Antisolvent Crystallization of Biapenem: Estimation of Growth and

Article pubs.acs.org/jced

Antisolvent Crystallization of Biapenem: Estimation of Growth and Nucleation Kinetics Yang-Hui Luo, Guo-Gan Wu, and Bai-Wang Sun* Crystallization Process and Control Laboratory, College of Chemistry and Chemical Engineering, Southeast University, Nanjing 211189, P. R. China ABSTRACT: A process mathematic model of seed batch desupersaturation experiments and induction time experiments for the investigation of growth and nucleation kinetics of biapenem through an antisolvent procedure in water/ethanol (antisolvent) system was developed in this work. The kinetic parameters for growth and nucleation were estimated by using in situ technology: attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy for solute concentration, focused beam reflectance measurement (FBRM) for CLD moments, and particle vision and measurement (PVM) for particle image measurement. The challenging aspect for the development of this model was the recovery of crystal size distributions (CSDs) from the chord length distribution (CLD) moments; batch experiments were designed for the estimation of this relationship. The mathematic model in this work was confirmed by a comparison between model predictions and experimental data. or batch experiments.11−13 While the kinetics of agglomeration and breakage often determined by construct accurate models.14,15 For antisolvent crystallization process, the four mechanisms are all exist under most conditions, but the main mechanisms are nucleation and growth; the existence of agglomeration and breakage can be estimated by a specific range of volume shape factor of crystals.16−19 There have many reported techniques for the measurement of nucleation and growth rates. Garside and Mersmann20 have made an overview of this. Jochen et al10 combined in situ attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy and focused beam reflectance measurement (FBRM) to monitor the growth kinetic of L-glutamic acid ((S)-2-aminopentanedioic acid) by using seeded batch desupersaturation experiments and employed population balance modeling as well as an optimization routine. Regarding antisolvent crystallization, Garside and Mersmann also successfully employed the same method to measured the growth kinetic of PDI 747 (2[[1-[3,5-bis(1-methylethoxy)phenyl]-3-ethyl-7-methoxy-6isoquinolinyl]oxy]-ethanol) and used this growth kinetic to calculate the nucleation rate through antisolvent induction time experiments.21 In addition, Granberg22 and co-workers investigated the influences of solvent composition on the crystallization kinetics of paracetamol in acetone−water through antisolvent process, Zhou23 and co-workers designed a new approach for antisolvent crystallizations through feedback control. In these works, the volume of antisolvent, the quantity of seed crystal, the addition rate of antisolvent, the

1. INTRODUCTION Crystallization process is a wildly used technology in pharmaceutical and fine chemical industry for purification and obtaination of particulate products. It is of significant importance because such properties as the polymorphic form, crystal size distribution (CSD), and crystal habit are determined by it.1 For pharmaceutical solids, these properties have close correlation with dissolution rates, bioavailability, or drug delivery.2 It has been suggested that in the pharmaceutical industry, more than 80 % products are obtained through at least one crystallization step to get desired quality.3 So, the knowledge of the kinetics of dominated mechanisms of crystallization process is of significant importance. Crystallization process contains many methods: cooling, evaporation, reactive, pH control, and antisolvent.4 Cooling and evaporation methods require remarkable solubility changes with temperature and certain thermal stability of the compounds; the successive separation between phases can be obtained by change temperature. But this is not suitable for antisolvent crystallization process.5 Antisolvent crystallization is a time-saving method which depends on the distinction of different solubilities in two different solvents. The addition of specific substances (solids, liquids (antisolvents), or gases) to the initial solution leads to the decrease of the solute solubility, which creates supersaturation consequently.6−9 It is especially suitable for the separation of solutes from multicomponent solutions.9 The fundamental mechanisms in crystallization process involves nucleation, growth, agglomeration, and breakage, which determine the particle size distribution, shape, and polymorphic form of the crystallized product.10 The kinetics of nucleation and growth can be obtained by a train of continuous © 2013 American Chemical Society

