Sodium Ibuprofen Dihydrate on the Crystallization Kinetics of

Effects of Homochiral Molecules of (S)-(+)-Ibuprofen and (S)-(-)-Sodium Ibuprofen Dihydrate on the Crystallization Kinetics of Racemic (R,S)-(()-Sodium Ibuprofen Dihydrate Tu Lee,*,†,‡ Ying Hsiu Chen,† and Yeh Wen Wang†

CRYSTAL GROWTH & DESIGN 2008 VOL. 8, NO. 2 415–426

Department of Chemical & Materials Engineering and Institute of Materials Science & Engineering, National Central UniVersity, 300 Jhong-Da Road, Jhong-Li City 320, Taiwan, R.O.C. ReceiVed January 16, 2007; ReVised Manuscript ReceiVed NoVember 5, 2007

ABSTRACT: The aim of this paper is to identify the effects of homochiral molecules such as (S)-(+)-ibuprofen and (S)-(-)sodium ibuprofen dihydrate on the crystallization kinetics: the induction period, the crystal growth rate, and the end point of the racemic compound of (R,S)-(()-sodium ibuprofen dihydrate. Crystallization kinetics of racemic species of sodium ibuprofen dihydrate in the presence of small amounts of homochiral parent molecules of (S)-(+)-ibuprofen and its constituent enantiomers (S)-(-)sodium ibuprofen dihydrate were studied by electrical conductance, optical microscopy, differential scanning calorimetry, and wideangle powder X-ray diffraction. Racemic (R,S)-(()-sodium ibuprofen dihydrate with self-association property was sensitive to processing history and deserved a tight control for reproducibility on scale-up. Crystals grown from a racemic water-acetone solution of sodium ibuprofen dihydrate and vaccuum-dried at 90 °C for 4 h produced racemic species of R-form racemic compounds and γ-form racemic conglomerates having a R:S w/w ratio of about 45:55 (enantiomeric excess of the solids, ee ) 10% in S) by the addition of no additives, and 0.02 g of (S)-(+)-ibuprofen or 0.02 g of (S)-(-)-sodium ibuprofen, respectively. Fundamental parameters of the crystallization kinetics of racemic species of sodium ibuprofen dihydrate such as the induction time, τ; the interfacial energy, γ; the Gibbs energetic barrier, ∆G cr; the nucleation rate, J; the critical size of stable nuclei, rc; the crystal mass growth rate, RG; the power number, g; and the end point were evaluated with different initial supersaturation ratios, S0, and compared. In general, τ, ∆G cr, and rc decreased and J increased when S0 increased or homochiral additives were added. γ decreased in the presence of homochiral additives. RG increased as S0 increased in the presence of (S)-(+)-ibuprofen. g ranged from 0.5 to 1.7. The end point decreased in the presence of additives or with the increase in S0. At high S0, the effects of homochiral additives on the induction period, the crystal growth rate and the end point became to diminish. Adoption of such inexpensive, simple, and robust methods as electrical conductance, optical microscopy, and differential scanning calorimetry in common research laboratories offers the opportunity to the pharmaceutical industry to lower manufacturing cycle times and end product variability in a crystallization process that would result in shorter time to market and a reduced likelihood of drug product failures. The addition of configurationally similar homochiral molecules such as the parent acid or the same constituent enantiomer to the racemic solution may have opened a new doorway for the generation of racemic species that cannot be obtained by the addition of other impurities. Introduction Crystallization is the self-assembly and self-recognition of atoms, ions, and molecules being packed precisely in a longrange 3D order under the orchestration of intermolecular forces. Consequently, crystallization is an important process of separation and purification, for example, for the recovery of pharmaceutical products. Generally, the dynamic event of crystallization comprises three evolving stages of supersaturation, nucleation, and crystal growth.1,2 Degraded products, byproduct, and additives in the solution are known to interfere with nucleation and the crystal growth process of the solute through (1) the alteration of the equilibrium solubility of the solute and the solution-solid interfacial energy, (2) the Langmuir adsorption of additives on the crystal surfaces, and (3) the incorporation of impurities into the crystal lattice.1,3–10 These seemingly undesirable effects of foreign molecules actually have become the key working principle of the asymmetric crystallization method in which an external chiral additive, S′, is added to a supersaturated racemic (R + S) solution to delay the crystallization of one of the enantiomers, S. By so doing, a kinetic resolution of racemic * Corresponding author. Telephone: 886-3-422-7151ext. 34204. Fax: 8863-425-2296. E-mail: [email protected]. † Department of Chemical & Materials Engineering, National Central University. ‡ Institute of Materials Science & Engineering, National Central University.

crystals into their constituent enantiomers is made possible.9,11–13 Therefore, the chiral symmetry breaking has profound implications in the origin of homochirality on earth,14 biomineralization,15 and industrial processes.16 However, little attention has been paid to the effects of adding a relatively small amount of one of the same constituent enantiomers, S, or the enantiomers’ parent molecules, SP, to the supersaturated racemic (R + S) solution as free molecules rather than as enantiopure crystal seeds.17 Because the avoidance of introducing any foreign impurities to the development of active pharmaceutical ingredients (APIs) is always the concern of the pharmaceutical industry,18,19 the aim of this paper is to identify the effects of homochiral molecules such as (S)-(-)sodium ibuprofen dihydrate (S) (Figure 1a) and its parent acid (S)-(+)-ibuprofen (SP) (Figure 1b) on the crystallization kinetics of racemic compound of (R,S)-(()-sodium ibuprofen dihydrate (R + S) (Figure 1c) by the classical nucleation theory so that the optimization of the existing process operations and the development of new processes for new products could be made. All of the agents used are pharmaceutically active in this case and can serve as the precursors for one another. None of them are considered as unwanted chemicals. A sodium salt of a well-known racemic active pharmaceutical ingredient (API), (R,S)-(()-ibuprofen ((R,S)-(()-2-(4-isobutylphenyl)propionic acid) was chosen as a model system because of its parent acid (R,S)-(()-ibuprofen’s worldwide commercial

10.1021/cg070045c CCC: $40.75  2008 American Chemical Society Published on Web 12/14/2007

416 Crystal Growth & Design, Vol. 8, No. 2, 2008

Figure 1. Molecular structure of (a) (S)-(-)-sodium ibuprofen dihydrate, (b) (S)-(+)-ibuprofen, and (c) (R,S)-(()-sodium ibuprofen dihydrate.

