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- 1. cdm00 | ACSJCA | JCA10.0.1408/W Unicode | research.3f (R2.3.i6:3256 | 2.0 alpha 39) 2012/02/22 10:29:02 | PROD-JCA1 | rq_136596 | 2/27/2012 15:06:18 | 10 Article pubs.acs.org/IECR 1 Determination of the Crystal Growth Rate of Paracetamol As a 2 Function of Solvent Composition 3 C. T. Ó ’Ciardhá,* N. A. Mitchell, K. W. Hutton, and P. J. Frawley 4 Solid State Pharmaceuticals Cluster (SSPC), Materials and Surface Science Institute (MSSI), Department of Mechanical, Aeronautical 5 and Biomedical Engineering, University of Limerick, Castletroy, County Limerick, Ireland 6 ABSTRACT: Growth kinetics, growth mechanisms, and the effect of 7 solvent composition for the antisolvent crystallization of paracetamol in 8 methanol−water mixtures have been determined by means of isothermal 9 seeded batch experiments at constant solvent composition. A numerical 10 model incorporating the population balance equation based on antisolvent 11 free solubility was fitted to the desupersaturation data, and growth rate 12 parameters are evaluated. An attenuated total reflectance−Fourier transform 13 infrared (ATR-FTIR) probe was employed to measure online solute 14 concentration and focused beam reflectance measurement (FBRM) was 15 utilized to ensure negligible nucleation occurred. The model is validated by 16 the final particle size distributions (PSDs) and online solute concentration 17 measurements. Crystal growth rate was found to decrease with increasing 18 water mass fractions up to a mass fraction of 0.68 where an increase is 19 observed. A method has been introduced linking the effect of solvent 20 composition with the growth mechanism and the growth rates. Utilizing the growth mechanism it has been postulated that a 21 combination of the solubility gradient, viscosity, selective adsorption, and surface roughening are responsible for the reduction in 22 growth rates with solvent composition. Furthermore, the effects of seed mass, size and initial supersaturation on the crystal 23 growth rates were investigated to demonstrate the efficacy of the model at predicting these various phenomena. 1. INTRODUCTION and seeded desupersaturation experiments. There are numer- 51 24 Crystallization is a widely used technique in solid−liquid ous articles describing crystal growth from solutions where the 52 25 separation processes and is regarded as one of the most supersaturation is generated via cooling and precipitation.2−9 53 26 important unit operations in the process industries as many However, very few studies have focused on antisolvent 54 27 finished chemical products are in the form of crystalline solids. crystallizations, where the solvent plays a dominant role on 55 28 In antisolvent crystallization, supersaturation is generated by crystal growth. Single crystal studies using transient imagery 56 29 addition of another solvent or solvent mixture in order to were carried out on sodium nitrate in water and isopropox- 57 30 reduce the solubility of the compound. Antisolvent crystal- yethanol.10 Isothermal seeded batch experiments have been 58 31 lization is an advantageous method where the substance to be conducted for paracetamol and acetone−water mixtures, with 59 32 crystallized is highly soluble, has solubility that is a weak nonlinear optimization utilized to evaluate the parameters of a 60 33 function of temperature, is heat sensitive, or unstable in high power law expression to describe the growth rate, as a function 61 34 temperatures.1 Antisolvent processes have also been identified of supersaturation, from the experimental desupersaturation 62 35 as a means to produce crystals more efficiently from continuous curves.11 This work does not utilize online measurement 63 36 processes due to an ability to generate supersaturations quickly, techniques and similar studies have been conducted using 64 37 run at low temperatures isothermally, and a low tendency to isothermal seeded batch experiments, however employing 65 38 scale reactors which is a significant problem with cooling ATR-FTIR to track solution concentration online.8,12 This 66 39 crystallizations. Rigorous determination of an optimal batch work collects the previous results, methods, and observations in 67 40 recipe requires accurate growth and nucleation rate kinetics, the literature referenced above, however expanding them to 68 41 which can be determined in a series of batch experiments. Once improve the methods efficiency while attempting to analyze the 69 42 the particle formation kinetics are known, they can be used effect of composition on crystal growth rates. This work offers a 70 43 together with a population balance model to simulate the novel approach in estimating growth kinetics as a function of 71 44 influence of different process parameters on the final particle solvent composition from a population balance model solved 72 45 size distribution (PSD) of the product. utilizing the computationally efficient method of moments and 73 46 In precipitation processes, the crystal growth rate is a crucial 47 parameter since it determines the final specific properties of Received: September 5, 2011 48 crystals such as the final particle size distribution. Two methods Revised: February 20, 2012 49 are commonly described in the literature for the estimation of Accepted: February 20, 2012 50 crystal growth rate kinetics, namely single crystal growth studies © XXXX American Chemical Society A dx.doi.org/10.1021/ie2020262 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
