Crystallization from Solutions Containing Multiple Conformers. 2

Article pubs.acs.org/crystal

Crystallization from Solutions Containing Multiple Conformers. 2. Experimental Study and Model Validation L. Derdour,*,† C. Sivakumar,§ D. Skliar,‡ S. K. Pack,‡ C. J. Lai,† J. P. Vernille,‡ and S. Kiang† †

Drug Product Science and Technology, and ‡Chemical Development, Bristol-Myers Squibb, 1 Squibb Drive, New Brunswick, New Jersey 08901, United States § Department of Chemical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213, United States ABSTRACT: In this Article, the validity of a model derived for crystal growth rates and supersaturation for solids crystallized from solutions of materials containing multiple conformers is evaluated. A simple and straightforward method for determining crystal growth rates using FBRM and FTIR/ATR is utilized, which leads to a large amount of growth rate data from a single experiment. Supersaturation and crystal growth rate obtained experimentally were in good agreement with model predictions. In particular, data indicated that for the system at hand, crystal growth rate is inversely proportional to crystals size. Further, the solute integration coefficient determined from supersaturation measurements can be slightly overestimated due to surface nucleation and/or agglomeration that can result from supersaturation spikes during antisolvent addition. Last, crystal growth data obtained at different temperatures indicated that slow growth rate observed at low temperatures is likely to be due in part to surface poisoning by the wrong conformer. as reported by Snyder et al.3 However, as stated above, if crystallization is conducted at a temperature higher than the rotomers’ NMR peak coalescence temperature, it is impossible to obtain an accurate measurement of a given conformer by an off-line NMR analysis. The limitation in turn prevents building a model relating RC concentration to IR absorbance in the cases where IR is sensitive to conformational changes. This is the case for the crystallization reported in this study, where only the concentration of all conformers (and MSS) can be measured during crystallization. Therefore, for the model’s verification, only the following relationships previously derived for the concentration (and MSS) are employed in the computation to enable comparison with experimental data1 (the definitions of the terms are listed in the Nomenclature):

1. INTRODUCTION In another study, a model was derived for computing crystal growth rate and supersaturation for organic solids growing from multiconformer solutions (Derdour and Skliar1). The model is based on the approach of the right conformer, which assumes that only one conformer, the right conformer (RC), integrates onto the crystal surface (Derdour et al2). The other conformers, referred to as wrong conformers (WC), have to convert to the RC before integrating onto the crystal surface. This behavior is believed to occur when the energy barrier between conformers is higher than ca. 10 kcal. The approach of the RC is based on the assumption that the driving force of crystallization is the intrinsic supersaturation (ISS). The ISS is related to the measurable supersaturation (MSS), which corresponds to the classical definition of supersaturation by (the definitions of the terms are listed in the Nomenclature):2 ISS = MSSKeq /(Keq + 1)

n

C= (1)

mo − ρcr k v ∑i = 1 Ni(Li3 − Li30) M slt((Vsol)0 + ARmot )

In addition, the expression for crystal size is:

where MSS is expressed as:

H

(2)

MSS = C − C*

Li(t H) = [(Li0)2 + 2Φ∑ MSS(th)Δt ]2

Solution NMR is usually utilized to evaluate the conformers’ proportion in solution. NMR analysis is carried out off-line. When used for conformational analysis, NMR analysis is limited to temperature below the rotomers’ peak coalescence (Tpc). For crystallizations conducted at temperatures above Tpc, off-line NMR analysis is unreliable because it cannot detect different conformers. On the other hand, there is still a lack of conformer-specific probes that can be used in situ for conformer concentration measurement. IR can be used to determine the concentration of a given conformer in solution only if the IR spectrum is sensitive to changes in the environment of IR-responsive functional groups © 2012 American Chemical Society

(3) 1

h=1

(4)

and crystal growth rate was found to be a function of MSS according to the following relationship: Gi =

dLi ΦMSS = dt Li

(5)