values in analgesic, anti-inflammatory, and antipyretic therapy20 and (2) its abundant information in the literature.21–33 It is known that (S)-(+)-ibuprofen is the active agent and (R)-(-)-ibuprofen is partially converted into (S)-(+)-ibuprofen in humans. Therefore, ibuprofen is marketed as a racemic compound. However, (R,S)-(()-ibuprofen has disadvantageous formulation properties of poor water solubility of less than 1 mg/mL at 25 °C, low melting point of 77 °C, and possible esterification with excipients containing a hydroxyl group. These problems can be easily overcome by the use of racemic (R,S)-(()-sodium 2-(4isobutylphenyl)propionate dihydrate ((R,S)-(()-sodium ibuprofen dihydrate)34,35 whose potential values over (R,S)-(()ibuprofen has made the studies of its crystallization kinetics more meaningful. Interestingly, racemic (R/S)-(()-sodium ibuprofen dihydrate amphiphilic molecules self-aggregate in water above a critical micelle concentration (CMC) of 0.18 M at 25 °C.36 The conductivity nature of the racemic solution of sodium ibuprofen dihydrate in the presence of water has made the study of its crystallization kinetics easily be monitored by the sensitive in-line electrical conductance.37 This simple, inexpensive, in situ analytical method if combined with optical microscopy, differential scanning calorimetry, and powder X-ray diffraction could have provided valuable understanding and control of crystallization process no less than other costly process analytical technology (PAT).38 Materials and Methods Solvents. Acetone (CH3COCH3, HPLC/Spectro grade, 99.5%, bp: 56 °C, MW ) 58.08, Lot.: 411050) and reversible osmosis (RO) water was clarified by a water purification system (model Milli-RO Plus) bought from Millipore (Billerica, MA). Active Pharmaceutical Ingredients. Ibuprofen sodium salt (C13H17NaO2, MW ) 228.29, batch 085K0716) purchased from SigmaAldrich (St. Louis, MO) actually was racemic (R,S)-(()-sodium-2-(4isobutylphenyl)propionate dihydrate with a molecular formula of

Lee et al. C13H17NaO2 · 2H2O and MW ) 264.29 as determined by the thermogravimetric use test of about 12.8 wt % water loss near the boiling point of water. (S)-(+)-ibuprofen (C13H18O2, MW ) 206.3, batch 10608BI) was R-methyl-4-(2-methylpropyl)-benzeneacetic acid. It was directly purchased from Sigma-Aldrich (St. Louis, MO). (S)-(-)-sodium ibuprofen dihydrate was synthesized in house by the neutralization of sodium hydroxide (NaOH, MW ) 40.00, batch SP2631W) purchased from Showa (Tokyo, Japan) and an equimolar amount of solid (S)-(+)-ibuprofen.39 NaOH (0.2 g) was dissolved in 0.7 mL of distilled water. The basic aqueous solution was slowly added to the solution of (S)-(+)-ibuprofen (1.03 g) in acetone (6 mL) at 25 °C. The mixture was stirred for 30 min and precipitation occurred. The slurry was cooled to 5 °C for 30 min and the solids were collected by filtration, air-dried at 25 °C to give (S)-(-)-sodium ibuprofen dihydrate, and characterized by differential scanning calorimetry and thermal gravimetric analysis. Instrumentations. Electrical Conductance. An electrical conductivity meter (CONSORT K611, Conductivity Instruments, Turnhout, Belgium) was used to monitor the conductivity of the 325 mL wateracetone racemic solution of (R,S)-(()-sodium ibuprofen dihydrate during crystallization as a function of time. The instrument was calibrated with 0.01 M of KCl each time before use with an extrapolated conductivity of 1413 µS at 25 °C. Differential Scanning Calorimetry (DSC). DSC analysis was used to identify the solid–liquid (melting) or solid–solid transformation temperature. Thermal analytical data of 3-5 mg samples in perforated aluminum sample pans (25 µL) were collected on a Perkin-Elmer DSC-7 calorimeter (Perkin-Elmer Instruments LLC, Shelton, CT) with a temperature scanning rate of 10 °C/min from 50 to 200 °C under a constant nitrogen 99.990% purge. The instrument was calibrated with indium 99.999% (Perkin-Elmer Instruments LLC, Shelton, CT). Powder X-ray Diffraction (PXRD). PXRD patterns were obtained from samples using a wide-angle powder X-ray diffractometer (model D/Max-IIB, Rigaku Co., Tokyo, Japan). X-ray radiation CuK R1 (λ ) 1.5405Å) was set at 30 kV and 20 mA passing through a nickel filter with divergence slit (0.5°), scattering slit (0.5°), and receiving slit (1 mm). Samples were subjected to X-ray powder diffraction analysis with a sampling width of 0.01° in a continuous mode with a scanning rate of 1°/min over an angular range of 2-35° 2θ. Scanning Electron Microscopy (SEM). A scanning electron microscope (SEM) (Hitachi S-3500N, Tokyo, Japan) was used to observe the morphology of the crystals. Both secondary electron imaging (SEI) and backscattered electron imaging (BEI) were used for the SEM detector and the magnification was 15 to 300 000-fold. The operating pressure was 1 × 10-5 Pa vacuum and the voltage was 15.0 kV. All samples were mounted on a carbon conductive tape (Prod. 16073, TED Pella Inc., CA) and then sputter-coated with gold (Hitachi E-1010 Ion Spotter, Tokyo, Japan) with a thickness of about 6 nm. The discharge current used was about 0-30 mA and the vacuum was around 1 × 10 Pa. Optical Microscopy (OM). Crystal habits were examined and measured by an Olympus SZII Zoom Stereo Microscope (Olympus, Tokyo, Japan) equipped with a Sony SSC-DC 50A digital color video camera (Sony Corporation, Tokyo, Japan). Experiments. Recrystallization of racemic (R,S)-(()-sodium ibuprofen dihydrate was carried out in a three-neck, round-bottom flask with a working volume of 350 cm3 by an antisolvent method. The round-bottom flask was immersed in a water bath at 25 °C for all times. A known amount of racemic (R,S)-(()-sodium ibuprofen dihydrate was first dissolved in 20 mL of water. To ensure a complete dissolution and to eliminate the invisible seeds, the 20 mL unsaturated aqueous solution of racemic (R,S)-(()-sodium ibuprofen dihydrate was warmed to 35 °C for 30 min. It was then cooled back down to 25 °C while being stirred by a magnetic spin bar for 1 h. To provide a batch precipitation, we rapidly introduced 315 mL of acetone into the flask as an antisolvent. The electrical conductance of the resultant solution was then monitored as a function of time. All experiments were run for at least twice to test for reproducibility. To study the effects of (S)-(+)-ibuprofen on the crystallization kinetics, we premixed 0.02 g of (S)-(+)-ibuprofen with the 315 mL of acetone. The acetone solution was stirred at 250 rpm for 1 h at 25 °C before it was introduced to the racemic solution as an antisolvent. To study the effects of (S)-(-)-sodium ibuprofen dihydrate on the crystallization kinetics, we premixed 0.02 g of (S)-(-)-sodium ibuprofen

Kinetics of Racemic (R,S)-(()-Sodium Ibuprofen Dihydrate

Figure 2. Calibration of the electrical conductance vs the concentration of the 325 mL acetone–water racemic solution of sodium ibuprofen dihydrate at T ) 25 °C with a linear fit of y ) 7369.52x + 195.93 with the value of the correlation coefficient of 0.96.