- 2. Industrial & Engineering Chemistry Research Article74 simultaneously investigating the underlying mechanism of how Equation 2 can be multiplied through by Lk and integrated to 12275 the solvent affects the growth rates. The moments of the result in an equation in terms of the moments mk: 12376 distribution are reconstructed directly using a simple yet dm 077 accurate method yielding a very fast and effective means of =B dt (4)78 estimating growth rates. These reconstructed distributions are79 then compared to distributions obtained experimentally. In the case where the system is sufficiently seeded, negligible 12480 Capturing the effects of solvent composition on the growth nucleation can be assumed. Ensuring that no nucleation is 12581 rate is critical to building a population balance model. present is critical as seeding simplifies the mathematical 12682 Neglecting the influence of solvent composition will lead to treatment of the experimental data. Under this condition the 12783 discrepancies between experimental and modeled data. A second moment of the seed particle size distribution can only 12884 growth rate model that considers its parameters to be functions be influenced by the growth of the crystal and no other 12985 of antisolvent mass fraction has previously been shown to be competing factors. 13086 superior to a model without such functionality.13 The During the crystallization process, the mass balance of the 13187 nucleation kinetics for paracetamol in methanol−water solution phase can be described as 13288 mixtures has been evaluated elsewhere and shown to be dc ∞ 289 strongly dependent on solvent composition.14 This study aims dt = −3k vρcG 0 ∫ nL dL (5)90 to utilize a population balance to determine growth rates based91 on power law equations, while offering an insight into the where ρc and kv are the solid density and the volume shape 13392 growth mechanism and the effect of solvent composition. The factor of paracetamol crystals, respectively. In the above 13493 focus of the work is also to determine parameters for power law equation, the integral term represents the second moment of 13594 expressions which can be used in predicting and optimizing the seed crystals, m2 which is proportional to the total surface 13695 crystal size distributions. To date the literature does not contain area of crystals present. A value of 1332 kg/m3 will be 13796 any work detailing the estimation of growth kinetics of employed for the crystal density of form I of paracetamol.15 13897 antisolvent systems utilizing the method of moments together The following initial and boundary conditions apply: 13998 with in situ measurement techniques. In addition to this, a C(o) = C0 (6)99 greater effort has been made to gauge the effect of solvent100 composition on growth rate kinetics by linking with the n(0, L) = n0(L) (7)101 estimated growth rate mechanism. n(t , 0) = 0 (8) 2. POPULATION BALANCE MODEL AND PARAMETER with C0 being the initial concentration of the solute, n0(L) the 140102 ESTIMATION PROCEDURE initial PSD, and B is the nucleation rate per unit mass. The 141103 A mathematical model based on population balance equations supersaturation correlations used in this work for absolute 142104 (PBEs) is used in combination with a least-squares supersaturation and supersaturation ratio are as follows: 143105 optimization and the experimental desupersaturation data to ΔC = C − C* (9)106 determine the growth rate parameters of paracetamol in C107 methanol/water solutions as a function of solvent composition. S=108 2.1. Population Balance. In a perfectly mixed batch C* (10)109 reactor the evolution of the crystal size distribution can be where C is the solute concentration and C* is the antisolvent 144110 described as follows free solubility. The antisolvent free solubility is calculated and 145 described elsewhere.14 The crystal size distribution was 146 ∂n(L , t ) ∂n(L , t ) reconstructed from the moments utilizing a novel technique 147 + G (t ) =0 ∂t ∂L (1) developed by Hutton.16 This technique is outlined in more 148 detail by Mitchell et al.9 149111 where n(L,t) is the population density of the crystals and G(t) 2.2. Optimization. For the estimation of the growth 150112 is the crystal growth rate which is assumed to be independent kinetics parameters the following least-squares problem had to 151113 of size. The above equation is solved using the method of be solved: 152114 moments, detailed below. Nd Nd 2115116 The standard method of moments is an efficient method of transforming a population balance into its constituent mo- min ∑ R t2 = min ∑ ⎡(Stexp − Stsim(θ))⎤ ⎣ ⎦ i=1 i=1 (11)117 ments. The low order moments of the distribution represent118 the total number, length, surface area, and volume of particles where θ is the set of parameters to be estimated, represents Stsim 153119 in the crystallizing system. Using the standard method of the predicted supersaturation ratios, Stexp represents the 154120 moments, eq 1 becomes measured supersaturation ratios at each time or sampling 155 interval, and Nd is the number of sampling instances. The 156 dmk (t ) MATLAB optimization algorithm f minsearch which employs a 157 = kG(t )mk − 1(t ) dt (2) Nelder−Mead simplex method was utilized to find the optimal 158 set of parameters. 159121 where 3. EXPERIMENTAL SECTION ∞ k mk = ∫0 L n(L , t )dL (3) 3.1. Materials. The experimental work outlined was performed on Acetaminophen A7085, Sigma Ultra, ≥99%, 160 161 B dx.doi.org/10.1021/ie2020262 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
