Control of Polymorphism in Continuous Crystallization via Mixed

Article pubs.acs.org/crystal

Control of Polymorphism in Continuous Crystallization via Mixed Suspension Mixed Product Removal Systems Cascade Design Tsai-Ta C. Lai,† Jan Cornevin,‡ Steven Ferguson,† Nahan Li,† Bernhardt L. Trout,† and Allan S. Myerson*,† †

Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue 66-568, Cambridge, Massachusetts 02139, United States ‡ ETH Swiss Federal Institute of Technology Zurich, Institute of Process Engineering, Sonneggstrasse 5, Zürich 8092, Switzerland S Supporting Information *

ABSTRACT: Control of polymorphism of the enantiotropic p-aminobenzoic acid at either the α or β polymorph while maintaining high yield was achieved by mixed suspension mixed product removal (MSMPR) cascade design. A systematic approach was developed to identify the operational window of the process variables, stage temperature and residence time, in which the stringent polymorph purity criterion (>95 wt %) and high yield were met. The comprehensive understanding of the polymorphism of the model compound, p-aminobenzoic acid, was the key for the identification of the operational window. On the basis of single-stage MSMPR experiments, three temperature regimes thermodynamic control, energy barrier control, and kinetic competitionwere identified, and the interplay between the crystallization kinetics and the thermodynamics in each regime was elucidated. Experimental studies also demonstrated the first polymorph specific MSMPR for enantiotropic systems. Single-stage MSMPRs at low temperature, e.g., 5 °C, were found to be β polymorph-specific at steady states across multiple operating conditions. Two-stage MSMPR was designed to alter the polymorphism at the 5 °C stage from β polymorph-specific to α polymorph-specific. The first stage temperature was selected in the thermodynamic control regime (30 °C) at which the steady state polymorphism was α-specific. Feeding continuously to the second stage, the α crystals generated at the first stage increased the total surface area and thereby the secondary nucleation and mass deposition rates of the α polymorph in the 5 °C stage. This in turn increased the α polymorph from 0 wt % to at least 75 wt %, proving that it is feasible to control the polymorphism via design of the MSMPR cascade.

1. INTRODUCTION

yield and polymorph purity, for this system was identified based on simulation results. 1.1. Toward Continuous Crystallization. Control of polymorphism is studied intensively in batch systems, and it often requires seeding and a well-designed desupersaturation profile. In recent years, there has been increased interest in moving pharmaceutical manufacturing from batch to continuous processes due to economic and control benefits.2 This has resulted in a growing amount of studies, featuring subjects like MSMPR cascade design,3,4 evaporative liquid recycle,5 and membrane-based separation,6 to better understand and design continuous crystallization processes in order to achieve desired yield, purity, and CSD.7−11 Nevertheless, the same kind of systematic and comprehensive studies are nonexistent in the control of polymorphism in continuous crystallization. There are only a few studies touching on polymorphism in batch-like kinetic systems, and control strategies were briefly discussed based on these batch-like systems.12−15 True continuous

Polymorphism is one of the key control objectives, alongside yield, purity, and crystal size distribution (CSD), of pharmaceutical crystallization processes, directly impacting the drug product quality. Changing from one polymorph to another can cause variations in solid solubility, stability, crystal morphology and other important physical and chemical properties. These changes in properties can significantly affect the quality of the final product by influencing the bioavailability of the active pharmaceutical ingredients (APIs) and the drug processability in downstream processes, such as filtration, drying, and tableting.1 While continuous crystallization, notably, mixed suspension mixed product removal (MSMPR) systems, enjoys higher controllability2 compared to batch systems, an unexplored question is whether the desired polymorphism can be reached at steady state while optimizing other control variables. In this paper, using p-aminobenzoic acid as the model compound, we expanded our understanding of the polymorph dynamics in single-stage MSMPR and explored the efficacy of controlling the final polymorphism via MSMPR cascade design. The operational window, targeting © 2015 American Chemical Society

Received: April 3, 2015 Revised: May 26, 2015 Published: May 27, 2015 3374

DOI: 10.1021/acs.cgd.5b00466 Cryst. Growth Des. 2015, 15, 3374−3382

Crystal Growth & Design

Article

Figure 1. Illustration of a desupersaturation profile in steady state (a) PFR systems and (b) MSMPR systems.