Figure 3. Experimental Z-shaped curves of the concentration of an acetone–water racemic solution of pure sodium ibuprofen dihydrate vs time and the calculated S-shaped curves of the crystal mass growth vs time at T ) 25 °C with initial supersaturation ratios of (a) S0 ) 1.17, (b) S0 ) 1.19, (c) S0 ) 1.25, and (d) S0 ) 1.30. dihydrate with the 20 mL aqueous solution of racemic (R,S)-(()-sodium ibuprofen dihydrate right at the beginning. The total volume of 20 mL of water + 315 mL of acetone gave 325 mL of water-acetone solution. Because the solubility of racemic (R,S)(()-sodium ibuprofen dihydrate in the water-acetone solution was 5.18 mg/mL at 25 °C, 1.98, 2.0, 2.1, and 2.2 g of racemic (R,S)-(()-sodium ibuprofen dihydrate were used for the preparation of the initial supersaturation ratios, S0, of 1.17, 1.19, 1.25, and 1.30, respectively, in 325 mL of water-acetone solution.

Results and Discussion The electrical conductance of the water-acetone solution containing racemic sodium ibuprofen dihydrate was linearly proportional to the concentration of the dissolved racemic sodium ibuprofen dihydrate in the solution (Figure 2). In general, experimental curves of concentration versus time obtained in the batch system during crystallization exhibited a typical Z shape with three consecutive stages (Figures 3-5). At the beginning, the concentration of the solution was constant for a certain period of time, namely, the induction period of crystallization. The concentration of the solution, C, then dropped

Crystal Growth & Design, Vol. 8, No. 2, 2008 417

Figure 4. Experimental Z-shaped curves of the concentration of acetone–water racemic solution of sodium ibuprofen dihydrate vs time and the calculated S-shaped curves of the crystal mass growth vs time with the addition of 0.02 g of (S)-(+)-ibuprofen at T ) 25 °C having initial supersaturation ratios of (a) S0 ) 1.17, (b) S0 ) 1.19, (c) S0 ) 1.25, and (d) S0 ) 1.30.

Figure 5. Experimental Z-shaped curves of the concentration of an acetone–water racemic solution of sodium ibuprofen dihydrate vs time and the calculated S-shaped curves of eth crystal mass growth vs time with the addition of 0.02 g of (S)-(-)-sodium ibuprofen dihydrate at T ) 25 °C having initial supersaturation ratios of (a) S0 ) 1.17, (b) S0 ) 1.19, (c) S0 ) 1.25, and (d) S0 ) 1.30.

gradually as the amount of racemic sodium ibuprofen dihydrate was depleted (i.e., desupersaturation) in the mother liquor for the continuous growth of stable nanometer-sized nuclei into crystals. At the end, the concentration was settled at a final equilibrium value of solubility, C*, at 25 °C. Supersaturation and Nucleation. The induction period, τ, is the sum of time needed for the supersaturation reaching the steady-state of the primary nucleation, ttr, the time of primary nucleation, tn, and the time required for the critical nucleus to grow to a detectable crystal size, tg.40 τ ) ttr + tn + tg

(1)

We started measuring the induction time right after the rapid addition of the antisolvent of acetone or acetone solution. The transient period was assumed to be unimportant (ttr ) 0) here in the moderate water-acetone supersaturated solutions with good micromixing. Because of the excellent sensitivity of the electrical conductance, the nucleation time, tn, could be accurately measured as the time period between the creation of the supersaturation and the decrease in the conductivity of solution due to the formation of nuclei.


Lee et al.

4πr2c γ (6) 3 The growth of the clusters governed by the Gibbs-Thompson equation is41,42 ∆Gcr )

Figure 6. ln τ vs (ln S0)-2 plot of (a) pure racemic sodium ibuprofen dihydrate, (b) with the addition of 0.02 g (S)-(+)-ibuprofen, and (c) with the addition of 0.02 g of (S)-(-)-sodium ibuprofen dihydrate.

If the nucleation time, tn, turns out to be much larger than the growth time, tg, the plateau of the Z-shaped desupersaturation curve will appear longer than the shoulder portion near the turning point on the desupersaturation curve. The induction time can then be assumed as mostly the time of primary nucleation that is inversely proportional to the rate of primary nucleation, J. Therefore, τ ) tn ∝ J-1

(2)

The rate of primary nucleation as given by the classical theory assumes that clusters are formed in the solution by an addition mechanism until a critical size is reached. The energy required to form a critical size of cluster in nucleation, ∆Gcr, is analogous to the activation energy in a chemical reaction. It is the difference between the average energy of those molecules that do form the critical cluster size and the average energy of all molecules. Consequently, the rate of primary nucleation has an Arrhenius type of expression40

[

∆Gcr J ) J0 exp kT

]

(3)

in which J0 is the pre-exponential factor, k is the Boltzmann’s constant, and T is the temperature. For homogeneous nucleation, the free-energy change for the formation of the solid phase is the sum of two competing terms: (1) the free-energy change for the formation of the nucleus surface (a positive quantity), and (2) the free-energy change for the phase transformation (a negative quantity). For a spherical nucleus41,42 4 ∆G ) 4πr2γ + πr3∆GV 3

(4)

where r is the radius of a cluster, γ is the solution-solid interfacial energy, and ∆Gν is the free energy change for the phase transformation. Clusters greater than the critical size resulted in a decrease in ∆G and partook in the nucleation process. The critical size, rc, was found by minimizing the freeenergy function of eq 4 with respect to the radius41,42 rc ) -

2γ ∆GV

(5)

Substituting for ∆Gν from eq 5 in eq 4 to solve for ∆G, the energy required to form a critical size of cluster in nucleation, ∆Gcr, in eq 3 is41,42

C0

) ln S0 )

2γυ kTr

(7) C where C0 is the initial bulk concentration of clusters of size r, C* is the concentration of clusters at equilibrium (equilibrium solubility), S0 is the initial supersaturation ratio, and υ is the molecular volume (molecular weight/(density × Avogadro’s number)).43 The C* of racemic (R,S)-(()-sodium ibuprofen dihydrate in the 325 mL water-acetone solution was about 5.18 mg/mL or 0.02 M at 25 °C. Smaller clusters dissolved, whereas larger clusters grew until they reached a critical size, rc, and then a new phase was created. Substituting for rc in eq 6 from eq 7, the energy barrier in eq 3, namely, the free energy difference of the critical 3D nucleus became41,42 ln

