Application of Attenuated Total Reflectance− Fourier Transform

1 Pesek Road, Jurong Island, Singapore 627833. On-line attenuated total reflection-Fourier transform infrared (ATR-FTIR) spectroscopy and focused-beam...
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Ind. Eng. Chem. Res. 2006, 45, 438-444

Application of Attenuated Total Reflectance-Fourier Transform Infrared (ATR-FTIR) Technique in the Monitoring and Control of Anti-solvent Crystallization Zai Qun Yu,† Pui Shan Chow,‡ and Reginald B. H. Tan*,†,‡ Department of Chemical and Biomolecular Engineering, National UniVersity of Singapore, 10 Kent Ridge Crescent, Singapore 119260, and Institute of Chemical and Engineering Sciences, Ltd., 1 Pesek Road, Jurong Island, Singapore 627833

On-line attenuated total reflection-Fourier transform infrared (ATR-FTIR) spectroscopy and focused-beam reflectance measurement (FBRM) were used to monitor and control anti-solvent crystallization of paracetamol from an acetone-water mixture, which was conducted isothermally in a 1-L crystallizer with a flat bottom. After analyzing the particle size distribution (PSD) and transient relative supersaturation data from constant anti-solvent addition rate experiments, a simple calculation method for the set point of anti-solvent addition rate, to maintain constant supersaturation via ATR-FTIR, was developed and implemented for feedback control of unseeded and seeded crystallization. The results of the controlled feeding rate experiments show that the particle size and PSD, as well as the total batch time, can be favorably manipulated simultaneously. 1. Introduction In anti-solvent crystallization, supersaturation is created by mixing a third component with the saturated solution, to reduce the solubility of the solute. Proceeding at or near ambient temperature, it has proved to be the most common technique for the separation and purification of many heat-sensitive pharmaceuticals and agrochemicals.1 Anti-solvent crystallization is usually performed in a semibatch manner, whereby anti-solvent is pumped into the crystallizer at a constant flow rate. However, it has been found that a predetermined time-varying flow rate can yield a better particle size distribution (PSD) by matching the generation rate of supersaturation with the growing crystal surface area.2-4 The derivation of such a flow-rate profile requires prior knowledge of the exact crystallization kinetics, which is difficult and timeconsuming to obtain for industrial conditions. Furthermore, operating conditions such as seed size distribution, seeding timing, impurity content, and starting solute concentration often change from batch to batch and are difficult to be tracked precisely, which will render the predetermined profile not optimal anymore. Capable of accurately measuring in situ the liquid composition in the presence of solids,5-10 the attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy technique enables crystallization control to be implemented without the requirement of kinetic knowledge. After the profile of solute concentration is determined, the liquid concentration measured by ATR-FTIR spectroscopy can serve as a feedback signal by which the flow rate of anti-solvent can be manipulated accordingly. The ATR-FTIR technique has been successfully applied to feedback control of the cooling crystallization. Feng and Berglund11 obtained optimal cooling curves for crystallization of succinic acid by keeping the working solute concentration close to the solubility curve. They manifested the flexibility and * To whom correspondence should be addressed. Tel.: +65-68746360. Fax: +65-6779-1936. E-mail address: [email protected]. † Department of Chemical and Biomolecular Engineering, National University of Singapore. ‡ Institute of Chemical and Engineering Sciences, Ltd.