Received: September 15, 2012 Accepted: January 16, 2013 Published: February 28, 2013 588

dx.doi.org/10.1021/je3011997 | J. Chem. Eng. Data 2013, 58, 588−597

Journal of Chemical & Engineering Data

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measurement (FBRM), and lasentec particle vision and measurement (PVM); ATR-FTIR was used to record IR spectra of the liquid phase, FBRM was used to record in situ chord length distributions (CLDs) of the suspended particle population, and PVM was used to record the particle images of the batch crystallization products. The measurement principles25−27 and the good accuracy and repeatability28,29 of these in situ techniques have been described in many places in the literature. In this work, the ATR-FTIR measurements were conducted using a ReactIR 15 system from Mettler-Toledo (Schwerzenbach, Switzerland) equipped with a MCT detector composed of a 9.5 mm × 1.5 m AgX immersion probe and a SiComp crystal. ATR-FTIR spectroscopy can be used to obtain the solute concentration as well as the solvent/antisolvent ratio during crystallization process. The knowledge of these was of significant importance for the estimation of nucleation and growth kinetics, The FBRM measurements in this work were carried out by using a laboratory scale Lasentec S400 from Mettler-Toledo (Schwerzenbach, Switzerland), accompanied with version 4.1 FBRM Control Interface software. It can be used for two aspects: for seeded growth experiments (to estimate the growth kinetics), it can be used to conform that there was no significant nucleation occurred during the seeded growth experiments; while for the induction time experiments (to estimate the nucleation kinetics), it was used to monitor the onset of particle formation. FBRM was not used as a particle sizer to characterize crystal size distributions (CSD), but the CSD can be recovered from the measured CLD by geometric modeling.30−32 The relationship between them will be discussed in detail in section 3.2. The PVM measurements in this work were carried out using a Lasentec V700S-5-C22-K PVM from Mettler-Toledo (Schwerzenbach, Switzerland). The shape of the particle is of importance for the estimation of nucleation and growth kinetics. 2.3. Solubility in Mixed Solvent System for Antisolvent Crystallization Process. The solubility in the mixed solvent presents nonlinear relationship because of the dilution effect and binding effect of the antisolvent. There are many ways for the determination of solubility in the mixed solvent. Borissova25 and co-workers employed a physicochemical method for the determination of the solubility of benzophenone in methanol/water system; Jochen et al.26 adopted gravimetrical methods to determining the solubility of PDI 747 in methanol/water system. The accuracy of these methods has been validated by ATR-FTIR spectroscopy. In this work, we employed the gravimetrical method which similar with Jochen’s to calculate the solubility of biapenem in the water/ethanol mixture solvent at 298 K with the range of ethanol mass fractions of 0 to 0.8. Solubility of biapenem in the mixed solvent was measured as follows: An excess amount of biapenem (5 g) was added into

rate of stir, and the induce time are the factors that affect the quality of the crystals and the yield of crystallization. In this work, we investigated the antisolvent crystallization process of biapenem (6-[[(4R,5S,6S)-2-carboxy-6-[(1R)-1hydroxyethyl]-4-methyl-7-oxo-1-azabicyclo[3.2.0]hept-2-en-3yl]thio]-6,7-dihydro-5H-pyrazolo[1,2-a][1,2,4]triazol-4-ium inner salt) (Figure 1). Biapenem is a new non-natural

Figure 1. Chemical structure of biapenem.

parenteral carbapenem antibiotic with a wide range of antibacterial activity.24 The final isolation step in the industrial production process is the antisolvent crystallization of aqueous biapenem solution through the addition of alcohol. The determination of the optimum crystallization method is of crucial importance. Hence in this work, we focused on the estimating of the nucleation and growth kinetics of biapenem and designing an optimum way to obtain the desired product. To the best of the author’s knowledge, the measurements of nucleation and growth kinetics for antisolvent crystallization in the reported works were all resorted to off-line CSD measurement, which are inconvenient and time-consuming. Therefore, a process mathematic model for antisolvent crystallization is critical. This work designed six batches of crystallization experiments using in situ technology: ATR-FTIR spectroscopy, FBRM, and particle vision and measurement (PVM), which, combined with the population balance theory, and the CSD recovered from chord length distribution (CLD) moments, developed a process mathematic model for antisolvent crystallization of biapenem and estimated growth and nucleation parameters.