Received: July 13, 2012 Revised: September 6, 2012 Published: October 8, 2012 5188

dx.doi.org/10.1021/cg300975s | Cryst. Growth Des. 2012, 12, 5188−5196

Crystal Growth & Design

Article

where Φ is the intrinsic solute integration coefficient:1 (−E + /(RT ))

Φ = αΨKe

Table 1. Correlations for Size-Dependent Growth Rate Extracted from the Literaturea

(6)

investigators

where α is a system-dependent constant, Ψ is the WC growth inhibition term, K = Keq/(Keq + 1) is a parameter dependent on the equilibrium between conformers, and E+ is the solute integration activation energy (kJ/mol). The intrinsic solute integration coefficient Φ needs to be estimated from experimental data. This is achieved by transient supersaturation data from a few crystallization experiments with different sets of conditions. The principle of the parameter estimation is to determine the value of Φ that leads to a minimum in the total difference between the experimental MSS and the estimated value:

∑ |MSSexp − MSSmod| t=0

⎡ ⎛ Φ /Φ ⎞ Ψ1 E+ ⎛ 1 1 ⎞⎤ = exp⎢ln⎜ 1 2 ⎟ + ⎜ − ⎟⎥ ⎢⎣ ⎝ K1/K 2 ⎠ R ⎝ T1 T2 ⎠⎥⎦ Ψ2

∑ cqLq) q=1

McCabe and Stevens19

G = 0.00177(MSS)1.8 L1.1

Bransom20

G = c0(MSS)c1Lc2

Abegg et al.

21

G = c1(1 + c 2L)c3 ,

Tai et al.22 Tai et al.23 a

c3 < 1 L≥0

kint = 2.31 L0.64 (surface integration coefficient) small crystals: G = 1.345 × 10−11L0.627(RSS)2.2 large crystals: G = 1.292 × 10−11L0.604(RSS)2.02

ci are constants, the values of which can differ between references.

(7)

Table 2. Correlations for Size-Dependent Growth Rate Extracted from the Literaturea

Parameter estimation also allows verification of the constancy of the intrinsic coefficient (i.e., whether its value changes with crystallization conditions). The principle of the parameter estimation is the following: Values of Φ are increased by increments within the range of its variation, and in each increment of Φ temporal variation of MSS is estimated stepwise by minimization of the error between the computed and experimental value. The calculation is executed by iteration starting from the initial MSS. The estimated Φ corresponds to the value that minimizes the total difference between computed and experimental MSS. Once Φ is obtained and confirmed to be constant, it can be used in eqs 2−5, which then can be solved numerically to determine concentration. The parameter estimation procedure and the resolution algorithm are described by the flowchart reported in another study.1 In eq 6, Ψ represents crystal growth inhibition by the wrong conformer. For systems where the crystallizing conformer is a high energy species, the population of the wrong conformer is expected to decrease and hence its inhibition effect to drop with increasing temperature. Therefore, higher values of Ψ are expected at higher temperature. The ratio of WC inhibition factor can be easily found to be:1 Θ=

Q

G = co(1 +

t final

E=

kinetics

Canning and Randolph4

investigators

kinetics

Mullin and Gaska24 Garside et al.25 Garside and Jancic26

KD = c1Lc2 KD: mass transfer coefficient in diffusion film

G = 9.610−8(C − c1)0.9 (1 + 61L)0.54 G(L̅) = (Lf−1 − Lf)/c1 ln(N(Lf)/N(Lf−1)) Lf−1, Lf−1: sizes between two time increments

White et al.27 Girolami and Rousseau 29

Mydlarz Mydlarz and Briedis30 Mydlarz and Jones31,32 Mydlarz and Jones

a

33

28

G = 2510−8(RSS)L0.4 G = (c1L /c 2)/(c3 + (1 − c3)L /c 2) G = c1(1 − exp(− c 2L)) G = c1(1 − exp[− c 2(L + c3)])