facility of the ATR-FTIR technique in crystallization control by intentionally altering seed loadings, seed size, and agitation speed. Nagy et al.12 demonstrated that the use of ATR-FTIR spectroscopy reduced the uncertainties in mean crystal size and yield of final products stemming from variations in kinetics and solubility. Fujiwara et al.13 obtained products with a narrow PSD and reduced agglomeration by directing the crystallizer temperature slightly below the metastable limit, to maximize crystal growth in the cooling crystallization of paracetamol from water. Gro¨n et al.14 studied constant supersaturation control for crystal growth in the unseeded cooling crystallization of monosodium glutamate from aqueous solution and produced more-uniform crystals than uncontrolled isothermal operation. They presented a control algorithm with two iteration loops on the basis of first derivative of the supersaturation function, with respect to temperature. Liotta and Sabesan15 and Fujiwara et al.16 have proposed that the feedback control strategy for cooling crystallization can be extended to anti-solvent crystallization. However, the implementation of feedback supersaturation control of anti-solvent crystallization with the use of ATR-FTIR spectroscopy, hitherto, has not been reported. Although Gabas and Lague´rie17 achieved constant supersaturation in the anti-solvent crystallization of D-xylose using an immersion refractometer to measure the solute concentration in situ, little detail was disclosed in the short communication about the structure of the control system. This present study represents an attempt to study the effects of supersaturation control on the mean particle size, size distribution, and overall batch time in seeded and unseeded anti-solvent crystallization. The paracetamol-acetone-water system will be used as the model system. The initial solvent is an acetone-water mixture (45 wt % acetone), and water will be used as an anti-solvent to decrease the solubility of the solute.18 By convention, the concentration of solute is expressed in terms of g/g, based on the unit mass of solid-free liquid phase (mixture of water and acetone), whereas acetone concentration has units of wt %, in reference to the mass fraction of acetone in the liquid phase.

10.1021/ie050660i CCC: $33.50 © 2006 American Chemical Society Published on Web 11/23/2005

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2. Experimental Section 2.1. Materials and Instrumentation. Paracetamol powder (which was supplied by Sigma Chemical Co.), pro-analysisgrade acetone (g99.5%, provided by Merck), and deionized (DI) water were used to prepare the solutions. Absorbance spectra were collected, with a resolution of 4 cm-1, on a Nicolet 4700 spectrophotometer (Nicolet Instrument Co.) that was equipped with a Dipper-210 ATR-FTIR immersion probe (Axiom Analytical, Inc.). Every spectrum was the average of 64 scans in the range of 600-4000 cm-1. The spectra of DI water at 23 °C were used as background. The FTIR spectrometer was purged continuously by purge gas that was supplied by a FTIR purge-gas generator (Parker Balston, model 75-52-12VDC). A focused beam reflectance measurement (FBRM) probe (Lasentec, model D600L) was inserted into the turbulent zone of the suspension. Its prominent advantage of in-situ measurement removes the errors that are incurred during off-line sampling and provides continuous information on the solid phase during the crystallization process. FBRM data were displayed and analyzed in the Control Interface software Version 12, which provides chord length distribution (CLD) and related statistics which can be correlated with PSD. For instance, the total count of chord lengths per unit time recorded by FBRM can be linearly correlated with solid concentration in a certain range.19,20 The square-weighted CLD has been observed to have a resemblance to the conventional laser diffraction distribution.21 Moreover, some researchers have proposed first-principle models to restore PSD from CLD under certain assumptions.22,23 In this paper, the total count of chord lengths is used to indicate the changes in particle population. Cumulative mass distribution of final products was obtained by sieve analysis (Sonic sifter, model L3P from ATM Co.). The smallest aperture used was 150 µm and the largest was 1000 µm. All particles retained on one sieve were assumed to have the same mean size, i.e., the arithmetic mean aperture size of two adjacent sieves. The average particle size (L) is defined as mass-weighted particle mean size. The coefficient of variation (cv) in the PSD was used as a measure of size distribution spread. 2.2. Procedures for Calibration of IR Spectra. Calibration of the IR spectra for paracetamol-acetone-water solutions was conducted in a 500-mL jacketed crystallizer with a flat bottom and a magnetic stirrer (IKA RCT basic) that was operating at 700 rpm. The temperature in the crystallizer was controlled by a heating and cooling circulator (Julabo, model FP50-HL). At the beginning of each calibration run, the temperature was elevated to ∼10 °C above the saturation point and maintained there for 20 min to ensure that all crystals have dissolved. The crystallizer then was cooled at a rate of 0.5 °C/min while spectral data were collected every 2 min. 2.3. Procedures for Anti-solvent Crystallization. The experimental setup for anti-solvent crystallization studies is shown schematically in Figure 1. The main vessel was a 1-L flat-bottomed glass crystallizer with an inner diameter of 100 mm. It was fitted with four glass baffles on the inner wall. A marine-type impeller that was made of stainless steel with a diameter of 42 mm driven by a variable speed overhead stirrer motor was used to provide agitation. The gap between the impeller and the crystallizer bottom was 43 mm, about onethird of the final working height of the suspension. A variablespeed peristaltic pump (MasterFlex 7550) was used to add antisolvent. The injection point was 5 mm above the impeller tip to accelerate dispersion.

