The total form space is expected to expand dramatically if various solvent compositions of binary mixtures, temperatures, and ternary solvent systems also are considered. Solid generation by temperature cooling only was applied in the yellow regions, yet the same crystallization mode could be applied to the blue regions in the solvent-miscibility table (see Table III). For the green regions (see Table III), solid generation is achieved isothermally by adding an antisolvent. Generally, no attempts are made for solid generation in the regions of immiscible solvent pairs (represented by the purple boxes), bad solvents (represented by the red boxes), and cosolvents of bad solvents (i.e., binary mixture of miscible bad solvents) (represented by the white boxes) in the solvent miscibility table (see Table III). References of other miscible solvents pairs from organic solvents other than the 23 solvents listed in Table III are available in the literature (19, 20).

When the positions of the 23 solvents were located within the 3-D space of a dispersion-force component (δ_d), a polar component (δ_p), and a hydrogen-bonding component (δ_h) according to their corresponding coordinates of (δ_d, δ_p, δ_h, ) in Table I and all the good solvents were represented by yellow and bad solvents by red in the form space (see Table III), a cluster of yellow domains were formed. The contour of these yellow domains outlined a 3-D volume of solubility in space. Good solvents were those solvents within the volume, bad solvents were solvents outside the volume (see Figure 5). This space could be represented by a solubility sphere with center coordinates (δ_d,API, δ_p,API, δ_h,API) and interaction radius (RS-API), for (R, S)-(±)-sodium ibuprofen dihydrate in the 3-D Hansen plot.

Figure 5

By trial and error, the center coordinates (δ_d,API, δ_p,API, δ_h,API) were determined using the following (15):

in which D_S–API was the distance between the solvent location and the center of the sphere. For the 23 solvents listed in Table I with their corresponding sets of Hansen parameters (δ_d,s, δ_p,s, δ_h,s ), 23 D_S–API would result for any chosen set of center coordinates (δ_d,API, δ_p,API, δ_h,API). Only one particular set of center coordinates of (δ_d,API, δ_p,API, δ_h,API) giving 9 D_S–API values for nine corresponding good solvents that were < the 14 D_{S–API values} calculated from the 14 bad solvents. The largest value among the nine D_S–API values was the interaction radius of the solubility sphere. For (R, S)-(±)-sodium ibuprofen dihydrate at 25 °C, the values of δ_d,API, δ_p,API, δ_h,API, and R_S–API with respect to the 23 solvents listed in Table I were determined to be 19.89, 16.19, 30.89 and 25.92 MPa^1/2, respectively (21, 22).

Figure 6

To verify the solubility sphere, the D_S–API values of n-propanol and cyclohexane were calculated using Equation 4. They were 18.18 and 35.24 MPa^1/2, respectively indicating that n-propanol was inside the solubility sphere (18.18 MPa^1/2 < 25.92 MPa^1/2 ), but cyclohexane was outside (35.24 MPa^1/2 > 25.92 MPa^1/2 ). These calculations agreed with the experimental observations that (R, S)-(±)-sodium ibuprofen dihydrate dissolved well in n-propanol at 25 °C with a solubility of 53 mg/mL but dissolved poorly in cyclohexane at 25 °C with a solubility < 0.27 mg/mL.

Table IV: Enthalpy of dehydration, enthalpy of melting, and crystallinity of (R, S)-(6)-sodium ibuprofen dihydrate produced from seven of nine solvents arranged by the total ascending Hildebrand values.

Solids generated from all nine good solvents were isolated and analyzed with DCS, TGA, and PXRD. Solids, however, grown from benzyl alcohol and DMSO (two solvents with high-boiling points) were still wet after oven-drying in air at 40 °C for 4 h and formed solvates with ill-defined DSC and TGA results. Only seven of nine solids could be represented by a typical DSC response of solids generated from water (see Figure 6). The wide-base endotherm from 50–100 °C as supported by the boiling point of water and an approximately 13% weight loss in Figure 2 was corresponded to the enthalpy of dehydration. The enthalpies of dehydration (ΔH_dehydration) of seven solvents are summarized in Table IV. The enthalpies of dehydration were 6.6–12.2 kcal/mol of water loss (23).