Mydlarz34

G = c1(1 − exp[− c 2(L + c3)])

Rojkowski35

G = c1(1 − exp[− c 2(L + c3)])


Table 3. Correlations for Size-Dependent Growth Rate Extracted from the Literaturea investigators

(8)

Θ can be evaluated from experimental measurement of Φ at different temperatures and from the knowledge of the solute integration activation energy (E+). For systems where the WC is the low energy conformer, a decrease of Θ can indicate crystal growth inhibition by the WC. The model predicts a decrease of growth rate with increasing crystal size. The prediction of a decreasing crystal growth rate with crystal size is opposite to the general consensus that crystal growth should increase with crystal size as shown in Tables 1−3, which provide a summary of correlations between growth rate and crystal size found in the literature. The model’s prediction of a growth rate decreasing with crystal size is mainly due to negligible crystal defects and surface nucleation because of the slow growth and low levels of supersaturation achieved during crystallization. In this case, crystal growth occurs mainly via step propagation, and the step advance velocity is only a function of supersaturation. At a given supersaturation, and hence at a given step advance velocity, the step will cover the crystal face in a shorter time for small crystals as compared to

kinetics

Rojkowski36

G = (c1 + c 2c3L)/+ c 2L

Ramanarayann et al.37

G~ = (L − c1)/t

Sherwin et al.38

G = G(C)[1 + c1L] G(C): function of C only G = c1c 2L

Ishii and Randolph39 Randolph and White13 Tavare16

a

Y(X) = 2/(1 + (1 + 4/Pe)1/2) ex[(Pe/2)(1 − (1 + 4/Pe)1/2)X)] y = nG̅ 2/B: dimensionless population density functions Pe = G̅ 2τ/DG: Peclet number (−) DG: growth rate diffusivity (m2/s) G̅ : overall linear growth rate (m/s) τ: mean residence time (s) x: dimensionless crystal size, X = LG̅ /τ n: population density (no./(m kg)) B: nucleation rate (no./(s kg))


larger ones. As a result, for a given supersatuation, crystals size will increase at a faster rate for smaller crystals as compared to larger ones. 5189



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In the experimental section, crystal growth data and supersaturation were determined experimentally on a Bristol-Myers Squibb’s proprietary substance denoted as compound D for the sake of confidentiality. The crystal structure of D was solved crystallographically, and it was found that the crystal lattice contains only one conformation, which is referred to as CC. In addition, HNMR data obtained at 20 °C revealed that D is present in two main conformations in solution with proportions of 9:1.2 The energy barrier between the two conformers estimated from solubility measurements is relatively high (12.2 kcal/mol). This was in agreement with ab initio calculations, which found a global potential minimum 8.1 kcal/mol lower than the local minimum obtained when using CC in the computation.2 Furthermore, crystallization of D below the NMR rotomer’s peak coalescence temperature was very slow, indicating a limitation on the equilibration kinetics among conformers and/or low concentration of the RC. On the basis of these data, it is assumed that the minor conformation in solution is RC, and thus the approach of RC is applicable to the system at hand.