Figure 1. Experimental setup for anti-solvent crystallization.

Initial solutions were prepared in such a way that they were slightly supersaturated when cooled to 23 °C. Proportionate amounts of paracetamol were dissolved in 400 g of a wateracetone mixture with 45 wt % acetone. The temperature then was elevated to 45 °C and maintained for 30 min to ensure that all paracetamol crystals have dissolved. The temperature then was reduced to 23 °C and allowed to stabilize for 10 min before the addition of anti-solvent. A total of 500 g of water were pumped into the crystallizer, and the agitation speed was fixed at 500 rpm for all runs. It has been shown that, under our present experimental conditions, a stirring speed of 500 rpm was sufficient for effective dispersion of the anti-solvent and a reduced speed localized nucleation near the injection point.24 The final acetone concentration was ∼20 wt %. At the completion of every run, crystal products were isolated by vacuum filtration of the slurry, followed by ambient drying. In seeded experimental runs, milled seeds were added to the initial solution after its temperature stabilized at 23 °C. Observations under the microscope (Olympus model BX51 equipped with a CCD camera) revealed that the average size of milled seeds was 5 µm, with a standard deviation of 3 µm. 3. Results and Discussion 3.1. Calibration Results for Infrared Spectra and Solubility Measurement. Temperature and the infrared (IR) spectra in the range of 800-1800 cm-1 from 644 calibration measurements were correlated with the paracetamol and acetone concentration through chemometric methods, as detailed by Togkalidou and co-workers.7,9 The acetone concentrations ranged from 7 wt % to 70 wt %, and three different paracetamol concentrations were prepared at every acetone concentration. The average prediction intervals are 3.54 × 10-4 g/g and 0.09 wt % for the paracetamol concentration and acetone concentration, respectively, at the 95% confidence level. These tight prediction intervals provide the necessary reliability for monitoring and controlling purposes. To check the accuracy of the ATR-FTIR technique, the solubility of paracetamol in acetone-water mixtures at 23 °C was measured using the calibration results achieved previously. The solubility data in the acetone range of 15-50 wt % are shown in Figure 2. The corresponding data from the literature18 are also illustrated in the figure for comparison, and close agreement indicates that the ATR-FTIR technique is a convenient and reliable tool for solubility measurement. The dissolution process can be monitored on-line and removes much of the “blind” long waiting time that is commonly encountered in the gravimetric method. The solubility data measured by

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Figure 4. Development of total counts of chord lengths with the addition of anti-solvent in unseeded and seeded crystallization. Figure 2. Solubility of paracetamol in water-acetone mixtures at 23 °C, as measured by the attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy technique. Literature refers to data from ref 15.

Figure 3. Cumulative mass distribution of crystal products from unseeded and seeded crystallization. Cs and q values are as noted in the figure, and the corresponding average particle size (L) and coefficient of variation (cv) values are as follows: (+) L ) 669 µm, cv ) 43.24%, (]) L ) 545 µm, cv ) 33.79%, (0) L ) 612 µm, cv ) 31.23%, and (4) L ) 458 µm, cv ) 21.70%.

