Article pubs.acs.org/OPRD
Statistical Design of Experiment on Contact Secondary Nucleation as a Means of Creating Seed Crystals for Continuous Tubular Crystallizers Yuqing Cui, Juan J. Jaramillo, Torsten Stelzer, and Allan S. Myerson* Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States S Supporting Information *
ABSTRACT: In the pharmaceutical industry, it is often desired to produce seed crystals with an appropriate narrow size distribution of the desired polymorph. This study describes a system that generates such crystals continuously in a small-scale tubular crystallizer at low supersaturation via contact secondary nucleation. A response surface model was constructed by conducting a statistical design of experiment that models the nucleation rate as a function of contact force, area, and frequency. This model reveals that within a certain range the nucleation rate is linearly related to all three factors in this system. A combination of in-line video analysis and off-line microscope image analysis was used to determine the particle size distribution of seed crystals obtained in this system, and the majority of the crystals were found to be under 20 μm. This seems to be a feature of contact secondary nuclei in general and does not vary significantly with contact force, area, and frequency. Furthermore, the seed crystals generated are of the same polymorph as the parent crystals as a result of the attrition process. This study shows that generating seed crystals with a narrow size distribution using contact secondary nucleation for a continuous tubular crystallizer can be realized at a controlled rate by quantitative variation of certain design parameters.
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INTRODUCTION The interest in continuous crystallization in tubular crystallizers has been increasing recently1−4 because of the relatively consistent fluid-mechanical conditions and the superior heat transfer rates exhibited by tubular crystallizers, which should lead to a more reliable environment for the formation of crystals with consistent properties.3 Among these properties, crystal size distribution is especially important in the pharmaceutical industry, where a well-controlled narrow particle size distribution improves drug dissolution rate and tableting properties.5−7 Polymorphism is another important property of the crystals that needs to be controlled. Much effort has gone into obtaining the desired polymorph by various methods.8−10 Obtaining a narrow particle size distribution and the desired polymorph simultaneously is challenging: antisolvent crystallization often yields small crystals with a narrow size distribution because it creates extremely high supersaturation levels in a short period of time,11 but the polymorph of crystals generated through antisolvent addition is difficult to manipulate because of the high rate of crystallization. Bulk nucleation through cooling is a commonly used crystallization process, but it usually leads to a broad crystal size distribution. Previous studies have overcome this problem by introducing a different phase to segregate the solution into droplets and thus to confine the size of crystals to the diameter of the droplets.1 However, careful process design is required to achieve control over polymorphism at the same time.12 Seeding with the desired polymorph with crystals of a narrow size distribution is ideal. Previous studies have successfully produced crystal masses on a gram per minute scale in a continuously seeded, continuously operated tubular crystallizer,2 but in a continuous © XXXX American Chemical Society
crystallization process, continuous seeding of crystals with a narrow size distribution would require continuous milling. In view of these difficulties, continuous-contact secondary nucleation may offer a superior solution to this problem over other methods because of some of its intrinsic properties. Contact secondary nucleation is the generation of nuclei due to contact of existing crystals. The majority of the nuclei generated through contact secondary nucleation are under 20 μm.13−15 At a reasonable force, contact secondary nucleation is believed to be mainly triggered by microattrition of the parent crystal,13 and thus, the seed crystals often take on the same polymorph as the parent crystal, achieving control over polymorphism. In addition, contact secondary nucleation requires low supersaturation,16 which is often an advantage in industrial crystallizers. Such a continuous seeding device through contact secondary nucleation in which seed crystals were generated through grinding of a compressed tablet of the parent crystal powder has previously been described.4 However, grinding sometimes leads to disintegration of tablets due to shear. In this study, we improved upon this system by eliminating the shear force and retaining only the normal force exerted on the parent crystals. The improved setup resembles the contact apparatus from some previous studies where the contact energy imparted to the parent crystal was controlled by dropping a rod from a certain distance.17−19 The current setup automated such contacts at a controlled frequency. Special Issue: Engineering Contributions to Process Chemistry Received: July 10, 2014
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Contact secondary nucleation is dependent on several factors, including contact energy, supersaturation of solution, contact frequency, hardness of crystal surface, etc.16 A statistical design of experiment was carried out to gain a better and more quantitative understanding of how various factors impact contact secondary nucleation in this system. Supersaturation was maintained at a low level in this study to minimize the risk of clogging. Three factorscontact force, frequency, and areawere varied to quantify the effect of these factors on the nucleation rate and particle size distribution of the seed crystals generated. Both responses were characterized using in-line video microscopy of a segment of tube that seed crystals immediately entered after they were generated. In-line video microscopy is a powerful tool to monitor particles because of its ready availability and its capability to digitally capture sequences of images quickly. A wide range of information can be obtained from in-line video microscopy, including particle length, size, shape factors, etc.20 The objective of this study is to gain a quantitative understanding of a system where seed crystals are generated continuously by contact secondary nucleation. This would allow for better process control where one can target a precise response by manipulating factors investigated in this study.