The increase of growth rate with crystal size was mainly attributed to the following causes: (1) Higher diffusion limitations for smaller crystals due to lower relative velocity crystal-fluid for small crystals as compared to large crystals: Canning and Randolph4 and Garside et al.5 indicate that small crystals are more prone to following fluid streams and eddies, which results in low relative velocity crystal-fluid for small crystals. In addition, according to Canning and Randolph,4 diffusion limitations are more pronounced in the case of crystallization of solvates or hydrates because two species (solute and solvent) have to overcome diffusion resistance to integrate into the surface of the solid. However, there are some accounts of contradiction to this behavior: Harriott6 found that relative velocity crystal-fluid decreases with size, while Levins and Glastonbury7 found that the increasing relative velocity crystal-fluid with crystal size for potassium sulfite translated to a decreasing mass transfer coefficient with size. (2) Size-dependent surface integration kinetics is the most plausible cause for increasing growth rate with crystal size according to Langer and Offerman.8 This was attributed to higher kink densities in larger particles due to higher crystal surface stress and higher surface defects originating from collisions. (3) Higher (kinetic) solubility for smaller crystals due to the Gibbs−Thompson effect and increasing internal stress with decreasing crystal size:9,10 This behavior translates into lower supersaturation for smaller crystals (as compared to larger ones), which results in lower growth rate. This situation is only expected to affect submicrometer particles and hence is unlikely to impact crystal growth in the size range normally encountered in industrial crystallization. (4) Crystal growth dispersion can also be the source of sizedependent crystal growth as reported by various researchers since the early 1970s.11−18 In most growth rate dispersion theories, the type of size-dependence of crystal is also size-dependent, but there are few accounts of size-independent rates as reported by Ristic et al.9 for sodium chlorate. Growth rate dispersion can also lead to an apparent rate size-dependence as pointed out by Zumstein and Rousseau.18 Published work related to the dependence of crystal growth upon crystal size was established for the classic definition of solution concentration, that is, the concentration of all conformers combined. In addition, a large number of data reported in the literature focused on inorganic compounds for which both growth rate and final particle size are much higher as compared to organic molecules. High growth rate and large crystals imply higher density of dislocations and higher density of crystal defects for larger crystals. This translates to an increasing growth rate with size. Smaller crystals are more prone to follow fluid streamlines and as a consequence lead to lesser collisions than larger crystals. Moreover, lower kinetic energy is associated with motion of small crystals, which leads to lower impact energy upon crystal−crystal contact, resulting in lower defects from collision. In addition and as mentioned above, slow growth typically generates less surface defects, which in turn translates to lower growth rates.

2. MATERIALS AND METHODS 2.1. Experimental Equipment. Crystallization experiments were carried out in an experimental setup depicted in Figure 1.

Figure 1. Experimental setup. It consists of a jacketed 200 mL reactor, equipped with an overhead stirrer, Chemglass, IP42, range 50−2000 rpm, and a 4-pitch-blade agitator. Temperature was controlled by an external circulator (Thermo Electron Corp., Model Haake Phoenix II P2), using glycol/water as the heat transfer fluid. In situ chord length distribution was measured online via a FBRM probe, Lasentec S400, Mettler-Toledo. Mixture temperature was monitored continuously using a thermocouple connected to a digital data logger. In situ FTIR/ATR, Mettler Toledo ReactIR-4000, was utilized to determine the concentration during crystallization after a calibration model was established to correlate solute concentration and IR absorbance. Concentration was also determined off-line during crystallization by HNMR using a JEOL AS 400, JEOL Ltd., to ensure the calibration model was providing an accurate reading of the solute concentration. Evolution of the chord length distribution during crystallization was monitored using FBRM. Particle size distribution was determined by laser light scattering from a Malvern Mastersizer 2000, equipped with a 5190