Figure 7

Based on the similar DSC response (see Figure 6) and weight-loss pattern (see Figure 2) for all solids grown from THF, n-butyl alcohol, IPA, DMF, ethanol, methanol, and water, only one pseudopolymorph was identified for (R, S)-(±)-sodium ibuprofen dihydrate. The typical DSC response (see Figure 6) showed that the chemically bonded water molecules sandwiched between a layer of all (R)-(±)-sodium ibuprofen molecules (R-layer) and a layer of all (S)-(–)-sodium ibuprofen molecules (S-layer) in the racemic (R, S)-(±)-sodium ibuprofen dihydrate compound were completely removed near 100 °C (see Figure 2) (12).

Figure 8

An endothermic solid–solid transformation with structural editing from a racemic compound to an anhydrous racemic conglomerate started to take place as indicated by the many small peaks from 100–190 °C because the enthalpies of fusion of S–S or R–R interactions (10.49 kcal/mol) were higher than those of R–S interactions (8.71 kcal/mol) (24). As the temperature increased, the anhydrous (R, S)-(±)-sodium ibuprofen eventually melted into liquid around 200 °C . The sandwiched layer of water in the racemic (R, S)-(±)-sodium ibuprofen dihydrate also was completely removed by vacuum-drying either at 40 °C for 4 h or at 90 °C for 2 h (see Figure 7) (24). The DSC scan of an anhydrous sodium ibuprofen obtained by vacuum-drying either at 40 °C for 4 h or at 90 °C for 2 h exhibited a hump from 50–90 °C (see Figure 7), indicating an endothermic, ongoing diffusive restructuring of the R–S packing to form a higher energy state of the S–S or R–R packing that had not been completely finished during the annealing period at 40 °C for 4 h or 90 °C for 2 h under vacuum.

Figure 9

A typical PXRD diffractograph of (R, S)-(±)-ibuprofen dihydrate solids grown from water and oven-dried at 40 °C for 4 h in air is shown in Figure 8. A SEM micrograph (see Figure 9) showed when the water molecules of racemic (R, S)-(±)-sodium ibuprofen dihydrate partially were removed under the high vacuum inside the SEM chamber, the R-layer and the S-layer stacked in the [001] direction were unzipped like a zipper in the [100] direction as seen in Figure 10, which was redrawn (12) by computer software (Diamond 3.1, Crystal Impact GbR, Brandenberg Germany). The authors believe the tiny elongated pores of the anhydrous sodium ibuprofen gave rise to its hygroscopic nature.

Figure 10

Crystallinity of all crystals harvested from solvent screening was approximated using the following relationship (13, 25):

All of the DSC endotherms (melting peaks) for racemic (R, S)-(±)-sodium ibuprofen dihydrate crystals produced from seven of nine good solvents and oven-dried at 40 °C for 4 h in air were compared with the DSC endotherm for racemic (R, S)-(±)-sodium ibuprofen dihydrate crystals grown from methanol with the highest heat of melting of 54.95 J/g near 200 °C as a standard. These results are summarized in Table IV.

Figure 11

The crystal habit and aspect ratio of length-to-breath of (R, S)-(±)-sodium ibuprofen dihydrate crystals produced from the nine pure solvents are shown in Figure 11. Most of the crystals grown from THF, n-butyl alcohol, IPA, benzyl alcohol, ethanol, methanol, and water were hexagonal plates. There was a strong correlation between high values of the polar component (δ_p) and the aspect ratio of crystals. For polar aprotic good solvents such as DMF and DMSO, high δ_p might have induced the rapid growth of polar (001) faces containing sodium ions and carboxylic groups (12, 26) in the [010] direction to form long needles rather than two-dimensional plates as verified by the SEM micrograph showing the (001) faces without the sandwiched layers as the major (010) planes (see Figures 10 and 12). The hexagonal plate and rod-like crystal habits grown from the nine pure solvents were all plotted against the Hansen parameters in Figure 13. To test the predictability of the 3-D Hansen plot (see Figure 13), (R, S)-(±)-sodium ibuprofen dihydrate was grown in another polar aprotic solvent, acetonitrile with a high δ_p of 18 MPa^1/2. Needle-shape crystals were produced as expected (see Figure 14).