2. MATERIALS AND METHODS 2.1. Materials. The experiments comprised of three compounds: biapenem, distilled water, and ethanol (as a precipitating agent). Ethanol and distilled water were purchased from Sinopharm. Biapenem (mass fraction purity > 0.998) was synthesized by us. The details of the chemicals used in the present work are also given in Table 1. 2.2. In Situ Monitoring Techniques for the Batch Crystallization Process. The experiments were conducted in a 500 mL Bunsen beaker with a temperature-controlled water bath at 298 K. The in situ monitoring techniques in this work were attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy, lasentec focused beam reflectance Table 1. Specification of Chemical Samples

a

chemical name

source

biapenem ethanol distilled water

synthesis Sinopharm Sinopharm

initial mole fraction purity

purification method

final mole fraction purity

analysis method

0.998

GCa

0.998 0.998

recrystallization none none

Gas−liquid chromatography. 589



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100 mL of ethanol/water solvent (mass fraction of water change from 1 to 0.2) and kept in a closed container in a temperature-controlled water bath for 6 h with stirring, then the slurries were filtered, weighed, and put into a vacuum oven to separate the liquid from the solid phase at 323 K and 500 mbar. The weight of the remaining dry solute particles together with the weight of the filtrate generated the solubility of the given mixed solvent system. 2.4. ATR-FTIR Calibration and Supersaturation Determination. The determination of concentration, solubility, and supersaturation of crystallizing systems was based on the application of ATR-FTIR spectroscopy. The principle of this methodology is revealed by the Lambert−Beer law: the intensity (absorbance or transmittance) of the IR spectral peaks of all components (solute, solvent, or antisolvent) is changed proportional to its concentration. This methodology was first developed for studying the cooling crystallization process, and temperature was considered the controlling parameter of this calibration model. Meanwhile, in the antisolvent crystallization process, the amount of antisolvent is the controlling parameter. The determination of the suitable calibration model in this work used the following protocol: 200 mL mixed solvents with ethanol mass fractions of (0, 0.1, 0.2, 0.3, and 0.4) were prepared; then (5.0, 3.6, 2.2, and 1.2) g of biapenem were added and dissolved into them, respectively. Later, we repeated the above procedure two more times with (4.0, 3.0, 1.6, and 0.8) g and (3.5, 2.6, 1.2, and 0.6) g of biapenem, respectively. Thus we prepared three different concentrations for each composition of mixed solvent. Then, the prepared mixtures were kept in a temperature-controlled water bath for 2 h at 298 K before the ATR-FTIR spectra were collected. Supersaturation, which is the driving force of the process of crystal formation, is the result of complex physicochemical interactions between solute, solvent, and antisolvent in the antisolvent crystallization process. Supersaturation is often conveyed in form of a difference or a ratio between the concentration c and the solubility c* at the corresponding temperature. In this work, the supersaturation S was defined as the ratio of concentration c and solubility c* assuming an ideal solution: c S= c*(wwater) (1)

Table 2. Initial Conditions for Seed Batch and Induction Time Experiments Msa/g

C/(wt %) Seed Batch Experiments Run 1

Msc /g 0.0218

0.29

Run 2

0.02

0.31

Run 3

0.03

0.32

Induction Time Experiments Run 4 Run 5 Run 6 a

b

285.7 (water 200 g, ethanol 85.7 g) 320 (water 240 g, ethanol 80 g) 350.5 (water 280.4 g, ethanol 70.1 g)

Masc/g 0.0278 0.025 0.0247

81 86 70

219 (water) 200 (water) 350 (water)

Mass of solvent. bMass of seed crystals. cMass of antisolvent.

operation, but crystal breakage can be minimized by using an impeller with rounded edges and stirring at the appropriate speed. In this work, the speed was 100 rpm. 2.6. Induction Time Experiments for the Determination of Nucleation Kinetics. In the antisolvent crystallization process, nucleation kinetics were determined by the period (induce time) from the time attained to the desired supersaturation level to the time-detected newly formed particles.35 In this work, the level of supersaturation was detected by ATR-FTIR, and the newly formed particles were detected by FBRM. The induction time experiments were conducted as follows (Table 2): a certain amount of aqueous biapenem solution was prepared, and the in-situ ATR-FTIR and FBRM were started simultaneously. After a few IR spectra and CLDs were collected to confirm the signal stability, a certain amount of antisolvent was added into the reactor to get different initial supersaturation levels. Later, the experiments were repeated twice to ensure precise and repeatable measurements of the induction time. Three different kinds of experiments were designed following the same protocol with different conditions.