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wet cell using isopropyl alcohol as dispersant. SEM images were obtained with XL30 ESEM ODP, FEI Co. 2.2. Measurement of MSS and Crystallization Procedure. Bristol-Myers Squibb compound D was obtained in house with a purity higher than 99.4% as determined by HPLC. Solvents were obtained from J. T. Baker and were all of HPLC grade. The chemistry provides a solution of the drug dissolved in 5 L/kgdrug of methanol (liters of solvent per unit mass of initially dissolved drug). The solution is heated to 50 °C, and 3.5−4.5 L/kgdrug of acetone (antisolvent) was added in 5 min to create supersaturation. Seeds were then introduced in the crystallizer, and the batch was aged for 4 h. After the seed aging period, 18 L/kgdrug of acetone was then added at a constant rate for each operation to drive and complete crystallization. Experimental concentration was determined by sampling periodically and filtering the slurry in a centrifuge at 14 000 rpm for 1 min. Supernatant was analyzed for concentration using HNMR. After the antisolvent addition was completed, the slurry was aged at 50 °C for 2 h, then cooled to 20 °C for 2 h, and aged at 20 °C for 2 h. The slurry was then filtered, and the cake was washed twice with 2 volumes of antisolvent followed by drying under vacuum at 50 °C until the residual solvent is below 0.5 wt % as measured by H NMR. 2.3. Measurement of Crystal Growth Rates. To determine crystal growth rates experimentally, only the seed aging section of the crystallization was needed. After equilibrating the solution at the crystallization temperature, a given amount of antisolvent is added to create the initial supersaturation. Next, a given amount of seeds was added, and chord length and concentration were continuously measured using FBRM and FTIR/ATR. No further antisolvent is added during the process, so that the supersaturation level drops throughout the experiment. Initial supersaturation was varied by changing the amount of antisolvent added, and initial crystal size was varied by seeding with materials of different sizes, but the seed loading was adjusted so that the total seed surface area is kept constant. During the desupersaturation, samples from the suspension were taken periodically and filtered in a centrifuge. Only the section of the experiment that displays no change in FBRM total counts was utilized for the measurement to minimize the adverse effect of agglomeration and attrition on the measurement (cf., Figure 2). The mother liquor

Correlations relating the average chord length to the average crystal size obtained by image analysis were determined for each experiment (Figure 3). FTIR and FBRM measurements were used to obtain a

Figure 3. Typical correlation between average crystal size obtained by microscopy and average chord length. continuous measurement of supersaturation and crystal size. The latter was used to determine experimental crystal growth rates.

3. RESULTS AND DISCUSSION 3.1. Minimizing Effects of Attrition, Breakage, and Agglomeration on Crystallization. Seeding procedure and antisolvent addition protocol were optimized to favor a growthdominated process for better control of the final crystal size distribution. The details of the optimization are beyond the scope of this study and will not be discussed here. The crystallization procedure after optimization was indeed dominated by crystal growth, and other phenomena were minimized. This result was confirmed by a good match between calculated crystal size for a growth-dominated process and experimental crystal size shown in Figure 4.

Figure 2. Typical variation of average chord length and FBRM total counts during desupersaturation used for crystal growth measurements.

Figure 4. Calculated final crystal size for a growth-dominated process versus experimental final crystal size.

was analyzed for concentration by H NMR to confirm the concentration measurement by FTIR/ATR. Crystal size of the solid was determined via optical microscopy image analysis on a population of at least 200 particles.

3.2. Experimental Determination of Crystal Growth Kinetic Constant (Φ). The intrinsic solute integration coefficient Φ (eq 6) was determined experimentally during linear antisolvent additions after aging the seeds. The number of classes 5191



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used. Comparison between experimental data and computation is shown in Figure 6a and b, and a statistical analysis of the computation is summarized in Table 6. As can be seen in this table, all of the coefficients of determination (R2) obtained for the computation of concentration are higher than 0.98, which indicate an excellent correlation between the experimental data and computed values. On the other hand, coefficients of determination obtained for computation of MSS are lower, but most are higher than 0.9, which indicates an acceptable fairly good prediction of MSS. The relationship between relative errors on the computation of MSS and concentration is found to be:

of particles can be set by the user and is dependent on the PSD of the seeds. In our calculation, 30 classes of particles were sufficient for the computation. Increasing the number of classes beyond 30 did not affect the calculations significantly. The initial crystal sizes are set by the PSD of the seeds, and the solubility is measured experimentally as a function of solvent composition. Seven experiments with conditions shown in Table 4 were conducted to check if Φ is constant within the design space of Table 4. Crystallization Conditions for the Determination of the Solute Integration Coefficient (Φ) exp no.