- 3. Industrial & Engineering Chemistry Research Article162 sourced from Sigma Aldrich. The methanol employed in this polynomial and the coefficients were computed in matlab with 223163 work was gradient grade hiPerSolv CHROMANORM for the regress function as follows: 224164 HPLC ≥99%, sourced from VWR.165 3.2. Apparatus. A LabMax reactor system from Mettler- Conc = 0.018 + 0.244Abs + 0.613Abs 2 − 0.0009Comp166 Toledo was utilized in this work to estimate the growth kinetics + 4.605Comp2 + 0.0005AbsComp R2167 of the paracetamol in a methanol/water solution system. The168 reactor was a 1-L round-bottomed borosilicate glass jacketed = 0.9979 (12)169 reactor, allowing controlled heating and cooling of solutions. The model was found to predict solution concentration with 225170 All experiments were carried out isothermally at 25 °C and at an average relative error of 0.95% over the concentration and 226171 constant solvent composition. Agitation of the solution was composition ranges investigated. A typical ATR-FTIR spectra 227172 provided by means of an overhead motor and a glass stirrer, for a paracetamol and methanol solution is shown in Figure 1, 228 f1173 with four blades at a pitch of 45°. The system allowed fluid with the peaks associated with the main functional groups 229174 dosing and the use of in situ immersion probes. The system highlighted. 230175 came with iControl LabMax software enabling real-time176 measurement of vital process parameters and full walk away177 operation. A custom wall baffle described previously9 was178 employed in all experiments to improve the level of mixing in179 the reactor. Antisolvent (water) addition into the solution was180 achieved using a ProMinent beta/4 peristaltic pump, which was181 found to be capable of a maximum addition rate of 30 g/min.182 An electronic balance (Mettler Toledo XS60025 Excellence)183 was used for recording the amount of the antisolvent added to184 the solution.185 3.2.1. FBRM Probe. A Mettler-Toledo Focused Beam186 Reflectance Measurement (FBRM) D600L probe was utilized187 in this work to track the evolution of the PSD and to ensure188 negligible nucleation occurred during desupersaturation experi-189 ments. For all FBRM measurements, the fine detection setting190 was employed, as the detection setting was found to produce a191 significant level of noise due to the agitation of the impeller.192 The instrument provided a chord length distribution evolution Figure 1. ATR-FTIR spectra of paracetamol in a methanol−water193 over time at 10 s intervals, which is useful for indicating the solution used for calibration.194 presence of nucleating crystals.195 3.3. ATR-FTIR Calibration. ATR-FTIR allows for the 3.4.1. Procedure. Measurement of Growth Kinetics. 231196 acquisition of liquid-phase infrared spectra in the presence of The measurement procedure for the independent determi- 232197 solid material due to the low penetration depth of the IR beam nation of growth rate kinetics is based on seeded batch 233198 into the solution. An ATR-FTIR ReactIR 4000 system from desupersaturation experiments realized at constant solvent 234199 Mettler-Toledo, equipped with a 11.75 ‘‘DiComp’’ immersion composition. Only the initial PSD of the seed crystals and the 235200 probe and a diamond ATR crystal, was used to track solution evolution of the solute concentration are needed for the 236201 concentration. The infrared spectra are known to be affected by determination of crystal growth rates. All experiments were 237202 concentration and solvent composition requiring calibration to conducted at 25 °C and at an impeller speed of 250 rpm. 238203 known experimental conditions. The amide functional group Scanning electron microscopy images were taken of the seed 239204 contained within paracetamol, which emits a bending frequency and the final product to ensure no change in crystal 240205 of 1517−1 in infrared spectroscopy. The calibration procedure morphology was observed and no polymorphic change 241206 employed in this work involves tracking the absolute height of occurred. The mass of solvent in the vessel ranged from 242207 one solute peak and correlating it to known solution 0.365 to 0.45 kg. A saturated solution was created upon mixing 243208 concentrations and solvent compositions. This method was paracetamol in a specific methanol/water mixture at 25 °C. The 244209 chosen as it was demonstrated to be capable of predicting solution was then heated 10 °C above the saturation 245210 solute concentration with a relative uncertainty of less than 3% temperature and held until complete dissolution was observed 246211 for a range of solution