/

16πγ3υ2 3(kT ln S0)2

∆Gcr )

(8)

where the term kT ln S0 is the initial chemical potential difference between the solution and the solid phase in an ideal solution.9 Generally, eq 8 is applied to homogeneous nucleation at higher supersaturation ratios. However, it could be adapted to describe heterogeneous nucleation more realistically occurred at a typical laboratory situation.9 Combining eqs 3 and 8, we obtained

[

J ) J0 exp

-16πγ3υ2 3k3T3(ln S0)2

]

(9)

Furthermore, substituting eq 9 into eq 1 and taking the natural logarithm on each side, the equation was reduced to a straight line

[

]

16πγ3υ2 (ln S0)-2 (10) 3k3T3 When a set of ln τ was plotted against a corresponding set of (ln S0)-2 at different time points extracted from the experimental curves of the electrical conductance versus time, the solutionsolid interfacial energy, γ, and the pre-exponential factor, J0, were estimated from the slope and the y-intercept of eq 10, respectively. Once γ was known, ∆Gcr, rc, and then ∆Gν were calculated for a given initial S0 by eqs 8, 6, and 5, respectively. J could simply be calculated by eq 2. Finally, the theoretical number of molecules in the critical nucleus, i*, was approximated from rc43 ln τ ) ln tn ) -ln J0 +

4πr3c (11) 3υ The electrical conductance of all crystallization experiments involving racemic (R,S)-(()-sodium ibuprofen dihydrate in a total volume of 325 mL of water-acetone solution at 25 °C was monitored as a function of time. The three sets of experiments were as follows: (a) without any additives, (b) with the addition of 0.02 g of (S)-(+)-ibuprofen, and (c) with the addition of 0.02 g of (S)-(-)-sodium ibuprofen dihydrate. Each set of experiments contained four different initial supersaturation ratios of S0 ) 1.17, 1.19, 1.25, and 1.30 with C* ) 5.18 mg/ mL or 0.02 M. The electrical conductance of all curves was then converted into the concentration values through the i/ )



Table 1. Tabulated Values of S0, τ, γ, and J0 of the Three Experimental Sets of Recrystallization of the Racemic (R,S)-(()-Sodium Ibuprofen Dihydrate (MW ) 264.29) (a) without Any Additives, (b) with 0.02 g of (S)-(+)-Ibuprofen Additives (MW ) 206.29), and (c) with 0.02 g of (S)-(-)-Sodium Ibuprofen Dihydrate Additives (MW ) 264.29), Having Different Initial Supersaturation Ratios of S0 ) 1.17, 1.19, 1.25, and 1.30 (C* was 5.28 mg/mL or 0.019 mol/L in 325 mL ofacetone–water solution) S0 ) C0/C*

γ (×10-5 J/m2)

τ (min)

J0 (×10-2 nucleus s-1 m-3)

Recrystallization of Racemic (R,S)-(()-Sodium Ibuprofen Dihydrate 28.85 ( 0.3 16.33 ( 0.2 9.32 ( 0.8 5.15 ( 0.2

1.17 1.19 1.25 1.30

125.4 ( 0.2

0.7 ( 0.0

Recrystallization of Racemic (R,S)-(()-Sodium Ibuprofen Dihydrate + 0.02 g of (S)-(+)-Ibuprofen 20.96 ( 0.8 12.16 ( 2.2 7.12 ( 1.5 3.37 ( 0.7

1.17 1.19 1.25 1.30

127.3 ( 3.4

1.0 ( 0.4

Recrystallization of Racemic (R,S)-(()-Sodium Ibuprofen Dihydrate + 0.02 g of (S)-(-)-Sodium Ibuprofen Dihydrate 8.25 ( 0.6 3.45 ( 0.5 3.35 ( 0.0 2.82 ( 0.0

1.17 1.19 1.25 1.30

100.7 ( 5.1

1.0 ( 0.1

Table 2. Tabulated Values of S0, ∆Gν, ∆Gcr, J, rc, and i* of the Three Experimental Sets of Recrystallization of the Racemic (R,S)-(()-sodium Ibuprofen Dihydrate (MW ) 264.29) (a) without Any Additives, (b) with 0.02 g of (S)-(+)-Ibuprofen Additives (MW ) 206.29), and (c) with 0.02 g of (S)-(-)-Sodium Ibuprofen Dihydrate Additives (MW ) 264.29), Having Different Initial Supersaturation Ratios of S0 ) 1.17, 1.19, 1.25, and 1.30 (C* was 5.28 mg/mL or 0.019 mol/L in 325 mL of acetone–water solution) S0 ) C0/C*

∆Gν (×105 J/m3)

∆Gcr (×10-22 J)

J (×10-5 nucleus s-1 m-)

rc (×10-10 m)

i*

13.9 ( 0.1 13.0 ( 0.0 10.1 ( 0.0 8.4 ( 0.0

30.6 ( 0.1 25.5 ( 0.1 12.0 ( 0.1 6.7 ( 0.0

Recrystallization of Racemic (R,S)-(()-Sodium Ibuprofen Dihydrate 1.17 1.19 1.25 1.30

-18.1 -19.2 -24.7 -30.0

101.0 ( 0.4 89.5 ( 0.4 54.1 ( 0.2 36.8 ( 0.2

57.76 ( 0.5 102.09 ( 1.1 178.83 ( 15.8 323.94 ( 12.9

Recrystallization of Racemic (R,S)-(()-Sodium Ibuprofen Dihydrate + 0.02 g of (S)-(+)-Ibuprofen 1.17 1.19 1.25 1.30 1.17 1.19 1.25 1.30