3. THEORIES 3.1. Mathematical Model of Biapenem Crystallization. The mathematical model for the crystallization process of biapenem was based on population balance equations (PBEs), with a least-squares optimization and the experimental desupersaturation data, to determine the kinetic parameters of biapenem growth and nucleation. 3.1.1. Population Balance Equations (PBEs). The population balances have different equations in terms of different aspects. When in terms of the number of time-dependent CSDs, n(L,t), the equations can be given as follows:36

where c is calculated from the ATR-FTIR band of biapenem at 1640 cm−1 and c* is its solubility. 2.5. Seed Batch Crystallization for the Measurement of Growth Kinetics. The monitoring of growth kinetics was based on the seeded batch desupersaturation experiments (Table 2).10,34 In this work, the experiments were conducted as follows: a supersaturated solution of biapenem was created by adding an appropriate amount of ethanol to an certain amount of aqueous biapenem solution in the temperature-controlled water bath (the mass fractions of water should be above than 0.6 to ensure precise concentration measurements). Then, the in situ monitoring with ATR-FTIR and FBRM was started, and a certain amount of seeds in dry form was introduced into the reactor at the beginning of the experiment. Three different kinds of batch experiments were designed following the same protocol with different conditions (Table 2). The determination of growth kinetics should be independent from breakage, agglomeration, and nucleation; the phenomenon of agglomeration and nucleation cannot be controlled by

∂(G(S , T , L ; fg )n) ∂n + = J(S , T , n; fj )δ(L − L0) ∂t ∂L (2)

where L is the crystal dimension and L0 > 0 is the characteristic dimension for nucleated crystals, T is temperature, t is the time, G is the crystal growth rate along the characteristic dimension, J is the nucleation rate, S is the supersaturation defined in section 2.4, and fg and f j are sets of parameters for growth and nucleation. The initial and boundary condition applied to the PBEs is: 590


Journal of Chemical & Engineering Data n(0, t ) = 0 ∀ t ∈ (0, ∞)

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related to μsi of the seed crystals by a proportionality constant φ:

(3)

The population balance equations can resolved to the system of ordinary equations (ODEs) differential when using moments, the ODEs of the population balance multiplying both aspects of eq 1 by Li, for i = 0, 1, 2, and integrating each term of 0 to ∞:36,37 dμ0 dμi dt

The initial value for μ3 can be calculated from the material balance:

(4)

= iGμi − 1 + JL0i

i = 1, 2, ...

∫0

∞

Lin(L , t )dL

(5)

(6)

μ0 = Jti

The CSD moments: μ0, μ1, μ2, and μ3 are functions of the total number, length, surface area, and volume of the crystals, respectively. For the seeded batch desupersaturation experiments, the differential equations were reset as follows:24 dμ0s dt dμis dt

=0

(7)

= iGμis− 1

i = 1, 2, ...

V L3

(9)

(10)

where V is the crystal volume that estimated from the microscopy images which measured by PVM. In this work, the density of the biapenem was determined to be ρc = 1490 kg·m−3;24 the volumetric shape factor was estimated to be kV = π/6. The initial and boundary conditions was c(t = 0) = c0, which is the initial concentration of biapenem measured immediately after seeding. 3.1. Kinetics Determination. The initial conditions for the seeded batch desupersaturation experiments in terms of ODEs from CSD calculation were expressed as follows: N−1

μi s =

k=1

1 GJti2 + JL0ti 2

(15)

μ2 =

1 2 3 G Jti + GJL0ti2 + JL02ti 3

(16)

μ3 =

1 3 4 3 G Jti + G2JL0ti3 + GJL02ti2 + JL03ti 4 2

(17)

G = kg S g

(18)

J = kjS jμ2

(19)

msd + c0msolv = (μ3 ρc kV + c)msolv

i

⎛ Lk + 1 + Lk ⎞ s ⎟ n (L k + 1 − Lk , 0) ⎠ 2

∑ ⎜⎝

μ1 =

where kg and g are the parameters to be estimated from the seed batch crystallization process of biapenem and kj and j are the parameters to be estimated from the induction time crystallization process of biapenem. 3.2. Relationship between CSD and CLD Moments. For the mathematical model of biapenem crystallization, we utilized the CSD moments; these data are not available in real time but can be estimated from the measured CLD by geometric modeling. Specifically the CSD is first recovered from the CLD before calculating its moments.31,32,38,39 The theory behind these modeling requires many premises, such as that the particles are perfectly backscatter light at all angles and all particles have a known shape. An optional effective approach for early stage design of pharmaceutical crystallization is to use the low-order moments of the CLD directly, which is based on a gray-box model that with lower data requirements and improved extrapolation capability and commonly used in process control. The theory behind this model is the assumption of the static mapping between the CLD and PSD. This work based on this approach to establish the relationship between the CSD and the CLD moments. At any experimental time point, the solute material balance can be written as:

where ρc and kV are the crystal density and the volumetric shape factor of biapenem, respectively, and μ2 is the surface area of the crystals. The volumetric shape factor kV is defined as follows: kV =