systems can possess a residence time distribution kinetically as an arbitrary combination of a nonmixing PFR and a completemixing MSMPR. Thus, an in-depth understanding of polymorphism in both scenarios is crucial for the control of polymorphism. An interesting question to ask is how polymorphism in batch-like continuous systems differs from the complete-mixing MSMPR system. In batch-like kinetic systems, notably, PFR and oscillatory baffled crystallizers (OBCs), the residence time distribution is a delta function in space. This indicates that each point on the desupersaturation curve on the phase diagram, as depicted in Figure 1a, represents the crystallization condition at a certain position in the crystallizer. To control the steady state polymorphism of these batch-like kinetic systems, one approach is to have the initial segment of the tubular reactor as a nucleation segment with carefully controlled polymorphism of the birth crystals;16 while this might be difficult to achieve consistently, a more straightforward method is to provide an external continuous seeding source of the desired polymorph and restrict the primary nucleation inside the crystallizer.14,15 Contrary to the continuous dynamic curve on the phase diagram of batch-like systems, steady state MSMPR systems are discretized points on the phase diagram as illustrated in Figure 1b. At steady state, the existing crystals in the MSMPR crystallizer offer sites for secondary nucleation and are themselves the source of crystal birthin a way, providing a “self-seeding” mechanism. This is ideal for polymorph control and indicates an intrinsic stability of the steady state polymorphism of MSMPR systems. The key for controlling the polymorphism in steady state MSMPRs is to elucidate the kinetic competition of the polymorphs subject to the operating conditions, notably, stage number, temperature, and residence time. 1.2. Challenges and Proposed Solution. Previously, we conducted the first polymorph dynamic study in MSMPR systems.17 Using L-glutamic acid as a model compound, polymorph-selective single-stage MSMPRs were achieved. It was also demonstrated that although seeding may connect the startup state to one of the polymorphic pure steady states, this steady state might be unstablesmall disturbances can induce a steady state transition toward another state with a different polymorph composition. On one hand, this showed the robustness of the steady state polymorphism in MSMPR systems; on the other hand, the study also indicated that it can be difficult to achieve the desired polymorph in single-stage MSMPRs while optimizing other control variables, e.g., yield. Herein, we proposed that the steady state polymorphism of the final product can be controlled via design of MSMPR cascade. As illustrated in Figure 2, using a two-stage MSMPR as an example, the first stage is designed to produce pure crystals of the desired form at the steady state. The crystals are

Figure 2. Illustration of the proposed polymorph control methodology: two-stage MSMPR.

continuously fed to the second stage which is designed to achieve optimum yield. Because of the continuous feed stream from the first stage, there is a large surface area of the desired polymorph in the second stage, providing sufficient mass deposition and secondary nucleation to outcompete the growth and nucleation of the undesired form, and thereby control the polymorphism at the final stage.

2. EXPERIMENTAL SECTION 2.1. Materials. The model compound selected in this paper is paminobenzoic acid. The compound has two polymorphs, α and β form, which are enantiotropic. The α polymorph is the commercial form, and it is the most stable polymorph above the transition temperature at 15 °C.18 The β form, the most stable form below the transition temperature, is relatively difficult to obtain under batch crystallization.19 It can only be produced at very slow supersaturation generation either in water or in ethyl acetate at low temperature.20 Water is selected as the solvent for this study. The α form paminobenzoic acid (>99% pure) was obtained from Sigma-Aldrich, St. Louis, USA. Pure β crystals were initially produced from slow cooling of aqueous p-aminobenzoic acid solution with a concentration of 5.5 g/kg solvent from 65 to 5 °C. Both polymorphs nucleated after the solution cooled to approximately 10 °C. Solvent mediated transformation to the β polymorph was completed after 2 days. More β crystals were created by seeded batch crystallizations of these β crystals. The crystals polymorphism was verified by X-ray powder diffraction (XRPD) which has a detection limit of 5 wt %. The XRPD patterns and the optical microscope images of the two polymorphs are shown in Figures 3 and 4, respectively. The α crystals are needles, whereas the β crystals are prismatic.

Figure 3. X-ray powder diffraction patterns of (a) the α polymorph and (b) the β polymorph. 3375



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β form in a finite amount of time. An equilibrium state with pure β polymorph was achieved using initial seeding of the β crystals. As hitherto mentioned, control of polymorphism in batch crystallization depends on both the desupersaturation profile (e.g., the cooling rate) and the seeding condition. 2.4. Continuous Crystallization Experiment. Cooling crystallization was performed using the MSMPR platform described previously. Single-stage MSMPR experiments were conducted to determine the steady state polymorphism at various operating conditions each with different stage temperature, residence time, and feed concentration. During startup, the MSMPR crystallizers were seeded with either pure α or β crystals. The system was held as a batch for 1−2 h before initiating the intermittent withdrawal scheme. Steady state was reached in 6−8 residence times. Upon reaching the steady state, the stability of the particular state was evaluated by the addition of crystals opposite to the dominant polymorph at that state. If the polymorphism at the steady state is metastable, a steady state transition toward the stable steady state which has a different polymorphic composition would be observed. Two-stage MSMPR experiments were designed based on the results obtained from the single-stage MSMPRs. The objective herein was to obtain both α and β polymorph-specific steady states where the second stage temperature was at 5 °C and under a fixed total residence time. This was achieved by manipulating the operating conditions of the first stage. 2.5. Liquid and Solid State Characterization. The mother liquor concentration in MSMPR crystallizer was measured using Fourier transform infrared spectroscopy (FTIR). The liquid samples were obtained by filtering the slurry and were heated up to 70 °C before measuring offline using the FlowIR instrument from Mettler Toledo. The characteristic peak at 1179 cm−1 was used for the solute concentration measurement. The calibration curve for solute concentration of p-aminobenzoic acid is presented in Figure 6a. The