-18.1 105.5 ( 8.5 79.52 ( 2.9 -19.2 93.4 ( 7.5 137.06 ( 25.0 -24.7 56.5 ( 4.5 234.25 ( 49.7 -30.0 38.5 ( 3.1 495.29 ( 100.9 Recrystallization of Racemic (R,S)-(()-Sodium Ibuprofen Dihydrate + 0.02 g of (S)-(-)-Sodium -18.1 52.2 ( 8.0 202.02 ( 15.6 -19.2 46.3 ( 7.1 483.09 ( 70.0 -24.7 28.0 ( 4.3 497.51 ( 3.9 -30.0 19.0 ( 2.9 592.07 ( 4.5

calibration curve in Figure 2 and transformed into the concentration versus time curves (i.e., desupersaturation curves) as illustrated in Figures 3-5, respectively. In each set of experiments, the four different induction times were plotted against the four corresponding initial supersaturation ratios in a fashion of ln τ vs (ln S0)-2 in Figure 6. γ and J0 could then be estimated directly from the slope and y-intercept, respectively, from Figure 6 according to eq 10 (Table 1). ∆Gν, ∆Gcr, J, rc, and i* could then be derived from γ and J0 (Table 2). In general, a short induction period, τ, is a result of a rapid nucleation rate (eq 2) achieved by lowering the Gibbs energy barrier of forming clusters with a critical size (eq 3). For example, the relatively short induction periods in Figure 5 compared with those in Figures 3 and 4 indicated that solutions doped with 0.02 g (S)-(-)-sodium ibuprofen dihydrate had the highest J value and the lowest ∆Gcr at any given initial S0 compared with the other two sets of experiments in Table 2. If both temperature T and the initial supersaturation ratio S0 are constant, the lower the solution-solid interfacial energy, γ, (eq 8), the smaller is the radius of the nucleus rc required for survival (eq 6), and thus the rate of nucleation J increases (eq 9) (Tables 1 and 2).10 In the case of T ) 25 °C and S0 ) 1.17 in Table 1, the lowest value of γ ) 100.7 ( 5.1 × 10-5 J/m2 under the condition of doping with 0.02 g (S)-(-)-sodium ibuprofen dihydrate made the survival of nuclei with the smallest rc )

14.1 ( 0.4 13.2 ( 0.4 10.3 ( 0.3 8.5 ( 0.3 Ibuprofen Dihydrate 11.1 ( 0.6 10.5 ( 0.6 8.1 ( 0.4 6.7 ( 0.4

31.9 ( 2.5 26.6 ( 2.2 12.5 ( 1.0 7.0 ( 0.6 15.8 ( 2.4 13.2 ( 2.1 6.2 ( 0.9 3.5 ( 0.6

11.1 ( 0.6 × 10-10 m possible as opposed to rc ) 14.1 ( 0.4 × 10-10 m and 13.9 ( 0.1 × 10-10 m for the conditions with and without the doping of 0.02 g (S)-(+)-ibuprofen, respectively. All estimated γ at 25 °C in Table 1 had comparable values as the ones for ampicilla3 of 5.83 mJ/m2, phenylbutazone44 of 5.65 mJ/m2, m-nitroaniline43 of 4.55 mJ/m2, and urea45 of 1.30 mJ/ m2. All rc values seemed to be reasonable because the unit-cell dimensions of (R,S)-(()-sodium ibuprofen dihydrate were in the range of 5.7-23.9 Å.35 Because it would have taken the shortest time for the formation of the smallest radius size, its nucleation rate must then be the fastest. Referring to the cases of T ) 25 °C and S0 ) 1.17 again, J ) 202.02 ( 15.6 × 10-5 nuclei m-3 s-1 was the fastest with the doping of 0.02 g (S)(-)-sodium ibuprofen dihydrate, compared with J ) 79.52 ( 2.9 × 10-5 nuclei m-3 s-1 and J ) 57.76 ( 0.5 × 10-5 nuclei m-3 s-1 with and without the doping of 0.02 g (S)-(+)-ibuprofen respectively. In general, the nucleation rate J increases as the critical Gibbs energy barrier ∆Gcr decreases when the initial supersaturation ratios S0 increase. The relatively fast nucleation rate J is the consequence of the formation of clusters with a small critical size rc. Unlike the effects of most impurities, the addition of (S)(-)-sodium ibuprofen dihydrate and (S)-(+)-ibuprofen to the water-acetone supersaturated solution filled with clusters of racemic sodium ibuprofen dihydrate of different sizes had


Lee et al.

Figure 9. SEM image of a typical racemic (R,S)-(()-sodium ibuprofen dihydrate crystalline particle grown in 20 mL of water + 315 mL of acetone at T ) 25 °C with thin layering structures, growing islands, and terraces, suggesting a 2D surface nucleation by a birth and spread mechanism (white arrows) (scale bar ) 10 µm).

Figure 7. Critical micelle concentration of racemic sodium ibuprofen dihydrate was determined to be the turning point C of the conductivity vs concentration curve in (a) water at 0.17 M at 25 °C, and (b) a 20 mL of water + 315 mL of acetone solution at 0.01 M at 25 °C.

Figure 10. RG vs ln St plot for the crystal growth of racemic (R,S)(()-sodium ibuprofen dihydrate without any additives at T ) 25 °C and initial supersaturation ratios of (a) S0 ) 1.17, (b) S0 ) 1.19, (c) S0 ) 1.25, and (d) S0 ) 1.30.

Figure 8. Concentration vs time curves of recrystallization of racemic sodium ibuprofen in 20 mL of water + 315 mL of acetone at T ) 25 °C and initial S0 ) 1.17; 315 mL of acetone was added to the 20 mL aqueous racemic solution of sodium ibuprofen after (a) 60 and (b) 80 min of stirring.

obviously shortened the induction period, τ, of forming stable nuclei of racemic (R,S)-(()-sodium ibuprofen dihydrate by a quarter or more (Table 1). This indicated that when configurationally similar additives were incorporated to the nuclei, a significant decrease in the Gibbs free-energy barrier, ∆Gcr, of forming clusters of a critical size was obtained. For example, with S0 ) 1.30, ∆Gcr ) 19.0 ( 2.9 × 10-22 J and 38.5 ( 3.1 × 10-22 J for systems with additives of (S)-(-)-sodium

ibuprofen dihydrate and (S)-(+)-ibuprofen, respectively, were lower than ∆Gcr ) 36.8 ( 0.2 × 10-22 J for the pure system (Table 2). The significant lowering of the solution-solid interfacial energy, γ, of the clusters of racemic (R,S)-(()-sodium ibuprofen dihydrate molecules upon the addition of (S)-(-)-sodium ibuprofen dihydrate molecules indicated that the bonding structure of the clusters in the presence of the additives was closer to the liquid structure of the solution than to the ones in the absence of the additives. It was because the interfacial energy, γ, is the thermodynamic work required in forming a new interfacial area. The interfacial energy, γ, is a direct manifestation of the unbalanced intermolecular forces of the molecules at the surface of the solid nuclei. Usually, the interfacial energy, γ, between a solid and a liquid approaches zero as the affinity between the solute and the liquid-phase molecules increase.10 Because γ was independent from the concentration of racemic (R,S)-(()-sodium ibuprofen dihydrate,


Figure 11. RG vs ln St plot for the crystal growth of racemic (R,S)(()-sodium ibuprofen dihydrate with the addition of 0.02 g of (S)(+)-ibuprofen at T ) 25 °C and initial supersaturation ratios of (a) S0 ) 1.17, (b) S0 ) 1.19, (c) S0 ) 1.25, and (d) S0 ) 1.30.