SL (%)

AR (mL/(g·min))

Vs (L/kgdrug)

Vas0 (L/kgdrug)

1 2 3 4 5 6 7

2 1 1 2 2 1 1

0.153 0.153 0.067 0.103 0.103 0.038 0.038

5.07 5.07 5.07 5.07 5.07 4.5 4.5

2.41 2.1 2.1 2.1 2.1 3.1 1.6

Erel MSS = ((Erel MSS)−1 − 10−2(C*/Eabs C))−1

Equation 10 shows clearly that the relative error between computed and experimental MSS is always higher than the one obtained for the calculation of concentration. Hence, it is expected that we obtain a better fit for concentration as compared to the one obtained for MSS. Table 6 shows the average absolute errors and the minimum relative error for each computation. These results also indicate that for this type of system, solute integration can be the limiting mechanism throughout crystallization. In addition, model validity in the range of crystallization conditions used indicates that for the system at hand, crystal growth rate decreases with crystal size. In the following section, experimental data of crystal growth rate are presented and compared to model prediction. 3.4. Measurement of Crystal Growth Rates: Model Verification. Crystal growth rates were determined following the procedure described above, and the data were fitted to eq 5. Initial conditions for crystal growth experiments are shown in Table 7 where TS is the total seed surface calculated as:

the crystallization. Experimental results are summarized in Figure 5. The same seed lot (same seed size) was used for all

TS = 10−2Ag m0SL

(11)

Table 7 summarizes the experimental conditions used for the desupersaturation experiments intended for crystal growth rate measurements. Figure 7 shows experimental data along with surface plots obtained by regression of the experimental data with a relationship of the type of eq 5. A good fit (i.e., high R2) would indicate that the growth rate is likely to be inversely proportional to crystal size. The regression allows estimating the solute integration coefficient at different temperatures. Values of Φ and R2 are reported in Table 8 along with the coefficients of determination. The R2 values ranging from 0.66 to 0.92 indicate that crystal growth rate for the system at hand is likely to be inversely proportional to crystal size in the range of sizes investigated. Comparison of values of Φ extracted from antisolvent addition crystallizations carried out at 50 °C to the one obtained from crystal growth measurements shows that the latter is slightly lower than the one obtained for Φ using MSS measurement (3.09 × 10−13 versus 11.77 × 10−13 m2/(mol/L)·s). This is possibly due to the fact that MSS measurements were performed during antisolvent addition, while data generated for crystal growth rate were obtained from desupersaturation without antisolvent addition. As can be seen in Figure 6a and b, the level of supersaturation reached during antisolvent addition is relatively high and can possibly trigger secondary surface nucleation and/or agglomeration. Figure 8 shows typical SEM images of crystal obtained from crystallization without antisolvent addition and constant total

Figure 5. Experimental determination of the solute integration coefficient (Φ).

experiments reported in Table 4 in which the seed loading (SL) is calculated as: SL = 100mseeds /m0

(10)

(9)

3.3. Measurement of MSS: Comparison between Model Prediction and Experimental Data. As can be seen from Figure 6, the solute integration coefficient can be considered constant in the range of operating conditions investigated: Φ = 11.77 × 10−13 m2/(mol/L)·s. In the following section, the value of Φ will be used in the resolution of eqs 2−5, and the model’s computation of C and MSS will be compared to experimental data generated during antisolvent crystallization of D. To check the validity of the model, several crystallization experiments were conducted, and the variation of the MSS was determined using FTIR/ATR. MSS was also determined using HNMR to ensure that the FTIR/concentration calibration model did not deteriorate over time. Equations 2−5 were solved numerically for any given set of experimental conditions to provide the variation of MSS during crystallization. Table 5 provides the experimental conditions 5192



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Figure 6. (a) Comparison between computed MSS and concentration with experimental data. (b) Comparison between computed MSS and concentration with experimental data.

Table 5. Crystallization Conditions for Experiments Used To Compare Experimental MSS To Model Predictions

Table 7. Initial Conditions for Crystal Growth Measurement Experiments

exp no.