Figure 4. Optical microscope image of (a) the α polymorph and (b) the β polymorph. 2.2. Experimental Setup. The MSMPR system was designed using an intermittent withdrawal scheme.21 The working volume of the glass-jacketed crystallizer (VWR international) was set to be 150 mL and controlled by the position of the outlet. The agitation rate was fixed at 300 rpm using an overhead mechanical stirring (IKA), and the crystallizer temperature was controlled by an internal temperature control system (Thermo Scientific SC100-A25). In a two-stage MSMPR system, as illustrated in Figure 5, the residence time of

Figure 5. Illustration of a two-stage MSMPR system. each stage was determined by the feed flow rate of the first stage and the slurry volume of the crystallizers. The flow between the two stages also utilized the intermittent withdrawal schemeeach withdrawal took away 10% of the slurry volume every one tenth of a residence time. This removal scheme ensured that there was no size classification upon withdrawal. 2.3. Batch Crystallization Experiment. Batch cooling crystallization was carried out with the same vessel (300 mL glass-jacketed crystallizer) used for the MSMPR experiments. An aqueous paminobenzoic acid solution with a concentration of 10 g/kg solvent was prepared by dissolving the commercial α form p-aminobenzoic acid in deionized water at 65 °C. The clear solution was then crash cooled in the batch to the set-point temperature5 or 30 °C. No primary nucleation was observed until the temperature reached the set-point. The batch was held until equilibrium while liquid and solid samples were taken every 2−3 h. As presented in Table 1, without seeding, only the α polymorph was detected in the 30 and 5 °C batch experiments. These results were expected, albeit the β form was the most stable polymorph at 5 °C since the α form was kinetically more favorable during primary nucleation especially under fast cooling conditions. With limited primary nucleation of the β crystals, the system could not undergo solvent mediated transformation toward the

Figure 6. Calibration curve of (a) solute concentration measurement based on the infrared peak at 1179 cm−1 and (b) β polymorph mass ratio using the XRPD peak at 2θ = 20.21° normalized to the peak at 2θ = 9.70°. polymorphism of the solids was characterized by X-ray powder diffraction (XRPD). The measurement was conducted offline using the PANalytical X’Pert PRO Theta/Theta powder X-ray diffraction system with a monochromatic Cu Kα radiation source and nickel filter (λ = 1.5418 Å). The characteristic peak of the α polymorph at 2θ = 9.70° was used as an internal standard to normalize the β form characteristic peak at 2θ = 20.21°. The normalized peak was calibrated against the standard samples prepared by mixing pure α and β crystals. The calibration results are presented in Figure 6b. The detection limit for XRPD was identified to be 5 wt %. The particle sizes of the solids were monitored online via the focus beam reflectance measurement (FBRM) from Lasentec which tracks the evolution of the chord length distribution (CLD). The Lasentec S400 probe was used in this study.

Table 1. Experimental Results from Unseeded and Seeded Batch Crystallization batch experiments temperature (°C) initial concentration (g/kg solvent) startup condition equilibrium results ML concentration (g/kg solvent) polymorphisma

30 10 unseeded

5 10 unseeded

5 10 β seeded

6.01 pure α

2.47 pure α

2.19 pure β

3. EXPERIMENTAL RESULTS 3.1. Polymorph Dynamic in Single-Stage MSMPR Systems. Cooling crystallization experiment in single-stage MSMPR crystallizer was conducted on the aforementioned platform. The stage temperature was selected to be 5 °C, a relatively low temperature, to represent the scenario where

a

The polymorph purity is based on the results from XRPD which has a detection limit of 5 wt % 3376