Figure 12. RG vs ln St plot for the crystal growth of racemic (R,S)(()-sodium ibuprofen dihydrate with the addition of 0.02 g of (S)(-)-sodium ibuprofen dihydrate at T ) 25 °C and initial supersaturation ratios of (a) S0 ) 1.17, (b) S0 ) 1.19, (c) S0 ) 1.25, and (d) S0 ) 1.30.

as the initial S0 ) C0/C* increased, the effects of γ on ∆Gcr, rc and ∆Gν were diminished as illustrated by eqs 8, 6, and 5, respectively. Therefore, ∆Gcr, rc and ∆Gν all decreased as the initial S0 increased at any given γ. However, the slight increase in the solution-solid interfacial energy, γ, of the clusters of racemic (R,S)-(()-sodium ibuprofen dihydrate molecules upon the addition of (S)-(+)-ibuprofen molecules calculated from the slope of eq 10 in Figure 6b could have been due to the assumption that the molecular volumes of the clusters of racemic (R,S)-(()-sodium ibuprofen dihydrate molecules, υ, remained unchanged, which might no longer be valid in the presence of the configurationally different (S)-(+)ibuprofen molecules. Intriguingly, racemic (R,S)-(()-sodium ibuprofen dihydrate molecules are amphiphilic and they may undergo self-association46 not only in water above 0.17 M at 25 °C according to the literature36 (Figure 7a) but also in the 325 mL of wateracetone solution above 0.01 M at 25 °C (Figure 7b). Therefore, the processing history and the controlled environments of the


Figure 13. ln RG vs ln(St - 1) plot for the crystal growth of racemic (R,S)-(()-sodium ibuprofen dihydrate without any additives at T ) 25 °C and initial supersaturation ratios of (a) S0 ) 1.17, (b) S0 ) 1.19, (c) S0 ) 1.25, and (d) S0 ) 1.30.

Figure 14. ln RG vs ln(St - 1) plot for the crystal growth of racemic (R,S)-(()-sodium ibuprofen dihydrate with the addition of 0.02 g of (S)-(+)-ibuprofen at T ) 25 °C and initial supersaturation ratios of (a) S0 ) 1.17, (b) S0 ) 1.19, (c) S0 ) 1.25, and (d) S0 ) 1.30.

solution could be extremely important to the microstructure of the complex fluid. We found that prolong stirring of the aqueous solution of racemic (R,S)-(()-sodium ibuprofen dihydrate (1.98 g in 20 mL of water ) 0.37 M > 0.17 M) before the addition of the antisolvent acetone (1.98 g in 325 mL of water-acetone solution ) 0.023 M) could lengthen the induction period by 17 min at 25 °C (Figure 8). It was known that given a long enough time, polydispersed self-aggregates would have become more monodispersed.47 As the self-aggregates were getting more packed and stable, most likely it was harder for the selfaggregates to transform into nucleation clusters with a critical size even after the sudden increase in supersaturation by micromixing with the antisolvent acetone. Therefore, the induction period was process and species specific, and this particular system was sensitive to mixing. Species with self-association properties such as racemic sodium ibuprofen dihydrate deserved a tight control for reproducibility on scale-up. Therefore, the differences and trends of the parameters in Tables 1 and 2 were more important than the absolute numbers.


Lee et al.

Figure 15. ln RG vs ln(St - 1) plot for the crystal growth of racemic (R,S)-(()-sodium ibuprofen dihydrate with the addition of 0.02 g of (S)-(-)-sodium ibuprofen dihydrate at T ) 25 °C and initial supersaturation ratios of (a) S0 ) 1.17, (b) S0 ) 1.19, (c) S0 ) 1.25, and (d) S0 ) 1.30.

Crystal Growth. As soon as the clusters of racemic (R,S)(()-sodium ibuprofen dihydrate larger than the critical size were formed in a supersaturated solution, they began to grow into crystal particles, most likely in a layer-by-layer fashion48 as illustrated by the SEM image in Figure 9. But before the crystal face could continue to grow, a “center of crystallization” must

Figure 17. DSC thermograms of vacuum-dried racemates harvested from the racemic acetone–water solution of sodium ibuprofen dihydrate at T ) 25 °C and initial S0 ) 1.17 (a) without any additives, (b) with 0.02 g of (S)-(+)-ibuprofen, and (c) with 0.02 g of (S)-(-)-sodium ibuprofen. The R to β endothermic transition occurred between 75 and 113 °C. The β to γ endothermic transition took place around 175 °C. The melting point for the γ form was 199 °C.

come into place on the plane surface according to the GibbsVolmer theory.49 A monolayer island nucleus called a twodimensional nucleus was created. Once the surface nucleus was born, it was assumed to spread across the (010) surface48 at an infinite velocity. The (010) surface48 must then await the

Figure 16. Optical micrographs of crystal products harvested towards the end of the recrystallization of a racemic acetone–water solution of sodium ibuprofen at T ) 25 °C and S0 ) 1.17 (a) without any additives, (b) with 0.02 g of (S)-(+)-ibuprofen, and (c) with 0.02 g of (S)-(-)-sodium ibuprofen (scale bar ) 100 µm). Table 3. Tabulated Values of S0, Crystal Growth Time, RG, g, KGAt, and the End Point of the Three Experimental Sets of Crystallization of the Racemic R,S(()-Sodium Ibuprofen Dihydrate (MW ) 264.29) (a) without Any Additives, (b) with 0.02 g of (S)-(+)-Ibuprofen Additives (MW ) 206.29), and (c) with 0.02 g of S-(-)-Sodium Ibuprofen Dihydrate Additives (MW ) 264.29), Having Different Initial Supersaturation Ratios of S0 ) 1.17, 1.19, 1.25, and 1.30 (C* was 5.28 mg/mL or 0.019 mol/L in a 325 mL acetone–water solution; the crystal growth time and the end point measured the total amount of time required for desupersaturation from t ) τ and from t ) 0, respectively, on the basis of Figures 3-5) S0 ) C0/C*

crystal growth time (min)

1.17 1.19 1.25 1.30

19.9 ( 0.0 14.4 ( 0.4 13.4 ( 4.7 10.5 ( 1.4

RG (g/min)

g

KGAt (g/min)

end point (min)

Recrystallization of Racemic (R,S)-(()-Sodium Ibuprofen Dihydrate 0.2 0.3 0.4 0.5