SL (%)

AR (mL/(g·min))

Vs (L/kgdrug)

Vas0 (L/kgdrug)

T (oC)

SL (%)

D50seeds (μm)

RSSo (wt %)

TS (m2)

8 9 10 11 12 13 14 15

1 1 2 1 1 1 1 1

0.100 0.103 0.153 0.150 0.150 0.150 0.038 0.038

5.07 5.07 5.07 4.5 4.5 5.5 5.5 5.5

2.1 2.1 2.1 1.6 3.1 3.1 3.1 1.6

50 50 50 40 30

1 1.5 1 1 1

10.6 27 10.6 10.6 10.6

6.8 6.8 3.6 3.6 3.6

0.114 0.115 0.114 0.114 0.114

and agglomerates for the crystals obtained by antisolvent crystallization. This observation is in agreement with the BET surface area measured for the samples shown in Figure 8: 0.46 m2/g for the desupersaturation versus 0.68 m2/g for the antisolvent addition crystallization. The SEM images also show some defects even on the crystals obtained during crystal growth measurement experiments. This highlights the evidence that total elimination of phenomena such as secondary nucleation and attrition/breakage is impossible and that these phenomena still occur to a certain extent even at relatively low supersaturations. Surface nucleation and/or agglomeration cannot be captured by FBRM measurements because of the decrease of particle counts resulting from suspension dilution. The occurrence of surface nucleation and/or agglomeration can lead to overestimating the solute integration coefficient estimated during the second antisolvent charge because the assumption is made that

Table 6. Statistical Analysis for Computation of MSS exp no.

R2_MSS

R2_C

(Eabs_C)ave (mol/L)

(Erel_MSS)min

(Erel_C)min

8 9 10 11 12 13 14 15

0.967 0.965 0.985 0.904 0.708 0.990 0.877 0.979

0.995 0.990 0.996 0.994 0.987 0.998 0.996 0.998

0.0017 0.0019 0.0007 0.0018 0.0014 0.0005 0.0011 0.0016

4.63 3.37 1.86 5.80 13.11 2.21 7.32 3.70

1.37 1.50 0.42 1.50 2.88 0.57 1.46 1.08

FBRM counts and images of crystals obtained for antisolvent crystallization. This figure shows clearly more surface defects 5193



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Figure 7. Comparison of experimental crystal growth rates with model predictions for crystallization conducted at 50, 40, and 30 °C (surface plots represent data fit with model).

3.5. Estimation of Crystal Growth Inhibition by the Wrong Conformer. The following empirical relation of Φ = f(T) was obtained from the experimental data reported in Table 8 and plotted in Figure 9:

neither surface nucleation nor agglomeration occurs during crystallization. Table 8. Solute Integration Coefficients and Coefficient of Determination Obtained at Different Temperatures T (°C)

Φ (m /(mol/L)·s)

R

30 40 50

7.78 × 10−15 5.29 × 10−14 3.09 × 10−13

0.84 0.92 0.66

2

Φ = 1.094×10−12T7.937

(12)

2

On the other hand, the following correlation was obtained for K = f(T) from data published previously:2 K = 5.39×10−4T1.68

(13)

Figure 8. SEM images of crystals. 5194



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parameters if crystal growth is the dominant phenomenon during crystallization. Last, the WC crystal growth inhibition term was found to decrease with temperature, which indicates that the observed slow growth at low temperature is likely to be in part due to surface poisoning by the WC.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: (732) 227-6702. Fax: (732) 227-3002. E-mail: lotfi. [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We are grateful to Dr. Soojin Kim for pioneering the crystallization procedure of this BMS asset and to Dr. Qi Gao and Mrs. Alicia Ng for crystal structure elucidation. The Senior Leadership Team at Bristol-Myers Squibb Co. is also kindly acknowledged for providing means and incentives that made this study possible.