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steady states were the only stable states achieved in the 5 °C MSMPRs. The experimental finding herein highlights the differences between batch and MSMPR systems. Recall that in 5 °C batch crystallization, the β crystals were not attainable when the cooling rate was not slow enough albeit they were the most stable form at this temperature. This was because fast desupersaturation after the first formation of the α needles limited the chances of primary nucleation of the β polymorph. For a batch system, the β crystals must form somewhere on the continuous dynamic path (as illustrated in Figure 1) in order for the system to undergo solvent mediated transformation toward the pure β states. On the contrary, in steady state MSMPR systems, the crystallization process is represented by discrete dots on the phase diagram. The stable steady state conditions are independent of the seeding condition and are usually achievablewithout the need for specially designed startup process. The steady state polymorphism depends solely on the kinetic competition between the two polymorphs subject to the residence time distribution. Therefore, states that are difficult to attain in batch may be obtainable in the MSMPR framework. In the case herein, the previously hard-to-achieve pure β form states were easily, reliably, and consistently reached. 3.2. Temperature Effect. Similar single-stage MSMPR experiments were conducted at different temperatures. Variation in stage temperature affected the polymorph dynamics by changing the solubility and the Arrhenius activation energy term (energy barrier) of each polymorph and thereby altered the relative growth and nucleation kinetics between the polymorphs. In principle, the higher the temperature, the more the molecular kinetic energy dominates, and thus the smaller the effect of the energy barrier of growth and nucleation would impose on the kinetic rates. Therefore, it is expected that the most stable polymorph with lower solubility would be more favorable in single-stage MSMPR at high temperature due to its larger thermodynamic driving force. In the case of p-aminobenzoic acid, the α polymorph was expected to be the dominant form at a temperature sufficiently higher than the transition temperature. This temperature range is illustrated in Figure 8 as the thermodynamic control regime.

optimal yield was achieved. The feed was prepared at 65 °C with a solute concentration of 10 g/kg solvent. The feed flow rate was controlled at 2.5 mL/min, giving a stage residence time of 60 min. During startup, the crystallizer was seeded with the commercial α crystals and ran as a batch for 1 h before initiating the MSMPR run. Solid and liquid samples were collected approximately every residence time and measured offline using XRPD and FTIR to determine the polymorph dynamics. As illustrated below in Figure 7, initially, the α

Figure 7. Evolution of the solute concentration and polymorphism of the 5 °C MSMPR from the startup state (seeded with α crystals) to the β polymorph specific steady state.

polymorph was the dominant form due to the secondary nucleation from the α seeds. However, the mass deposition and nucleation rate of the α crystals were not high enough to sustain the α polymorph dominant state, and an increasing amount of β crystals was observed. The initial β crystals were formed during the first residence time possibly from primary nucleation. The following secondary nucleation and growth of these new-born β crystals outcompeted the α crystals kinetically, and therefore, the β polymorph became the dominant solid form at steady state. No α crystals were detected at steady state according to XRPD measurements. The MSMPR experiment was repeated with β seeding. As summarized in Table 2 (expt 2), the same steady state polymorphism was reached regardless of the seeding conditions. This result indicated that the β-specific steady state was stable under this particular operating condition. In fact, within the operating range of the residence times and the feed concentrations in the experiments, β polymorph specific Table 2. Experimental Results from the 5 °C Seeded Cooling Crystallization of p-Aminobenzoic Acid in Single Stage MSMPR under Various MSMPR Residence Times and Feed Concentrations single stage MSMPR (5 °C, seeded) residence time (min) feed concentration (g/kg solvent) seed polymorph steady state results ML concentration (g/kg solvent) polymorphisma

expt 1

expt 2

expt 3

expt 4

60 10

60 10

120 10

60 5.5

α form

β form

β form

β form

2.84

2.83

2.43

2.58

pure β

pure β

pure β

pure β

Figure 8. Temperature regimes on the phase diagram of the enantiotropic p-aminobenzoic acid.

However, as the stage temperature approaching the transition point (15 °C), the difference between the thermodynamic driving forces of the two polymorphs diminishes. Thus, in this temperature region, the relative energy barriers of crystal growth and nucleation between the polymorphs determine which polymorph is more favorable. The form possessing the lowest energy barrier is more likely to be the dominant form at steady state. Note that the ratio of the Arrhenius prefactor

a

The polymorph purity is based on the results from XRPD which has a detection limit of 5 wt %. 3377



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MSMPR cascade design. For simplicity, a two-stage MSMPR system was studied. As illustrated in Figure 9, the first stage

between the polymorphs also plays an important role herein. This temperature region is represented by the energy barrier control regime in Figure 8. Moving toward lower temperature on the phase diagram, the system has both the energy barriers and the thermodynamic driving forces of the polymorphs playing crucial roles in determining the steady state polymorphism. Complete calculation of the relative growth and nucleation rates between the polymorphs is required to predict the steady state polymorph ratio. This is described as the kinetic competition regime in Figure 8. Since low temperature is desired for achieving high yield in cooling crystallization processes, the final stage temperature of a continuous crystallization process is likely to reside in this kinetic competition regime. Given the intrinsic complexity of the competing kinetics in this regime, it is not straightforward to design the MSMPR system in order to obtain the desired polymorph while achieving optimal yield. To validate the above assertions, single-stage MSMPR experiments were conducted at different temperature regimes and their results are presented in Table 3. As expected, at

Figure 9. MSMPR cascade design for obtaining α polymorph specific steady states at the final stage.