1.0 0.8 0.8 0.5

0.2 0.3 0.4 0.3

48.7 ( 0.3 30.8 ( 0.2 22.8 ( 3.9 15.6 ( 1.6

Recrystallization of Racemic (R,S)-(()-Sodium Ibuprofen Dihydrate + 0.02 g of (S)-(+)-Ibuprofen 1.17 1.19 1.25 1.30

30.7 ( 7.0 10.9 ( 3.1 12.0 ( 3.7 7.0 ( 2.2

0.1 2.0 0.3 0.7

0.7 1.6 1.7 0.6

0.03 1.5 0.5 0.5

51.7 ( 6.2 23.1 ( 0.9 19.2 ( 5.2 10.4 ( 1.6

Recrystallization of Racemic (R,S)-(()-Sodium Ibuprofen Dihydrate + 0.02 g of (S)-(-)-Sodium Ibuprofen Dihydrate 1.17 1.19 1.25 1.30

7.3 ( 0.0 7.7 ( 1.9 8.6 ( 0.2 7.4 ( 2.2

0.1 0.2 0.2 0.2

0.5 0.7 0.6 0.6

1.4 ×10-2 0.1 0.1 0.1

15.6 ( 0.6 11.1 ( 1.4 12.0 ( 0.2 10.3 ( 2.2



∆Gcr )

πhγedgeυ kT ln St

(16)

where St is the supersaturation ratio at any time t after the nucleation time, tn. Again, the rate of 2D nucleation, J′, can be expressed in the form of the Arrhenius reaction velocity equation49

(

J′ ) B exp

)

[

-∆Gcr -πhγedgeυ ) B exp 2 2 kT k T ln St

]

(17)

The relative growth rate, RG, was verified to be inversely proportional to the critical overall Gibbs free energy of a secondary 2D nucleation, ∆Gcr23 RG ∝

Figure 18. PXRD patterns at ambient temperature of vacuum-dried racemates harvested from the racemic acetone–water solution of sodium ibuprofen dihydrate at T ) 25 °C and initial S0 ) 1.17 (a) without any additives, (b) with 0.02 g of (S)-(+)-ibuprofen, and (c) with 0.02 g of (S)-(-)-sodium ibuprofen.

formation of another surface nucleus. Therefore, the rate determining step was the formation of the surface nucleus. Similar to the homogeneous 3D nucleation, the overall Gibbs free energy of a secondary 2D nucleation at a lower supersaturation is49 ∆G ) aγedge + V∆GV

(12)

where a and V are the area and volume of the 2D nucleus and γedge is the specific surface free energy of the edge of the nucleus. If the nucleus is a circular disk of radius r and height h49 ∆G ) 2πrhγedge + πr2h∆GV

(13)

Maximizing eq 13 with respect to the radius, the critical size, rc, becomes49 rc ) -

γedge ∆GV

(14)

Substituting for ∆Gν from eq 14 in eq 13, we have ∆Gcr ) πrchγedge

(15)

which can be expressed in a form similar to eq 8 by substituting eq 7 into eq 1549

(18)

in Figures 10-12, where linear fits of RG versus ln St gave high values of correlation coefficient of larger than 0.96. These results suggested that it is possible to have energetic barriers associated with incorporating material into the crystal (010) surface48 and there is a thin stagnant film of liquid adjacent to the growing crystal face through which molecules of racemic (R,S)-(()sodium ibuprofen dihydrate will have to diffuse. Growth in these directions can be both diffusion and surface integration controlled.23 Therefore, when an overall concentration driving force of Ct – C*, which is conveniently measured, is employed, a general equation for crystal growth in eq 18 can be written as RG )

Figure 19. Crystallization pathways of forming different racemic species in the present work.

1 ∝ ln St ∆Gcr

dmt ) KGAt(Ct - C/)g ) KGAt(St - 1)g dt

(19)

where mt is the mass of solid deposited in time t; KG is an overall crystal growth coefficient; At is the total surface area of all crystal particles at time t; Ct is the concentration of racemic (R,S)-(()-sodium ibuprofen dihydrate in the solution (supersaturated) at time t; C* is equilibrium saturation concentration (solubility) at 25 °C; St is the supersaturation ratio at time t > tn; and g is the order of the overall crystal growth process. To determine dmt/dt, we first converted the concentration versus time curves into the crystal mass growth versus time plots by realizing that the mass of the crystallizing material is the total dissolved mass minus the dissolved mass at any point of time during the process mt ) (C0 - Ct)V · MW

(20)

where C0 is the initial concentration of racemic (R,S)-(()sodium ibuprofen dihydrate in the solution (supersaturated); Ct is the concentration at any time t; V is 0.325 L of the total volume acetone–water solution; and MW is the molecular weight of racemic (R,S)-(()-sodium ibuprofen dihydrate of 264.29 g/mol. The crystal mass growth versus time S-shaped curves at T ) 25 °C and with S0 ) 1.17, 1.19, 1.25, and 1.30 of racemic water-acetone solution of sodium ibuprofen dehydrate: (a) without any additives, (b) with 0.02 g of (S)-(+)-ibuprofen, and (c) with 0.02 g of (S)-(-)-sodium ibuprofen dihydrate, were plotted in Figures 3-5, respectively, along with the Z-shaped concentration versus time curves. All Ct versus time and mt versus time curves were fitted by high-order polynomials. dmt/ dt for all mt versus time curves were then determined by differentiation, and polynomials of lower orders were generated. With the use of those polynomials, which were functions of time, specific pairs of Ct (or St) and dmt/dt (or RG) could be generated at the same time points, t, according to eq 19 on the basis of Figures 3-5. Taking the natural logarithm on both sides of eq 19


Lee et al.

Table 4. Enthalpy of Fusion and Solubility of Crystals Grown from Racemic Acetone–Water Solution of Sodium Ibuprofen Dihydrate at T ) 25 °C and with S0 ) 1.17 (a) without any additives, (b) with 0.02 g of (S)-(+)-ibuprofen, and (c) with 0.02 g of (S)-(-)-sodium ibuprofen crystals grown from 325 mL of acetone–water solution of racemic sodium ibuprofen dihydrate at 25 °C and with S0 ) 1.17 (a) without any additives (b) with 0.02 g of (S)-(+)-ibuprofen (c) with 0.02 g of (S)-(-)-sodium ibuprofen dihydrate

ln RG ) ln(KGAt) + g ln(St - 1)

racemic species

major form(s)

enthalpy of fusion ∆Hm

solubility in water at 25 °C (mg/mL)

racemic compound racemic conglomerate racemic conglomerate

R, γ γ R, γ

80.42 76.10 54.16

3.83 4.18 4.75

(21)