(14)

The nucleation and growth kinetic can be expressed by the following power-law expressions:

(8)

where μsi represent the moments of the seed crystals. Thus, the sets of eq 4 and 5 track the moments of all crystals in the slurry; the sets of eqs 7 and 8 track the moments of the crystals grown from the initial seed crystals. 3.1.2. Material Balance. The molar concentration c of biapenem in the liquid phase can be derived from the material balance in terms of CSD moments, that is:13 dC = (3Gμ2 + JL03)ρc kV dt

(13)

where msd is the mass of the seed crystal and msolv is the mass of the solvent. The value for φ was then calculated from eqs 11 and 13. Once the value of φ is known, the value of μi(t = 0) can be calculated from μsi (t = 0) with I = 0, 1, and 2. Because of the changeless of nucleation rate J and the growth rate G during the induction time, the integration of eq 4 and 5 between 0 and ti (induce time) leads to the following results:

where the ith CSD moment is defined as: μi =

(12)

msd = μ3 (t = 0)KV ρc msolv

=J

dt

μi = φμis

(20)

where c is the solute concentration accurately determined in situ from ATR-FTIR spectroscopy. From eq 20, μ3 can calculated at various time points and compared to the second-, third-, and fourth-order CLD moments of biapenem crystal μc2, μc3, and μc4, respectively. The CLD moments were estimated

(11)

where L1 and LN refer to the minimum and maximum crystal sizes and ns(Lk+1 − Lk,0) is the number of crystals in a seed with sizes between Lk+1 and Lk at time t = 0. μi of the crystals are 591



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growth rates. Two bands in the IR spectra at about 1045 cm−1 and 1640 cm−1 (Figure 3) were identified to represent the absorbance of antisolvent ethanol and solute biapenem, respectively. For three-component systems, the calibrations are often based on principal component analysis (PCA) or canonical discriminant analysis (CDA). But we can build independent univariate calibration models when the signal intensity at each of the selected bands is exclusively influenced by the concentration of the corresponding substance. Biapenem in the water/ethanol solvent system was used in this case. The calibration for its concentration was given in wt % of total mass, and the solvent/antisolvent composition was calibrated in wt % on a solute-free basis. The IR spectra of deionized water taken as a background spectrum. The calibration results are given in Figure 4, where concentration and solvent/antisolvent composition calibrations exhibit linear behavior with R2 values close to one in both cases. 4.3. Growth and Nucleation Kinetics of Biapenem. 4.3.1. CSD and CLD Moment Relationship. The crystals of biapenem show a cubic shape (Figure 5), and there is no agglomeration and breakage during the crystallization process. Therefore, the CSD can recover from the CLD moments. From eqs 20 and 21, we compared μ3 with the second-, third-, and fourth-order CLD moments of biapenem crystal by using the in situ experimental solute concentration recorded by ATR-FTIR spectroscopy and moments μci (for j = 2, 3, and 4) measured by FBRM for all of the runs. We found that the best fit for μ3 in this system is μc3 (Figure 6), so the relationship between CSD and CLD moments for biapenem can be given as an empirical correlation:

based on the superposition principle, in which the overall CLDs were given by: N−1 c

μi =

∑ k=1

i

⎛ Lkc+ 1 + Lkc ⎞ c c ⎜ ⎟ n (Lk + 1 − Lkc) ⎝ ⎠ 2

(21)

where Lc1 and LcN refer to the minimum and maximum chord lengths (1 and 1000) μm, respectively, and nc(Lck+1 − Lck) is the number of chord lengths between Lck+1 and Lck. The relationship between CSD and CLD moments was estimated through the comparison between μ3 and the scaled μci of each order.