Figure 2. Experimental setup. A supersaturated solution of diphenhydramine hydrochloride in isopropanol was pumped into a “nucleator” where seed crystals were generated by contacting the parent tablet of diphenhydramine hydrochloride. The solution containing seed crystals then flowed through a segment of glass tube that was observed and recorded by a microscope video camera.
opening of the nucleator allowed for the insertion of a stainless steel rod to make contact with the parent tablet. Four rods were machined to have the desired diameters of 0.2382, 0.3114, 0.4191, and 0.5265 cm. When making contacts, the rod was connected to the plunger of a linear solenoid via a shaft collar. The plunger was suspended on top with a spring onto a fixed object (not shown). The solenoid was connected to an external circuit composed of a power source with a variable output voltage and a solid-state relay controlled by LabView (National Instruments). The contact frequency was adjusted through LabView by controlling the on/off frequency of the circuit. The magnitude of the contact force was controlled by controlling the voltage output of the power source and monitored using the force gauge. As the solution containing seed crystals exited the nucleation stage, it was introduced into a short glass tubing section. This segment was fully submerged into water in order to match the refractive index of the content inside the tube with that of the medium outside the tube; this reduced the bending of light across the tube wall and enhanced the quality of the images obtained. Figure 3 shows examples of images obtained with a 2.5× objective lens. Statistical Design of Experiment. The three factors investigated in this study are the contact force (F), area (A), and frequency (f). The range of each factor was determined on the basis of past experience and knowledge of the system. The responses are the nucleation rate (B) and the crystal size distribution. Typically in design of experiment, one big experiment does not give the answer. Thus, this study adopted an “overlapping two-level factorial design” strategy that employed essentially two sets of two-level factorial designs with overlapping ranges of variables. With this design, a total of four levels for each factor was achieved, enabling one to construct a response surface model; at the same time, the second set of experiments did not push the physical limits of each factor too far from the first set to risk failing the entire set of experiment. On the basis of this design strategy, the run conditions were designed as shown in Table 1. Data analysis of this design of experiment was performed using Minitab 16 (Minitab). Response analysis. Recorded microscope videos were analyzed frame by frame, and when a particle passes through
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EXPERIMENTAL METHODS Materials. Diphenhydramine hydrochloride (DPH) (99%) was purchased from Alfa Aesar. ACS-reagent-grade 2-propanol (IPA) (≥99.5%) purchased from Sigma-Aldrich was used as the solvent. The parent tablet with a diameter of 6 mm and a thickness of 4.5 mm was directly compressed from commercial powder using a Gamlen tablet press (450 kg force, two compressions). Solubility. The solubility of DPH in IPA was measured using a combination of Crystal 16 (Avantium) and HPLC (Agilent), as shown in Figure 1.
Figure 1. Solubility of diphenhydramine hydrochloride in 2-propanol.