Figure 12

Conclusion

Useful scale-up and drug development data of solubility, polymorphism, crystallinity, crystal habit, and drying schemes of (R, S)-(±)-sodium ibuprofen dihydrate crystals were generated by the initial solvent-screening method. Solubility data were processed and treated with the van't Hoff equation, form space, and solubility sphere. The dependency of crystal habits on solvents and drying schemes were derived using optical microscopy and scanning electron microscopy. The relationships between crystal habits and microscopic properties of solvents were plotted by a 3-D Hansen model. In principle, the initial solvent-screening strategy can be readily extended to and integrated with food, explosives, optoelectronics, agricultural, and ceramics products.

Figure 13

Acknowledgment

This work was supported by a grant from the National Science Council of Taiwan, Republic of China (NSC 95-2113-M-008-012-MY2). Assistance from Ling-I Hung, PhD, postdoctoral, at the Solid-State Inorganic Chemistry Laboratory on Diamond 3.1 computer software, suggestions from Jui-Mei Huang in differential scanning calorimetry and thermal gravimetric analysis, and Shew-Jen Weng in X-ray diffraction, all with the Precision Instrument Center at the National Central University gratefully are acknowledged.

Figure 14

Tu Lee,* PhD, is an assistant professor at the Department of Chemical and Materials Engineering and the Institute of Materials Science and Engineering, National Central University, 300 Jhong-Da Rd, Jhong-Li City 320, Taiwan, Republic of China tel. + 886-3-422-7151, ext. 34204, fax + 886-3-425-2296, tulee@cc.ncu.edu.twYing Hsiu Chen and Chyong Wen Zhang are graduate students, the Department of Chemical and Materials Engineering, National Central University.

*To whom all correspondence should be addressed.

Submitted: Dec. 11, 2006. Accepted:Jan. 24, 2007.

Key words: form space, Hansen model, racemic (R,S)-(±) sodium ibuprofen dihydrate, solubility sphere

References

1. B. J. Armitage, J. F. Lampard, and A. Smith, "Composition of S-Sodium Ibuprofen," US Patent 6,242,000 B1 (2001).

2. A. Gracin and A.C. Rasmuson, "Solubility of Phenylacetic Acid, P-hydroxyphenylacetic Acid, P-aminophenylacetic acid, P-hydroxybenzoic acid, and Ibuprofen in Pure Solvents," J. Chem. Eng. Data 47 (6), 1379–1383 (2002).

3. N. Rasenack and B. W. Müller. "Properties of Ibuprofen Crystallized under Various Conditions: A Comparative Study," Drug Dev. Ind. Pharm. 28 (9), 1077–1089 (2002).

4. P. D. Martino et al., "Influence of Crystal Habit on the Compression and the Densification Mechanism of Ibuprofen," J. Crys. Growth 243 (2), 345–355 (2002).

5. H. Cano, N. Gabas, and J. P. Canselier, "Experimental Study on the Ibuprofen Crystal Growth Morphoplogy in Solution," J. Cryst. Growth 224 (3-4), 335–341 (2001).

6. L. C. Garzón and F. Martínez, "Temperature Dependence of Solubility for Ibuprofen in Some Organic and Aqueous Solvents," J. Solution Chem. 33 (11), 1379–1395 (2004).

7. A.J. Romero, L. Savastano, and C.T. Rhodes. "Monitoring Crystal Modifications in Systems Containing Ibuprofen," Int. J. Pharm. 99 (2–3), 125–134 (1993).

8. A.J. Romeo and C. T. Rhodes, "Approaches to Stereospecific Preformulation of Ibuprofen," Drug Dev. Ind. Pharm. 33 (5), 777–792 (1991).