ATR-FTIR spectroscopy were utilized throughout all crystallization experiments. Because the solubility data are required later for quantitative calculation, they are fitted with a parabolic polynomial (with R2 ) 0.9994):

c* ) a0 + a1C + a2C2

(1)

where a0 ) -0.0166, a1 ) 0.0033, a2 ) 0.00007, and C represents the acetone concentration. 3.2. Monitoring of Crystallization Conducted at a Constant Feeding Rate of Anti-solvent. As the first step, ATRFTIR spectroscopy was used to monitor the relative supersaturation at constant addition rates of anti-solvent. The results of four runs of crystallization are reported in this section. The first two runs were unseeded crystallization with an addition rate of 1 and 2 g/min, respectively, and in the last two runs, anti-solvent was added at a rate of 2 g/min with seed loadings (Cs) of 0.5% and 1.0%, respectively. The FBRM was used to record the CLD during the runs simultaneously, and the final crystal products were sieved and analyzed as described earlier. The cumulative mass distribution of crystal products are shown in Figure 3. For unseeded crystallization, the addition rate of 1 g/min yielded a larger L than 2 g/min (669 versus 545 µm); however, the spread of PSD was widened significantly

(cv ) 43.24% versus cv ) 33.79%). Although a seed loading of 1% yielded the narrowest PSD with cv ) 21.7%, its L value decreased to the lowest values (458 µm) among the four runs; 0.5% seed loading brought L to a larger value, but its cV was impaired (31.23%). Although it is possible to obtain a narrower PSD with 0.5% seed loading at a lower addition rate (such as 1 g/min), the lengthened batch time may become a concern for industrial practice. It seems that constant flow rate operation is not able to optimize L, cv, and the batch time concurrently. Figure 4 shows the time evolution of total counts of chord lengths during the four crystallization runs, and the results indicate that the differences in the L value of the two unseeded runs are attributable to the variation in the number of nuclei formed during the nucleation stage. The total counts of chord lengths, which are proportional to the particle number in crystallizer, were ∼1000 counts/s upon the completion of nucleation stage when the addition rate of anti-solvent was 1 g/min, and were ∼1400 counts/s at an addition rate of 2 g/min. Therefore, the addition rate of anti-solvent defined the number of nuclei in unseeded crystallization and has a critical role in PSD control. The differing cv values of the two unseeded runs can be explained by the variation in lifetime distribution of crystals.3 In unseeded crystallization of many systems, it is difficult to separate nucleation from crystal growth, and early nuclei have more time to grow into big crystals. Late nuclei, mostly generated through secondary nucleation, do not have as long a time to grow in size. As can be deduced from Figure 4, ∼110 min had elapsed when nucleation was completed at an addition rate of 1 g/min (corresponding to 110 g of anti-solvent), while only 80 min were required at 2 g/min (corresponding to 160 g of anti-solvent). Therefore, the nuclei generated at 1 g/min had a wider lifetime distribution than at 2 g/min, which translated to a larger cv of the final PSD. The low cv value obtained from the run with a seed loading of 1% verifies that the practice of seeding provides an effective approach to narrow the PSD by separating nucleation and crystal growth if seed loading or the surface area of seeds is sufficient.25,26 Figure 4 demonstrates that the number of crystals was kept constant throughout operation at a seed loading of 1%, indicating that secondary nucleation was suppressed to a large degree and almost all final crystals originated from the narrowly sized seeds. By contrast, at a lower seed loading of 0.5%, significant secondary nucleation occurred, as indicated by the jump in the total counts of chord lengths, as shown in Figure 4 (from 400 counts/s initially to 1000 counts/s). Crystals derived from the original seeds constituted the bigger-size

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Figure 5. Transient relative supersaturation versus mass of anti-solvent in unseeded and seeded crystallization.