MSMPR was selected at a sufficiently high temperature, within the thermodynamic control regime, to guarantee achieving an α form specific steady state. The second stage was thus continuously fed with the desired α crystals. This increased the total surface area of the α crystals and thereby increased the secondary nucleation rate as well as the mass deposition rate of the α crystals in the 5 °C second stage MSMPR. We hypothesized that the high surface area of the α crystals resulting from the continuous inflow from the first stage could help the α polymorph to outcompete the β polymorph kinetically at steady state, leading to an α form specific steady state. The two-stage MSMPR experiment was conducted using the setup illustrated in Figure 5. The first stage temperature was set to be 30 °C, far away from the transition point, at which the α polymorph was the only form detectable at steady state. The temperature of the second stage was set at 5 °C, the same as the single stage experiments. The feed concentration was prepared as 10 g of solute/kg of solvent at 65 °C. The residence time in each stage was controlled at 60 min, and the agitation rate was fixed at 300 rpm The commercial α crystals were added in both stages initially. The experimental results are summarized in Table 4. Steady state was reached after two to three residence times. The steady state polymorphism was identified to be pure α form in both stages. The steady state was maintained for another four residence times, and there was no tendency of steady state transition. Subsequently, the polymorph stability of the steady

Table 3. Experimental Results of Single Stage MSMPR with Various Stage Temperatures single stage MSMPR stage temperature (°C) residence time (min) feed concentration (g/kg solvent) steady state results ML concentration (g/kg solvent) polymorphisma

expt 1

expt 5

expt 6

expt 7

5 60 10

15 60 10

20 60 10

30 60 10

2.88 pure β

4.37 pure β

4.89 pure α

6.73 pure α

a

The polymorph purity is based on the results from XRPD which has a detection limit of 5 wt %.

temperatures sufficiently higher than the transition temperature (expt 6 and expt 7), i.e., in the thermodynamic control regime, the most stable α form was the dominant polymorph at steady state. While at the transition temperature (expt 5) where the thermodynamic driving forces of the two polymorphs were the same, it was observed that the β polymorph was the dominant solid form at steady state, indicating that the β polymorph is kinetically more favorable. Note that this does not necessarily mean that the β polymorph has a lower energy barrier for both crystal growth and nucleation. As identified in a later section (Table 5), the β polymorph has a lower energy barrier for crystal growth but a higher barrier for nucleation. It is the combined effect of the energy barriers and prefactors of crystal growth and nucleation on the relative kinetics that makes the β form the favorable polymorph. Moving toward lower temperatures, e.g., 5 °C, the dominant polymorph at steady state under various operating conditions is still the β polymorph. It is kinetically favorable and the most stable form. This finding highlights a potential issue of single-stage MSMPR systems in which it is possible that the desired polymorph, say the commercial α form p-aminobenzoic acid, is not the dominant polymorph at optimal yield conditions, notably at low temperatures. 3.3. Polymorph Control by MSMPR Cascade Design. As the β polymorph is the dominant solid form in 5 °C singlestage MSMPR experiments, we herein explored the possibility to control the steady state polymorphism at the pure α form via

Table 4. Polymorphism of the 30 °C → 5 °C MSMPR Cascade two stage MSMPR stage no. stage temperature (°C) residence time (min) feed concentration (g/kg solvent) startup condition steady state results ML concentration (g/kg solvent) polymorphisma

1 30 60 10

2 5 60

stability test 1 30 60 10

pure α seeds

2 5 60

from previous S.S. with the addition of β crystals

6.82

2.81

6.71

2.78

pure α

pure α

pure α

75 wt % α crystals

a

The polymorph purity is based on the results from XRPD which has a detection limit of 5 wt %.

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state was examined by introducing a disturbance of β crystals in both stages at steady state (approximately 200 mg of β crystals is added to the 150 mL slurry in each stage). Interestingly, it was found that the polymorphism of the first stage returned to the α form specific state after several residence times; nevertheless, a state transition was observed in the second stage, and the final polymorphism was measured to be approximately 75 wt % of α crystals. This state transition indicates that the original α-specific steady state in the second stage was actually metastable. This metastable state was able to be sustained for a long period of time because the first stage had a stable steady state with pure α polymorph, and the concentration in the second stage was sufficiently low to limit primary nucleation of β crystals. Namely, no β crystal disturbance occurred throughout the experiment until we manually added the β crystals. These experimental findings showed that it is possible to control the steady state polymorphism of the final stage by designing a MSMPR cascade system which generated sufficient surface area of the desired polymorph in the initial stages and thereby facilitated the kinetic competition of the desired form against the undesired forms in the final stage. Compared to the single-stage experiments, the α polymorph ratio was increased from 0 wt % to at least 75 wt %. The results affirmed the feasibility to achieve both optimal yield and the desired polymorphism in MSMPR systems via cascade design, which is discussed in detail in a later section. We would also like to note that a similar strategy can be applied in monotropic polymorphic systems.