4. RESULTS AND DISCUSSION 4.1. Solubility of Biapenem in the Water/Ethanol System. The solubility of biapenem in the water/ethanol system is shown in Figure 2 as a function of solvent

μi = λiμic

(22)

where λi is a proportionality constant. This empirical correlation differs from some theoretical predictions,39 recalling that the theoretical predictions are based on many restrictive assumptions that do not apply to all particulate systems. This length-weighting expression may be commonly used in industrial practice. In the duration of seed batch experiments of runs 1, 2, and 3, no nucleation was detected, and the time evolution of the solute concentration and CLD moments was solely due to the growth of the crystals. The proportionality constants λi were calculated from:

Figure 2. Gravimetrically determined solubility data of biapenem as a function of solvent composition at 298 K; XW is the mass fraction of water, and S is defined as the mass of biapenem in per kilogram solvent.

composition at 298 K. There is only a little change of solubility with the mass fraction of water, which was less than 0.4, due to the dilution effect of antisolvent. 4.2. Calibration of ATR-FTIR Spectroscopy. The knowledge of online solute concentration and the solvent/antisolvent ratios are of importance for the determination of nucleation and

Figure 3. ATR-FTIR spectral data of biapenem solutions in mixed solvent. The arrows at about 1640 cm−1 indicate the reduction of biapenem concentration with the addition of antisolvent, while the arrows at 1045 cm−1 and 1092 cm−1 indicate the increase of antisolvent ethanol. 592



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Figure 4. Calibration data for the absorbance values at 1045 cm−1 and 1640 cm−1 at 298 K that correspond to the concentrations of biapenem and the antisolvent in mixed solvent. Xb: mass fraction of biapenem in the mixed solvent, Xe: mass fraction of antisolvent in the mixed solvent. The fitted equations are found to be A = 0.145Xb (R2 = 0.99565) and A = 0.016Xe (R2 = 0.99378).

With these λi values, the model CLD moments μc,md i,n calculated from eq 22 were used for comparison with experimental measurements μc,ex i,n to verify the accuracy of the model. Plotted in Figure 7 were the comparisons of model predictions and experimental data of different orders of CLDs moments for run 1. They show very good agreement between the model and the experimental data. 4.3.2. Parameter Estimation. The parameters which should be estimated for the determination of growth and nucleation kinetics were kg, g, kj, and j. From eqs 18 and 19, these parameters can be calculated from G, J, and S. For the seed batch desupersaturation process, the changes of the concentration and supersaturation profiles of biapenem in water/ethanol system for run 1 are shown in Figure 8; the seed crystals of biapenem were added to the crystallization system at the time of 0. The absorbance of biapenem at the band of 1640 cm−1 changes from 0.39 to 0.34 slowly (3D profiles in Figure 9B), and the corresponding concentration and supersaturation change from 21.78 to 18.96 and 3 to 2.6, respectively. Plotted in Figure 9 are the changes of the concentration and supersaturation profiles of biapenem in the induction time crystallization process for run 6. The solute concentration decreased from 24.7 to 13.697 solvent immediately after the addition of antisolvent. This phenomenon can be seen clearly from the 3D profiles of biapenem absorbance at the band of 1640 cm−1 (Figure 9B), and the characteristic absorption peak changes from 0.39 to 0.21 suddenly. The time between the point of antisolvent addition and the on-set of nucleation is called the induce time; determination of this period depends on the FBRM counts, which detects the increase of particle due to nucleation. For run 6, the induce time was determined to be 420 s (Figure 9C). The induce times for run 4 and 5, determined as in run 6, were 360 s and 390 s, respectively. The supersaturation profiles are shown in Figure 9C. The value of supersaturation soared to 2.1 with the addition of antisolvent and then decreased to a constant of 1.18 immediately. The supersaturation profiles of run 4 and 5 show the same trend. The growth kinetics G and nucleation kinetics J calculated from eqs 8, 9, 11 to 13 and eqs 18 to 21 as functions of supersaturation plotted as ln(G) and ln(J) vs ln(S) are given in Figure 10. The plots of ln(G) vs ln(S) were deduced from run

Figure 5. PVM image of biapenem slurry taken in-process during batch crystallization.

Figure 6. Comparisons between CSD moment μ3 (□) and CLD moment μc3 (○) for run 1. They show almost the same trend, and runs 2 to 6 all mirror the same situation.