a straight line is obtained. When ln RG is plotted against ln(St - 1), g is the slope; ln KGAt is the y-intercept. The ln RG vs ln(St - 1) plots for the crystal growth of racemic (R,S)-(()sodium ibuprofen dihydrate at T ) 25 °C and with initial supersaturation ratios S0 ) 1.17, 1.19, 1.25, and 1.30: (a) without any additives, (b) with the addition of 0.02 g of (S)-(+)ibuprofen, and (c) with the addition 0.02 g of (S)-(-)-sodium ibuprofen dihydrate were illustrated in Figures 13-15, respectively. The calculated values of crystal mass growth rate of crystals, RG; the order, g; and the product of the overall crystal growth coefficient and the surface area, KGAt, in the growth rate equation based on eq 19 are listed in Table 3 along with the crystal growth time and the end point that measured the total amount of time required for desupersaturation from t ) τ and from t ) 0, respectively. In general, RG increased as the initial supersaturation ratio S0 increased. As indicated in Table 2, with high initial S0, the nucleation rate, J, increased, which led to the explosion of a large number of nuclei providing high surface area, At, in eq 19 for the 2D nucleation to occur so that the crystal mass growth rate, RG, increased. Although At is supposed to be a time function in eq 21, the ln RG vs ln(St - 1) plots in Figures 13-15 were linear. This suggested that the total surface area of all crystalline thin plates did not alter too much as time went by under the layer-by-layer growth mechanism as shown in Figure 9. The order, g, was found to range from 0.5 to 1.7. With high S0 or in the presence of (S)-(-)-sodium ibuprofen dihydrate, the mononuclear 2D nucleation (g ) 1/2) and the birth-and-spread mechanism (g ) 5/6) might dominate. But when (S)-(+)-ibuprofen was added, surface integration rather than mass transfer might become the dominant mechanism and result in a spiral growth mechanism (g ) 2).3,50 At first glance, the presence of additives did not seem to disrupt the crystal mass growth rate, RG, of racemic (R,S)-(()sodium ibuprofen dihydrate at T ) 25 °C too much for almost all initial supersaturation ratios, S0, except for the RG of 2.0 g/min of the racemic solution of sodium ibuprofen dihydrate doped with 0.02 g of (S)-(+)-ibuprofen with S0 ) 1.19. With S0 ) 1.17, RG varied from 0.1 to 0.2 for all cases and the average crystal size was about the same (Figure 16). But to bring out the true nature behind the recrystallization of racemic species,51,52 all harvested solids prepared with S0 ) 1.17 were dehydrated in a vacuum oven at 40 °C for at least 2 h so that the polymorphism could be clearly identified by differential scanning calorimetry34 without the interference from the dehydration peak from 50 to 100 °C. DSC scans are illustrated in Figure 17. Because both R and β forms were racemic compounds, γ form was a racemic conglomerate (i.e., an equimolar physical mixture of the individual enantiomeric crystals, such that only one enantiomer is present in each crystal and in each unit cell of the crystal lattice),34 and there was a second endotherm at a higher temperature adjacent to the melting point of γ form around 199 °C, we proposed that the crystals originally grown from racemic water--acetone solution

of (R,S)-(()-sodium ibuprofen dihydrate (a) without any additives contained racemic compounds of R-form (R,S)-(()sodium ibuprofen dihydrate and with the addition of (b) 0.02 g of (S)-(+)-ibuprofen and (c) 0.02 g of S(-)-sodium ibuprofen contained racemic conglomerates of γ-form sodium ibuprofen dihydrate having a R:S w/w ratio of about 45:55 (enantiomeric excess of the solids,13 ee ) 10% in S) on the basis of the melting point phase diagram developed by Zhang et al.34 But as the S0 increased from 1.19 to 1.30, the DSC scans of all solids looked like Figure 17a regardless of any additives or not, indicating the formation of racemic compound only. PXRD diffractograms34 in Figure 18 further provided complementary results. The crystals originally grown from racemic water-acetone solution of (R,S)-(()-sodium ibuprofen dihydrate (a) without any additives were composed of the R- and γ-forms of (R,S)-(()-sodium ibuprofen dihydrate with the characteristic peaks at 2θ ) 6 and 4°, respectively, (b) with the addition of 0.02 g of (S)-(+)-ibuprofen contained a much smaller amount of the R-form and mainly the γ-form of (R,S)-(()sodium ibuprofen dihydrate, as indicated by the much weaker characteristic peak at 2θ ) 6°, and (c) with the addition of 0.02 g of (S)-(-)-sodium ibuprofen possessed both R- and γ-form of (R,S)-(()-sodium ibuprofen dihydrate having the characteristic peaks at 2θ ) 6 and 4°, respectively. Clearly, the addition of (S)-(+)-ibuprofen and (S)-(-)-sodium ibuprofen dihydrate to the racemic water-acetone solution of sodium ibuprofen dihydrate in the very beginning of the crystallization process as free molecules could have determined the crystallization pathways that would result in different qualities in final drug products (Figure 19). Their enthalpy of fusion and solubility characteristics in water at 25 °C are tabulated in Table 4. Solubility increased as the enthalpy-offusion related crystallinity decreased. In addition, the introduction of homochiral molecules from the drug development point of view seemed to accelerate the crystallization process, as revealed by the shortening of the induction period, the crystal growth time, and the end point. Conclusions The fundamental parameters of crystallization kinetics useful for optimization and drug development such as the critical micelle concentration, the induction time, the nucleation rate, an equation for crystal growth, and the solubility have been conveniently evaluated for the racemic species of sodium ibuprofen dihydrate crystals by electrical conductance at T ) 25 °C. Adoption of this inexpensive, simple, and robust method in common research laboratories offer the opportunity to the pharmaceutical industry to lower manufacturing cycle times and end-product variability, which would result in shorter time to market and a reduced likelihood of drug product failures. The addition of chiral parent molecules such as (S)-(+)-ibuprofen to daughter racemic solution of sodium ibuprofen dihydrate or (S)-(-)-sodium ibuprofen dihydrate to the solution of sodium ibuprofen dihydrate seemed to resolve it asymmetrically to


γ-form racemic conglomerates as determined by differential scanning calorimetry and wide-angle powder X-ray diffraction. Acknowledgment. This work was supported by a grant from the National Science Council of Taiwan, R.O.C. (NSC 95-2113M-008-012-MY2). Suggestions from Ms. Jui-Mei Huang in differential scanning calorimetry and Ms. Ching-Tien Lin in scanning electron microscopy at National Central University Precision Instrument Center and High Valued Center are gratefully acknowledged. We also thank the assistance from Mr. Ren Chiang Luo at the National Tsing Hua University Instrument Center on wide-angle powder X-ray diffraction.

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CG070045C

Sodium Ibuprofen Dihydrate on the Crystallization Kinetics of

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