rate is calculated from the growth rate multiplied by the total crystal surface area. The initial condition of the concentration is measured right before initiating the MSMPR. Ci ,in − Ci dCi 1 = − τi dt 2

∂t

+ Gi , j

∂ni , j ∂x

=

ni − 1, j − ni , j τ

∂ni , j ∂t

+ Gi , j

∂ni , j ∂x

=−

ni , j τ

Gi , j = kg 0, j

Bi , j = kb0, j

ni , j (t , x = 0) =

ni , j ·x 2 dx (4) (5)

⎞g ⎛ Eg , j ⎞⎛ C exp⎜ − − 1⎟⎟ ⎟⎜⎜ ⎝ RT ⎠⎝ Csat, i , j ⎠

(6)

⎞b ⎛ E b , j ⎞⎛ C exp⎜ − − 1⎟⎟ MT2/3 ⎟⎜ ,i,j ⎝ RT ⎠⎜⎝ Csat, i , j ⎠

(7)

(1)

(i = stage no. = 1, j = α , β)

Figure 10. Tracking the evolution of crystals growth of the seed crystals and the new-born crystals using the Lagrangian-based method of characteristics.24,25

characteristic lines are introduced as the smallest sized characteristic curve grows to the largest nuclei size, r0. The simulation is completed when steady state is reached. The numerical methods, e.g., discretization and nuclei size distribution, used herein are detailed in the Supporting Information. The Lagrangian approach was proposed and described in more detail in Aamir et al. (2009)24 and Nagy et al. (2011).25

(2)

Bi , j Gi , j

∞

where kg0,j and kb0,j are the pre-exponential factors, Eg,j and Eb,j are the energy barrier for growth and nucleation, Csat,i,j is the polymorph solubility at the given temperature and MT,i,j is the total solid mass per crystallizer volume of a specific polymorph. The partial integral-differential equations were solved numerically using the method of characteristics. This discretization method finds the curves on the x-t hyperplane, or characteristic curves, along which the PDEs can be converted to a family of ODEs.22,23 On the basis of the Lagrangian framework, the evolution of the crystals, either from the seeds or nuclei, is determined by solving the ODEs coupled with the mass balance equation, as illustrated in Figure 10. New

where ni,j (t,x) is the number density distribution of polymorph j in stage i, x represents the crystal size, G is the sizeindependent crystal linear growth rate, and τ is the residence time of the MSMPSR crystallizer. The initial and boundary conditions of the partial differential equations are as follows. The initial crystal size distribution is predetermined by the seeding condition. The boundary condition is determined by the ratio between the nucleation rate and the crystal growth rate. ni , j (t = 0, x) = ni , j ,seed

j=α ,β

∫0

where Cin is the feed concentration, and ρ is the crystal density and is assumed to be the same for both polymorphs (1370 kg/ m3). The surface area of the crystals is derived from the second moment of the crystals and the surface shape factor, kS. The surface shape factor of the α needles is set as 0.88 (with kS/kV = 4.2) and that for the β prism is 2 (with kS/kV = 5). As represented in eqs 6 and 7, the crystal growth rate, G, was assumed to be size-independent and surface integration dominated. The nucleation rate, dominated by secondary nucleation, was estimated by the semiempirical equation. It is a function of supersaturation and the magma density in the crystallizer.

(i = stage

no. > 1 , j = α , β)

ρGi , jk S, j

Ci(t = 0) = C i,0

4. DYNAMIC SIMULATION 4.1. Model Equations. The mathematical modeling for single stage MSMPR system was described in detail in our previous work.17 One dimension population balance model was introduced to describe the crystallization of p-aminobenzoic acid polymorphs in each stage. The governing equations are presented below. ∂ni , j

∑

(3)

The population balance equations of the two polymorphs are coupled by the total mass balance of p-aminobenzoic acid, in solid and liquid states. As described in eq 4, the mass deposition 3379