Experimental Setup. A general schematic of the setup is shown in Figure 2. A feed solution of 62 mg of DPH/g of IPA was delivered at a flow rate of 6 mL/min in PFA polymer tubing into the “nucleator”, where contact secondary nucleation occurred at 24.0 °C. The nucleator is a stage through which the solution was driven horizontally, as shown in Figure 2. In the middle of the stage, a vertical, cylindrical opening with a diameter of 7 mm allowed for the insertion of a stainless steel platform onto which the parent tablet was mounted. The platform was supported by a stainless steel rod whose bottom end was attached to a force gauge that could monitor the normal force exerted onto the platform in real time. The top B
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Figure 3. Sample microscope images of crystals generated by contact secondary nucleation flowing through the glass tube segment.
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RESULTS AND DISCUSSION Determination of Polymorph. The polymorph of the seed crystals was confirmed to be the same as that of the parent crystals, as shown by Raman spectra (see the Supporting Information). This is likely due to the fact that most of the seed crystals were generated by attrition from the DPH parent tablet and therefore inherited the polymorph of the parent crystals. Nucleation Rate. The cumulative number of particles passing through the segment of tube in the field of view was plotted as a function of run time for each set of run conditions (see the Supporting Information for plots). The nucleation rate at steady state for each run was determined from the slope of the linear portion of each plot. The time needed to reach the steady state was determined from the time required for the curve to become linear. The results are summarized in Table 2.
Table 1. Run conditions of the design of experiments run
F (±0.02 N)
A (cm2)
f (s−1)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.20 0.12 0.20 0.12 0.16 0.24 0.16 0.24 0.20 0.20 0.12 0.12 0.16 0.24 0.16 0.24
0.22 0.22 0.22 0.22 0.14 0.14 0.14 0.14 0.076 0.076 0.076 0.076 0.044 0.044 0.044 0.044
0.30 0.10 0.10 0.30 0.40 0.40 0.20 0.20 0.30 0.10 0.10 0.30 0.40 0.40 0.20 0.20
Table 2. Nucleation rate results for all runs
the segment of tube in the field of view, the time was recorded. The cumulative number of particles that have passed the segment of tube was then plotted as a function of time, and the slope of the linear portion of the figure is the nucleation rate at steady state. To analyze crystal size distribution, each frame of image containing particles was analyzed using ImageJ (open source image analysis software). The minimum caliper diameter of each particle was recorded. Since some particles appeared blurry in the images due to the line-by-line input nature of CMOS cameras, the particle size distribution was verified by filtering (0.2 μm pore size filter paper), drying and analyzing crystals under a polarized optical microscope. The polymorph of these collected crystals were also analyzed with Raman microscope (785 nm laser, Kaiser) and compared to that of the parent crystals. Replicates and Validation Run. Three replicates of a run selected at random were performed to obtain the uncertainty related to experimental error. The replicate conditions were identical to those of run 9. A validation run was performed to confirm that the model constructed could predict a random condition within the range of variables investigated. The condition of the validation run had a contact force, area, and frequency of 0.22 ± 0.02 N, 0.14 cm2, and 0.18 s−1, respectively.
run
time to reach steady state (s)
nucleation rate (s−1)
R2 value of the linear fita
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
42 33 negligible negligible 114 negligible 106 55 100 negligible negligible 106 101 negligible 30 negligible
0.66 0.56 0.59 0.58 0.55 0.57 0.47 0.52 0.49 0.38 0.35 0.45 0.46 0.49 0.35 0.41
0.999 0.998 0.999 0.999 0.996 0.999 0.999 0.998 0.997 0.999 0.999 0.996 0.998 0.998 0.997 0.997
a The R2 value shows the goodness of the linear fit to the linear portion of each curve after the steady state is established.