fraction of the final products, and crystals derived from secondary nucleation represented the smaller-size fraction; this led to a wider PSD, as shown clearly in Figure 3. Recall that, because only a small share of solute molecules in the solution deposited on the surfaces of secondary nuclei, the resulting average particle size was larger than that in the run with a seed loading of 1%, where the depositing solute molecules were shared more evenly by all seeds. The transient relative supersaturation curves in Figure 5 provide a clear picture of the driving force behind the phenomena observed in Figures 3 and 4. For instance, the peaks in the profiles of the first two operations are a characteristic feature of unseeded crystallization. The peak height increased and the peak position shifted to the right as the addition rate of anti-solvent increased. As a result, there was a notable difference in the number of nuclei as addition rate of anti-solvent changed from 1 to 2 g/min. In the case of seeded crystallization, the peak height went up from 0.057 to 0.100 when the seed loading was changed from 1% to 0.5% at the same addition rate of antisolvent, causing secondary nucleation to happen. The different trajectories were a result of the balance between the consumption and generation rates of supersaturation. The in situ relative supersaturation can be used as feedback signals to adjust the addition rate of anti-solvent and, thus, solve the issue of optimizing L, cv, and batch time concurrently. Judging from the profiles of total counts and transient relative supersaturation for the run with 1% seed loading, it seems that secondary nucleation can be subdued successfully below the relative supersaturation of 0.057. Accordingly, the continuous ATR-FTIR measurements can be coupled with the measured solubility data to provide a basis for controlled constantsupersaturation operation, and this will be discussed in the following section. 3.3. Feedback Control of Supersaturation. The control strategy chosen for this study was adapted from the work by Liotta and Sabesan15 and Fujiwara et al.16 The control principle includes a set point calculation block for manipulated variables (crystallizer temperature or addition rate of anti-solvent) and their lower level feedback controllers (may be of PID types). This is an improved version of commonly used control strategy for batch processes wherein no steady operating-state operating point exists. In this study, constant supersaturation is to be achieved by manipulating the addition rate of anti-solvent based on the values of solvent and solute concentration. The peristaltic pump used in this study is computerized and has its own control system of flow rate (i.e., the lower level controller mentioned above). It is connected with and receives control commands

from the control computer via RS232 cable. Therefore all we need to do is to define how the set point for anti-solvent addition rate is to be calculated. 3.3.1. Process Dynamics and Calculation of the Set Point for Anti-solvent Addition Rate. A simple method to determine the addition rate of anti-solvent, based on the measured paracetamol and acetone concentration, can be defined by analyzing the dynamics of relative supersaturation. The following information about the process is known prior to crystallization: (a) the solubility curve, as expressed by eq 1; (b) the initial mass of liquid phase inside the crystallizer (M0) and initial acetone concentration (C0); and (c) the set point of relative supersaturation (σs). At instant tk, the solute concentration ck and the acetone concentration Ck are measured by ATR-FTIR spectroscopy. The corresponding saturation solute concentration is given as

c*k ) a0 + a1Ck + a2Ck2

(2)

The actual relative supersaturation (σk) can be calculated as follows:

σk )

ck - c*k c* k

(3)

The mass of liquid phase inside the crystallizer (Mk) can be calculated by performing a mass balance on acetone:

Mk )

C0M0 Ck

(4)

The average rate of depletion of solute from the liquid phase gk during the sampling period from tk-1 to tk then is given by the expression

gk )

ck-1Mk-1 - ckMk ∆t

(5)

where Mk-1 and ck-1 are obtained at the previous instant tk-1. If there is a discrepancy between σk and σs, then the control system will decrease (when σk > σs), or increase (when σk < σs) the addition rate of anti-solvent, to bring the relative supersaturation at time tk+1 to σs. For example, consider the case of σk < σs. Suppose the total mass of liquid phase inside the crystallizer needs to increase to Mk+1 at tk+1 to make σk ) σs.

ckMk - gk+1∆t - c*k+1 Mk+1 σs ) c*k+1

(6)

2 where c* k+1 ) a0 + a1Ck+1 + a2Ck+1 or by incorporating eq 4:

( )