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4.2. Parameter Estimation. The kinetic parameters for crystal growth and nucleation of the two polymorphs were fitted against the steady state crystal size distribution and mother liquor concentration of both single-stage and two-stage MSMPR experiments. As mentioned previously, single-stage MSMPR at 20 and 30 °C contained only α crystals at steady state, and thus the steady state data of which were used to estimate the kinetic parameters of the α polymorph. In the twostage MSMPR experiment (30 °C → 5 °C), metastable steady state with pure α polymorph was achieved and was maintained for several residence times. The steady states in both stages were sufficiently stable to be used for parameter estimation. As for the β polymorph, single-stage MSMPR experiments conducted at 5 °C under various operating conditions (as listed in Table 1) along with the MSMPR at 15 °C were used to estimate the kinetic parameters. The estimated parameters of the two polymorphs are reported in Table 5. Some of the fitting results are shown in Figure 11 and detailed in the Supporting Information.

assess the feasibility to meet this stringent polymorph purity requirement while maintaining high yield. Herein, a two-stage MSMPR system was simulated with the total residence time fixed as 120 min, feed concentration of 10 g of solute/kg of solvent, and the final stage temperature at 5 °C. The operating variables were the temperature of the first stage and the residence time assigned to the first stage, which is represented by RT% (τstage/τtotal × 100%). As illustrated in Figure 12a, with

Figure 12. Yield (relative to the equilibrium batch) and α polymorph purity in the final stage (5 °C) as a function of (a) the residence time assigned to the first stage (30 °C) and (b) the temperature of the first stage.

Table 5. Estimated Parameters for Crystal Growth and Secondary Nucleation of p-Aminobenzoic Acida

a

parameter

α form

β form

kg0 (μm/min) Eg (kJ/mol) g (−) kb0 (#/(m3·min)) Eb (kJ/mol) b (−)

(2.30 ± 1.84) × 1010 54.04 ± 1.93 1.02 (5.54 ± 4.43) × 1010 23.20 ± 2.41 2.285

(2.62 ± 2.41) × 107 38.53 ± 2.22 1.08 (1.34 ± 1.23) × 1020 72.15 ± 2.77 2.396

the first stage temperature fixed at 30 °C, it was found that the more the residence time assigned to the first stage, the higher the α polymorph purity in the final stage. This is not surprising since the first stage at 30 °C was more selective toward the α form. Nonetheless, since the solubility at higher temperature was higher, the overall mass deposition decreased with more residence time distributed in the first stage. Hence, there was a trade-off between the polymorph purity and the yield. Note that the yield was calculated as a relative value to the yield of the equilibrium batch at 5 °C. In another case study, the residence time in the first stage was fixed at 60 min (50 RT%), and the first stage temperature was relaxed. As shown in Figure 12b, the α polymorph purity in the final stage was found to increase with decreasing temperature in the first stage from 30 to 20 °C. The final α polymorph purity then dropped significantly as the temperature approached the transition point at 15 °C. The yield in the final stage remained somewhat the same. The simulation results indicated the choice of the first stage temperature to be around 20 °C in order to achieve both high yield and α polymorph purity in the final stage; however, it

With 95% confidence interval.

4.3. Dynamic Simulation. Our experimental studies demonstrated the possibility to control polymorph purity while achieving high yield by applying the MSMPR cascade design. Moving from single-stage to two-stage MSMPR, the mass ratio of the desired polymorph (α form) at the final 5 °C stage increased from 0 wt % to 75 wt %. Nevertheless, the criterion for polymorph purity is more stringent in practice. The mass ratio of the desired polymorph should be more than 95 wt %; i.e., the amount of undesired polymorph presence should be undetectable under XRPD. Upon the basis of the fitted kinetic parameters, dynamic simulation was utilized to

Figure 11. Fitted crystal size distribution of (a) α polymorph-specific steady state MSMPR (20 °C and residence time of 60 min) and (b) β polymorph steady state MSMPR (15 °C and residence time of 60 min). 3380



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Figure 13. Contour plots of (a) yield and (b) α polymorph purity in the second stage MSMPR using the two operating parameters, temperature in the first stage and the residence time assigned to the first stage.

compete kinetically against the β polymorph as much in the second stage. Hence, the final α polymorph purity decreased. The aforementioned observations on how the two operating variables influenced the final yield and α polymorph purity were slightly complex, and it was still unclear what choice of the residence time and the temperature in the first stage would render the optimal yield and satisfactory α polymorph purity (>95 wt %). To find out this operational window, the white contour lines of the final α polymorph purity were overlapped with the contour plot of the final yield as shown in Figure 14.