It can be seen that the temporal steady state was established quickly in this system, with all runs reaching a steady state within 2 min. Once the steady state was reached, the nucleation rate was fairly constant, as shown by the high linearity of the plots 2 min after the onset of the process. Furthermore, it should be noted that the nucleation rate fell in the range of one seed crystal generated every 2−3 s. The fact that the seed C
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probability plot produced an approximately straight line, indicating that all of the points come from a normal distribution.21 The histogram illustrates an approximately normal distribution of residuals produced by the linear model. The residuals were further plotted versus the value of the fitted response (Figure 4), and the plot produced a distribution of points scattered randomly about 0 regardless of the size of the fitted value. Finally, the independence of residuals over run numbers was confirmed by the run sequence plot in Figure 4, which shows that the residuals are independent of the order of observation, i.e., the order of runs. These analyses indicate that the residuals are indeed well-behaved. An interaction plot was produced, and it confirmed the absence of substantial interactions among the different factors (see the Supporting Information). On the basis of the above analysis, the linear model is deemed to be sufficient to describe the nucleation rate of the system:
crystals are spaced out is ideal for tubular crystals in decreasing the risk of clogging due to agglomeration. The nucleation rate was first analyzed in Minitab 16 assuming a full quadratic model with all two-way interaction terms. The p values obtained for various terms are listed in Table 3. This crude model showed that only the linear terms Table 3. p values of various terms in response surface models for the nucleation ratea p value factor
full quadratic model
linear model
F A f F2 A2 f2 F·A F·f A·f
0.014 0.000 0.001 0.902 0.623 0.523 0.722 0.891 0.088
0.002 0.000 0.000 − − − − − −
B = 0.166 + 0.456F + 1.28A + 0.365f
(1)
The adjusted R2 value of this model is 0.95, and the R2 value is 0.96. The nucleation rate model represented in 3D is shown in Figure 5. In the range investigated, the nucleation rate is linearly correlated with the contact force, area, and frequency. Previous studies have shown in that in agitated crystallizers the contact secondary nucleation rate is usually proportional to the third power of the propeller tip speed (i.e., the contact force).22−24 This system is different from an agitated crystallizer in that there are no random contacts between crystals and crystals and between crystals and walls, as is the case in a crystallizer. The contact in this case is well-controlled in terms of magnitude, direction, and frequency. In effect, this system parses out the effect of a single contact on the nucleation rate of contact secondary nucleation. Interestingly, the coefficient of contact area is more than twice that of either force or frequency, indicating that the contact area plays a more
a
A full quadratic model including all quadratic and interaction terms yielded only three statistically significant terms, indicating that the correct model should only encompass these three terms. Upon applying a linear model that only includes the three linear terms, all variables were found to be statistically significant.
were in fact statistically significant (p < 0.05). Therefore, a new model for the nucleation rate with only linear terms was tested. The p values for all three terms in the linear model are smaller than 0.002 (Table 3), indicating that they are statistically significant. To validate the assumption behind ANOVA and classical regression analysis that residuals should be well-behaved, the residual normality was checked by the normal probability plot and the residual histogram shown in Figure 4. The normal
Figure 4. Residuals of the response surface model comparing model-predicted and experimental values. D
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Figure 5. Response surface plot of nucleation rate as a function of contact force, area, and frequency.
Figure 6. Three replicates of run 9 were performed. The nucleation rates of the four replicates were within 3.5% of each other.