Figure 9. Variation of the solute integration coefficient with temperature.

Θ is calculated by combining eqs 8, 12, and 13 for different temperatures and solute integration activation energies considering that E+ typically lies in the range of 5−20 kcal/mol (Garside et al.,5 Davey and Garside40). The result of the computation of Θ when T1 = 50 °C and T2 < 50 °C is plotted in Figure 9, which shows that the WC inhibition factor ratio increases with decreasing temperature (T2). This result indicates that the observed slowing crystal growth with decreasing temperature is likely to be in part due to growth inhibition due to adsoption of the WC on the crystal faces leading to poisoning of key integration sites (Figure 10).

■

Figure 10. Variation of the WC inhibition factor ratio with temperature and solute integration activation energy.

4. CONCLUSION Experimental data were generated to examine the validity of a model for crystal growth and supersaturation for solids growing from mutlti-conformer solutions. A new method to determine crystal growth rate as a function of supersaturation and crystal size using in situ FBRM and FTIR/ATR was utilized. Computed supersaturation was in agreement with experimental data obtained during crystallization. In addition, crystal growth rate data confirmed model’s finding that when the approach of the right conformer applies, growth rate is inversely proportional to crystal size. Furthermore, the solute integration coefficient was found to be practically independent of crystallization 5195

NOMENCLATURE ap = coefficient in polynomial expression of solubility versus time (−) Ag = specific area of particles (m2/g) AR = antisolvent addition rate reported in unit mass of m3/ (kg·s) dissolved solute before crystallization or mL/(g·min) C = concentration (mol/L) C* = solubility (mol/L) ci = constants in equations extracted from the literature D50 = highest sphere equivalent diameter of the (m) smallest 50% in volume of particles E = difference between MSS measured experimentally and mol/L estimated value E+ = energy of activation of solute integration (J/mol) Eabs = absolute error in calculation of concentration (mol/L) Erel = relative error (%) G = growth rate (m/s) H = highest index of time for computation of crystal size (−) ISS = intrinsic supersaturation (g/L) Keq = equilibrium constant (−) kv = volume-based shape factor (−) L = particles’ characteristic length (m) Lm = molecular length (m) mo = mass of dissolved solute before crystallization (kg) mseeds = mass of seeds (kg) Mwslt = molar mass of solute (kg/mol) MSS = measurable supersaturation (g/L) N = number of particles (−) n = number of class of particles (−) P = highest coefficient index/polynomial order for solubility correlation (−) Q = highest coefficient index/polynomial order for crystal growth correlation (−) R = universal gas constant (J/(K·mol)) R2 = coefficient of determination (−) RSS = relative supersaturation (RSS = 100 MSS/C*) (%) SL = seed loading (%) T = temperature (°C, K) Tpc = temperature of rotomers’ NMR peaks coalescence (°C, K) t = time (s) dx.doi.org/10.1021/cg300975s | Cryst. Growth Des. 2012, 12, 5188−5196


Article

TS = total seed surface (m2) V = volume (m3) Vm = molecular volume (m3) xAS = antisolvent content in solvent system (% wt)

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Greek Letters

Δt = increment of time in computation ρ = density (kg/m3) Ψ = crystal growth inhibition coefficient (−) σs = step thickness (m) Φ = intrinsic solute integration coefficient (m2/s) λA(hkl) = distance between kinks of the face A(hkl) (m) ν = molecular vibration frequency (s−1) Subscripts

0 = at the start of antisolvent addition as = related to antisolvent C = related to concentration cr = related to crystal exp = related to experiment f = index for crystal size for crystal growth correlation h = index of time for computation of crystal size i = index of class of particles mod = related to model MSS = related to MSS p = coefficient index/polynomial order for solubility correlation q = coefficient index/polynomial order for crystal growth correlation s = related to solvent seeds = related to seeds sol = related to solution

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REFERENCES

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Crystallization from Solutions Containing Multiple Conformers. 2

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