is still unclear on the optimal choice of residence time and temperature in the first stage when both variables are relaxed. Contour plots of yield and α polymorph purity in the second stage MSMPR were constructed using the two operating variables, residence time and temperature in the first stage, as shown in Figure 13, to identify the optimal operating conditions. The total residence time was fixed at 120 min, and the final stage temperature was set at 5 °C. As what we discussed previously, since the thermodynamic driving force was larger at low temperature, the final yield was higher when the temperature in the first stage was lower or the residence time in the first stage was smaller, as illustrated in Figure 13a. Optimal yield is located on the lower left corner of the contour plot. The relationship between the final α polymorph purity and the two operating variables was less straightforward. There seems to be a “sweet spot” for optimal α polymorph purity on the middle right of the contour plot, as shown in Figure 13b. Let us discuss this in more detail. In the contour plot, at fixed temperature the α polymorph purity in the second stage was found to increase when more residence time was assigned to the first stage. This is because the first stage polymorphism was more selective toward the α form; hence the longer the residence time in the first stage, the higher the final α polymorph purity. This trend was less obvious when the temperature approached the transition temperature at 15 °C since the steady state conditions in the first stage at these temperatures favored the β polymorph. In addition, it was found that with fixed residence time in the first stage, the final α polymorph purity peaked when the first stage temperature approached 20 °C. The decrease in the final α polymorph purity when temperature decreased from 20 to 15 °C can be explained by the same cause mentioned earlierthe system favored the β polymorph near the transition temperature. However, the α polymorph purity of the final stage was also found to decrease as the temperature increased from 20 to 35 °C even though the α polymorph purity in the first stage was higher at higher temperature. This was because that the total crystal mass deposition decreased with increasing temperature due to higher solubility. The total amount of α crystals generated in the first stage decreased as the temperature increased from 20 to 35 °C even though the α polymorph purity was actually higher. With less surface area of the α crystals in the second stage, the α polymorph could not

Figure 14. Overlapping the contour plots of yield and α polymorph purity to identify the operational window.

To achieve high yield (>90%) and suffice the polymorph purity criterion, the operating variables should be selected within the shaded region (gray triangle). Optimal yield can be achieved with operating conditions controlled in the vicinity of the lower left corner of the triangle. The operational window provides a range of combinations of the operating variables that can be further optimized to target other control objectives such as crystal size distribution, process response time, and startup time. It also provides crucial information on whether these control objectives are attainable. For example, assuming that one objective is to have the mean crystal size controlled at 300 μm, there is a possibility that this objective cannot be satisfy within the operational window, indicating that such objective is 3381



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ACKNOWLEDGMENTS We acknowledge the Novartis-MIT Center for Continuous Manufacturing for funding and technical guidance.

contradictory to the targets for yield and polymorph purity. It is also worth mentioning that by increasing the number of stages in the MSMPR cascade system, one can expand the range of the operational window.

5. CONCLUDING REMARKS This paper presents the first systematic approach for designing MSMPR cascade operation to control polymorphism. Using paminobenzoic acid as the model compound, the polymorph dynamics in single-stage MSMPR was elucidated. Three temperature regimesthermodynamic control, energy barrier control, and kinetic competitionwere identified, and the interplay between the crystallization kinetics and the thermodynamics in each regime was discussed. The β polymorph was found to be the dominant polymorph at steady state in single-stage MSMPRs below the transition temperature at 15 °C, while the α polymorph was the dominant form above this temperature. This is the first reported study of polymorphspecific MSMPR for enantiotropic systems. This work highlights the potential benefit in polymorph control when moving from batch to continuous systemthe previously hardto-attain pure β polymorph states in batch were easily and reliably achieved in the MSMPR system. However, it also showed that there could be a limitation for polymorph control when operating in single-stage MSMPR systems. In this particular case, we might lose the flexibility to attain α polymorph-specific steady state at low temperatures. Moving beyond single-stage MSMPRs, the feasibility of controlling polymorphism at the α form below the transition temperature via the MSMPR cascade design was examined. With the final stage remaining at 5 °C, the α polymorph ratio was successfully increased from 0 wt % to at least 75 wt % (100 wt % if starting with pure α seeds) using a well-designed two-stage MSMPR system. The first stage was selected at 30 °C, at which the system was α polymorph specific, to provide a continuous flow of α crystals to the second stage. The increase in the total surface area of the α crystals accelerated the secondary nucleation and mass deposition rates of the α polymorph in the second stage, facilitating the kinetic competition of the α polymorph against the β polymorph. A complete study of the effect of the temperature and residence time in the first stage on the final yield and α polymorph purity allows the identification of the operational windowin which the stringent polymorph purity constraint (95 wt %) was sufficient and high yield was achieved. Further optimization of other objectives, such as crystal size distribution, process response time, and startup time, can be studied in this operational window.

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ASSOCIATED CONTENT

S Supporting Information *

Polymorph mass content measurement calibration, parameter estimation results. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ acs.cgd.5b00466.

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*Phone: 617-452-3790. Fax: 617-253-2072. E-mail: myerson@ mit.edu. Notes

The authors declare no competing financial interest. 3382


Control of Polymorphism in Continuous Crystallization via Mixed

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