Although the model in this study came out to be linear with respect to all terms and there were no significant interactions among the factors, a design of experiment instead of the onevariable-at-a-time strategy was necessary because the latter strategy tacitly assumes that maximizing the response value with respect to one variable is independent of the level of others, which may not be the case. This model can be applied to the production of other compounds as well now that it has been revealed that the nucleation rate is linearly proportional to the contact force, area, and frequency. One only needs to determine the coefficients of the three factors in a certain range
important role in determining the nucleation rate for this system. The nucleation rate of three replicates of run 9 were analyzed and plotted in the same figure as the original run (Figure 6). The replicates are within 3.5% experimental uncertainty of each other. The validation run further confirmed the robustness of the model. Its cumulative number of crystals as a function of time is shown in Figure 7. The run conditions, predicted nucleation rate, and actual nucleation rate are summarized in Table 4. The actual value is within the experimental uncertainty of the nucleation rate predicted by the model. E
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The particle size distributions of the replicate runs and the validation run were similarly analyzed, and their d10, d50, and d90 statistics are shown in Table 6. They also fell into the same Table 6. Particle size distributions of the replicates and the validation run average size (μm) d10 d50 d90
Table 4. Validation run conditions and results compared to the model prediction nucleation rate (s−1) −1
F (N)
A (cm )
f (s )
predicted
exptl
0.22
0.14
0.18
0.511
0.503
and would be able to fine-tune the desired nucleation rate in this system for a new product. Another interesting feature of this system is that the parent tablet was not significantly consumed during the process: the tablet thickness measured over a course of 4 h of continuous production showed no reduction in thickness within an uncertainty of 0.5 mm. This finding agrees with those of previous studies.4 This is probably because as contact secondary nuclei are generated, the parent crystals are also growing in a supersaturated solution. This is an advantage for long-time continuous production. Crystal Size Distribution. The particle size distributions of each of the 16 runs were plotted (see the Supporting Information). All 16 runs seemed to give similar particle size distributions despite the different conditions, probably because all of the particles were generated by contact secondary nucleation and were thus directly “born into” sizes of under 20 μm. Because of such similarity, it was assumed for now that the particle size distributions were the same even under different run conditions. This allowed all of the particles (>1000 particles) to be combined together to generate a particle size distribution characteristic of this setup regardless of contact force, area, and frequency. This gave the statistics of d10, d50, and d90 as shown in Table 5. The tight range of these values indicates that the initial assumption that all run conditions gave similar particle size distributions is indeed valid.
replicate 3
validation
10 16 27
9 17 27
8 16 28
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CONCLUSION In the pharmaceutical industry, it is often desired to produce seed crystals with an appropriate narrow size distribution of the desired polymorph. The system described herein offers a solution to generate such crystals continuously on a small scale for tubular crystallizers at low supersaturation via contact secondary nucleation. The nucleation rate can be fine-tuned by changing the contact force, area, and contact frequency, as described in the quantitative response surface model obtained by statistical design of experiment. This model reveals that within a certain range the nucleation rate is linearly related to all three factors in this system. A combination of in-line video image analysis and off-line microscope image analysis was used to determine the particle size distribution of seed crystals obtained in this system, which was found to be narrow with a majority of the crystals under 20 μm. This seems to be a feature of contact secondary nuclei in general and does not vary much with different values of contact force, area, and frequency. Thus, this study shows that generating seed crystals with a narrow size distribution using contact secondary nucleation for a continuous tubular crystallizer can be realized in a controlled manner. Once these seed crystals are generated, they may be grown to larger sizes.
Table 5. Particle size distribution averaged across all 16 runs with an uncertainty range of two standard deviations (the size distributions of various runs were similar to each other) average size (μm) d10 d50 d90
replicate 2
10 17 26
range as for the 16 design of experiment runs, further confirming that the particle size distributions of seed crystals generated in this system follow the same trend. The particle sizes obtained from in-line microscope images were not identical to the real particle size distribution because some of the particles were out of focus and many had a long “tail” due to the nature of CMOS cameras, which convert light into electrons line by line and create a “snapshot” by piecing together those lines. These defects make the particles look bigger than they really are. To further confirm the particle size distribution of seed crystals generated in this system, the particles were filtered, dried, and analyzed under a polarized microscope. The images are shown in Figure 8. The particle size distribution obtained from this analysis, shown in Figure 9, indicates that the particles do actually have a narrow size distribution and that most of them are in fact under 20 μm. Future studies may focus on growing these seed crystals, generated at a constant and controllable rate with a narrow size distribution, to larger sizes using various previously studied methods.2,3,25 In the past, smaller inorganic crystals (