9. K. Skankland et al., "Structure Solution of Ibuprofen from Powder Diffraction Data by the Application of a Generic Algorithm Combined with Prior Conformational Analysis," Int. J. Pharm. 165 (1), 117–126 (1998).

10. G.L. Perlovich et al., "Thermodynamics of Sublimation, Crystal Lattice Energies, and Crystal Structures of Racemates and Enantiomers: (+)- and (±)-Ibuprofen," J. Pharm. Sci. 93 (3), 654–666 (2004).

11. A.H. Nada, S.M. Al-Saidan, and B.W. Mueller. "Improving the Physical and Chemical Properties of Ibuprofen," Pharm. Technol. 29 (11): 90–101 (2005).

12. Y. Zhang and D.J.W. Grant. "Similarity in Structures of Racemic and Enantiomeric Ibuprofen Sodium Dihydrates," Acta Cryst. C61 (9), m435–m438 (2005).

13. T. Lee, C. S. Kuo, and Y.H. Chen, "Solubility, Polymorphism, Crystallinity, and Crystal Habit of Acetaminophen and Ibuprofen," Pharm. Technol. 30 (10), 72–92 (2006).

14. L. Yu, S.M. Reutzel, and GA. Stephenson, "Physical Characterization of Polymorphic Drugs: An Integrated Characterization Strategy," Pharm. Sci. Tech. Today 1 (3), 118–127 (1998).

15. J. Burke, "Solubility Parameters: Theory and Application," as in Book and Paper Group Annual (The American Institute for Conservation, Vol. 3, 1984), http://aic.stanford.edu/sg/bpg/annual/v03/bp03-04.html, accessed Apr. 9, 2007.

16. I. Katzhendler, K. Mäder, and M. Friedman, "Structure and Hydration Properties of Hydroxypropyl Methylcellulose Matrices Containing Naproxen and Naproxen Sodium," Int. J. Pharm. 200 (2), 161–179 (2000).

17. R.A. Granberg and A.C. Rasmuson, "Solubility of Paracetamol in Binary and Ternary Mixtures of Water + Acetone + Toluene," J. Chem. Eng. Data 45 (3), 478–483 (2000).

18. L. Peterson et al., "Interactive High-Throughput Polymorphism Studies on Acetaminophen and An experimentally Derived Structure for Form III," J. Am. Chem. Soc. 124 (37), 10958–10959 (2002).

19. J.S. Drury, "Miscibility of Organic Solvent Pairs," Ind. Eng. Chem. 44 (11), 2744 (1952).

20. W.M. Jackson and J. S. Drury, "Miscibility of Organic Solvent Pairs," Ind. Eng. Chem. 51 (12), 1491–1493 (1959).

21. P. Bustamante, M.A. Pena, and J. Barra, "The Modified Extended Hansen Method to Determine Partial Solubility Parameters of Drugs Containing a Single Hydrogen Bonding Group and their Sodium Derivatives: Benzoic Acid/Na and Ibuprofen/Na," Int. J. Pharm. 194 (1), 117–124 (2000).

22. W.L. Archer, "Hansen Solubility Parameters for Selected Cellulose Ether Derivatives and Their Use in the Pharmaceutical Industry," Drug Dev. Ind. Pharm. 18 (5), 599–616 (1992).

23. L.R. Chen, and D.J W. Grant, "Extension of Clausius-Clapeyron Equation to Predict Hydrate Stability at Different Temperature," Pharm. Dev. Tech. 3 (4), 487–494 (1988).

24. G.G.Z. Zhang et al., "Racemic Species of Sodium Ibuprofen: Characterization and Polymorphic Relationships," J. Pharm. Sci. 92 (7), 1356–1366 (2003).

25. P.J. Haines, "Differential Thermal Analysis and Differential Scanning Calorimetry," in Thermal Methods of Analysis: Principles, Applications and Problems (Blackie Academic & Professional, New York, 1997), p.28.

26. J.M.E. Bunyan, N. Shankland, and D.B. Sheen, "Solvent Effects on the Morphology of Ibuprofen," AIChE Symp. Ser. 87 (284), 44–57 (1991).