C0M0 C0M0 + a2 Mk+1 Mk+1

/ ) a0 + a1 ck+1

2

(7)

There are two unknown variables in eq 6: gk+1 and Mk+1. The parameter gk+1 will not be known until the next sampling instant tk+1. Because the sampling interval of the control system is very short, in comparison to the total feeding time (1 min

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versus 3 h, normally), it is reasonable to approximate gk+1 by gk, so eq 6 becomes

ckMk - gk∆t - c*k+1 Mk+1 σs ) c*k+1 or

σs + 1 )

2ckMk - ck-1Mk-1 Mk+1c*k+1

(8)

which can be easily solved to yield Mk+1. Finally, the required addition rate of anti-solvent during the period from tk to tk+1 is given as

qk )

Mk+1 - Mk ∆t

Figure 6. Trajectories of relative supersaturation in crystallization under feedback control.

(9)

3.3.2. Control Parameters. The sampling interval for solute concentration and acetone concentration was 1 min, and the flow rate of anti-solvent was adjusted accordingly at the same frequency. The set point for constant relative supersaturation was set at 0.05, which is a sufficiently low value to suppress secondary nucleation, as observed previously. The minimum flow rate allowable by the peristaltic pump used in this study is 0.7 g/min; however, during the early stage of crystallization, the required addition rate of anti-solvent to keep relative supersaturation at its set point was sometimes much lower. The instrument limitation caused the system to operate in an on/off mode initially. Furthermore, preliminary experiments revealed that the calculated addition rate of anti-solvent becomes very high toward the end of operation, because of the large crystal surface area available for solute deposition. A high pumping rate and the resultant inefficient dispersion of antisolvent has a tendency to enhance secondary nucleation, and this would negate the control efforts that were invested previously. Therefore, the maximum addition rate was kept at 5 g/min in this study, which was determined to be effective in minimizing secondary nucleation during the controlled feeding experiments. 3.3.3. Crystallization Operated at Constant Supersaturation. For unseeded crystallization, the crystal surface must be created through nucleation before feedback control can be implemented. During the nucleation stage, anti-solvent can be added at a constant flow rate. As mentioned in the last section, the amount of anti-solvent pumped into the crystallizer upon the completion of the nucleation stage in unseeded crystallization increases with the flow rate of anti-solvent. As a result, the amount of remaining anti-solvent available for the control system to manipulate diminishes. Therefore, a relatively slow addition rate of anti-solvent during the nucleation stage is a prerequisite for a satisfactory performance of feedback control via the ATR-FTIR technique. Three experimental runs were undertaken to assess the performance of constant-supersaturation control during the crystal growth stage. In the first run, unseeded crystallization was conducted, with the flow rate of anti-solvent being kept constant at 1 g/min during the nucleation stage. The feedback control was not initiated until the relative supersaturation began to decline from its peak value. In the second and third runs, milled seeds (with seed loadings of 0.5% and 1%, respectively) were applied to the slightly supersaturated solution at the start. After the total counts of chord lengths stabilized, the control

Figure 7. Trajectories of accumulated mass of anti-solvent.