1 λi = Ns

Ns

∑ n=1

μi md ,n μic,ex ,n

(23)

where Ns is the number of sampling instances, μmd i,n are model predictions, and μc,ex i,n come from experimental measurements. 593



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Figure 7. Comparisons of model predictions and experimental data of run 1: (A) μc0 (# counts·s−1), (B) μc1 (# counts μm·s−1), (C) μc2 (# counts μm2·s−1), (D) μc3 (# counts μm3·s−1), (E) μc4 (# counts μm4·s−1). ○ represents model prediction, and □ represents experimental data.

Figure 8. Changes of the concentration (C) and supersaturation profiles (S) of biapenem in water/ethanol system for run 1: (A) concentration, (B) 3D changes of the concentration, (C) supersaturation.

Figure 9. Changes of the concentration (C) and supersaturation profiles (S) of biapenem in water/ethanol system for run 5: (A) concentration, (B) 3D changes of the concentration, (C) supersaturation. The induce time has been highlighted within the two vertical lines.

The growth exponent g ranges from 1 to 2 for diffusionlimited and surface integration-limited growth mechanisms, respectively. The results in this work indicated that the growth of biapenem was likely be controlled by both, but the integration-limited growth mechanism plays the main role. Besides, the low value of parameter kg may indicate inefficiency of the seed crystallization process for biapenem. 4.4. Model Validation. The validation of mathematic model for antisolvent crystallization process of biapenem was through the comparison of the model predicted average size of

1, while the plots of ln(J) vs ln(S) were deduced from run 4, 5, and 6. The estimated values of the parameters kg, g, kj, and j were given in Table 3. g and j values for biapenem crystallization process were in the reasonable ranges when considering the general crystal growth and nuclear mechanism,37 where the parameter g is usually between the valves 1 and 2, while the parameter j usually observed between 1 and 3. It can be said that the developed mathematic model for the antisolvent crystallization process of biapenem is reasonable. 594



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Figure 10. Growth and nucleation kinetics as a function of supersaturation plotted as ln(G) and ln(J) vs ln(S). The fitted equations are found to be: ln(G) = 1.68 ln(S) + 0.58 (R2 = 0.99156) and ln(J) = 1.19 ln(S) + 5.57 (R2 = 0.99554).

Table 3. Kinetics Parameter Estimates: kg and g for Crystal Growth and kj and j for Nucleation parameter estimation for biapenem growth, run 1 parameter estimation for biapenem growth, run 2 parameter estimation for biapenem growth, run 3 average parameter estimation for biapenem growth parameter estimation for biapenem nucleation

kg

g

1.8 1.83 1.826 1.8186 kj

1.6875 1.6712 1.68 1.6796 j

264.7537

5. CONCLUSIONS A process model for the antisolvent crystallization of biapenem, a new non-natural parenteral carbapenem antibiotic, was developed. The kinetic parameters for growth and nucleation were estimated based on seed batch desupersaturation experiments and induction time experiments by using in situ technology: ATR-FTIR spectroscopy, FBRM, and PVM. The basic theories of this mathematic model were population balance equations and the relationship between the CSD and CLD moments, which is the key aspect of this model. The CSDs recovered from the CLD moments make a convenient building of the in-process mathematic model instead of off-line CSD measurement. But the theory behind the CSD-CLD model requires that the particles have a known shape and no agglomeration and breakage in crystallization process, so the model in this work may not be suitable for other systems. The good agreement between the model results and the experimental data demonstrated a good predictive ability of this crystallization model.

1.1973

crystals with experimental data from run 1 to run 6. The model predicted average size L was calculated as follows: μ L= 1 μ0 (24) The plots of the average size from the model and experimental data are given in Figure 11, which indicated that the growth rates for the three seed batch experiments were similar. The good agreement of the data between model predicted and experimental demonstrated the predictive ability of this model. The slight differences between the mean sizes of the product crystals for the six runs may be caused by the supersaturation disparity during the crystallization process.

Figure 11. Comparisons between the model predicted (○) and experimental (□) average size for run 1 to run 6, A: run 1, B: run 2, C: run 3, D: run 4, E: run 5, F: run 6. 595



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AUTHOR INFORMATION

Corresponding Author

*Fax: +86-25-52090614. Tel.:+86-25-52090614. E-mail: [email protected]. Funding

This work has been supported by the prospective joint research project of Jiangsu province (SBY201220255) and the National Science Foundation for Young Scholars of China (31100055). Notes

The authors declare no competing financial interest.

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Antisolvent Crystallization of Biapenem: Estimation of Growth and

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