loop was activated and the relative supersaturation was kept at 0.05 to examine the effect of seed loading on batch time and PSD. The trajectories of transient relative supersaturation are shown in Figure 6. For the unseeded run, the relative supersaturation went beyond 0.05 and reached nearly 0.12 during the nucleation period. It then fell steeply and the control system was activated to maintain relative supersaturation at 0.05. In the latter part of the run, the supersaturation could not be sustained at 0.05 anymore, because of the maximum flow rate limit of the peristaltic pump. In the case of seeded runs, the relative supersaturation jumped to 0.05 from 0.01 in the beginning and then remained reasonably constant around the set point for some time. Toward the end of operation, the relative supersaturation dropped below the set point, as in unseeded crystallization. The profiles of accumulated masses of anti-solvent are shown in Figure 7. Three sections in each profile can be observed, corresponding to the patterns exhibited in Figure 6. For unseeded crystallization, the first section of the trajectory is linear and corresponds to the constant flow rate during nucleation stage. It is followed by a nonlinear section that extends from 100 g to 220 g of accumulated anti-solvent. It was in this section that the control system manipulated the addition rate effectively to match the expanding crystal surface area without incurring much secondary nucleation. Another linear section, which is associated with the maximum addition rate of 5 g/min (which, however, could not generate supersaturation fast enough to balance the depletion of solute), emerges after that point. For seeded crystallization, the first brief linear portion corresponds to the jump in relative supersaturation at the start of operation in Figure 6, when the flow rate of anti-solvent reached 5 g/min. The extent of the nonlinear section is dependent on seed loading. At a seed loading of 1%, the nonlinear section extends from 30 g to 140 g, whereas it extends from 30 g to 200 g at a seed loading of

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tk ) sampling instant ∆t ) sampling interval [min] C ) acetone concentration [%] Cs ) seed loading; percentage of seed mass in theoretical crystal yield [%] L ) average size of crystals [µm] M ) mass of liquid phase in crystallizer [g] R2 ) determination coefficient in polynomial fitting cv ) coefficient of variation σ ) relative supersaturation; defined as σ ) (c - c*)/c* σs ) set point of relative supersaturation in feedback control Subscript Figure 8. Cumulative mass distribution of crystal products under feedback control. Cs values are as noted in the figure, and the corresponding L and cv values are as follows: (+) L ) 641 µm, cv ) 34.64%, (0) L ) 597 µm, cv ) 22.54%, and (4) L ) 529 µm, cv ) 23.10%.

0 ) initial value at the beginning of crystallization k - 1, k, k + 1 ) value at sampling instants tk-1, tk, tk+1, respectively

0.5%. The second linear section emerges in the latter portion of operation when anti-solvent was added at 5 g/min. The batch time was decreased from 213 min to 156 min when the seed loading was changed from 0.5% to 1%. On-line FBRM data have shown that secondary nucleation was suppressed successfully when crystallization proceeded at a constant relative supersaturation of 0.05. Figure 8 gives the PSD of final products obtained under feedback control. Generally speaking, feedback control via ATR-FTIR spectroscopy exhibits the capability to regulate L, cv, and batch time simultaneously. When the seed loading was 0.5%, cv was reduced to 22.54% from 31.23% while L changed slightly, compared with the run operated at constant flow rate of 2 g/min. The batch time was reduced from 250 min to 213 min at the same time. For unseeded crystallization, improvement due to feedback control is also significant, when comparison is made between the two unseeded runs operated at constant flow rates of 1 and 2 g/min. Feedback control yielded a PSD with cv ) 34.64% and L ) 641 µm.

Literature Cited

4. Conclusion Crystallization of paracetamol with a constant addition rate of anti-solvent was studied using attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy, focused beam reflectance measurement (FBRM), and particle-size distribution (PSD) analysis. Seeding offers an effective mechanism to separate nucleation and crystal growth and yields a narrower PSD than unseeded crystallization. It is difficult to optimize the coefficient of variation (cv), the average particle size (L), and the batch time concurrently when operating at a constant addition rate of anti-solvent. A simple method was proposed for calculating the set point of anti-solvent addition rate to maintain constant supersaturation via ATR-FTIR spectroscopy. Feedback control of unseeded and seeded crystallization was successfully implemented, and results have shown that more-favorable values of cv, L, and batch time could be obtained simultaneously. Nomenclature a0, a1, a2 ) constants in the polynomial for solubility, eq 1 c ) solute concentration [g/g mixed solvent] c* ) equilibrium solute concentration [g/g mixed solvent] g ) depletion rate of solute from the liquid phase [g/min] q ) addition rate of anti-solvent [g/min]

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ReceiVed for reView June 8, 2005 ReVised manuscript receiVed October 10, 2005 Accepted October 18, 2005 IE050660I