systems.17 The procedure involves by FBRM. The solution was then cooled back to the saturation 247212 measuring the absorbance of particular peaks and increasing the temperature. A supersaturated solution was then created via the 248213 concentration at a set number of intervals until the solubility is addition of a known mass of antisolvent into the reactor. A 249214 reached. The calibration points are varied to cover a range of range of supersaturations can be induced while avoiding the 250215 concentrations and solvent compositions. The compositions solution nucleating with prior knowledge of the MSZW. The 251216 and concentrations were varied between 40% and 68% and MSZW was determined from the experiments conducted using 252217 0.010−0.218 kg/kg, respectively. The method requires the the FBRM probe to detect the onset of nucleation outlined 253218 solubility to be known prior to the calibration in order to further in previous work.14The masses of solution and 254219 remain in the undersaturated stable region. The solubility was antisolvent were chosen in such a way to obtain the constant 255220 measured via a gravimetric method and detailed in previous mass fraction of interest. ATR-FTIR and FBRM were employed 256221 work.14 The values of absorbance (ABS), composition (Comp) to monitor the solute concentration and chord length 257222 and concentration (Conc) were fitted to a second order distribution during the experiment. At time zero a specific 258 C dx.doi.org/10.1021/ie2020262 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
- 4. Industrial & Engineering Chemistry Research Article 259 mass of dry seeds was charged into the reactor. The experiment to maintain a similar shape during the experiment, indicating 276 260 was monitored until a stable signal was obtained from ATR- that growth of the seed crystals is the dominant supersaturation 277 261 FTIR, indicating that the solubility had been reached. All consumption mechanism. After each experiment the solution 278f2 262 desupersaturation experiments were performed twice. Figure 2 was filtered, dried, and weighed, and the particle size 279 distribution was measured using a Horiba L92O particle size 280 analyzer (PSA). Similar results were obtained for all growth 281 characterization experiments. A number of experimental 282 conditions were varied in order to determine the effect of 283 initial supersaturation, seed mass, and seed size. These results 284 are discussed in more detail in Section 4. Finally, the measured 285 growth rate parameters were estimated by comparison of 286 simulations to experiments at different operating conditions. 287 3.4.2. Seed Preparation. Seed crystals were prepared by 288 cooling crystallizations in order to produce a higher mass of 289 crystals. The crystals were subsequently wet sieved using three 290 stainless steel, woven wire cloth sieves, with squares apertures 291 of nominal sizes of 90, 125, and 250 μm, respectively. The 292 remaining seed crystal fractions in the size ranges of 90−125 293 μm and 125−250 μm were washed, filtered, and dried. The 294 PSDs of all the three seed fractions were measured using a 295 Horiba L92O particle size analyzer (PSA), using saturated 296 water at room temperature as the dispersal medium. A 297 Figure 2. Repeatability of two sets of desupersaturation experiments dispersant solution saturated with paracetamol and containing 298 presented in Section 2.4. sodium dodecyl sulfate at a concentration of 5 g/L was also 299 employed to ensure no agglomeration occurred during the 300 263 shows the typical reproducibility of the measured desupersatu- particle size measurement. The particle size distributions were 301 264 ration curves for two repeated runs of experiments at different measured three times in accordance with ISO33320 and all 302 265 initial conditions. It can be readily observed that the distributions were found to be less 5%, 3%, and 5% for the d10, 303 266 repeatability was satisfactory in both cases. The growth kinetics d50, and d90 respectively. 304 267 were estimated for a range of solvent compositions from 40% 268 to 68% mass water, respectively. This range was chosen as 4. RESULTS 269 experiments carried out above 70% result in dilution due to a Five seeded batch desupersaturation experiments were 305 270 low solubility gradient. The absence of significant nucleation performed at various solvent compositions. An additional 306 271 was assured by monitoring the CLDs using the FBRM during three experiments were performed to investigate the effect of 307 272 the experiment. Typical time-resolved CLDs are shown in initial supersaturation, seed size fraction, and seed mass. The 308f3 273 Figure 3. It can be readily observed that no significant increase experimental runs were labeled PM1−PM8, and the corre- 309 274 in the counts at small chord lengths occurred, thus indicating sponding experimental conditions are listed in Table 1 where 310 t1 275 the absence of significant nucleation. Also the CLD was found Minitial and Mfinal are the initial and final percentage of water in 311 the vessel, respectively. Mw is the mass of solvent added to the 312 Table 1. Experimental Conditions of Seeded Growth Experiments seed M initial M final mass (wt %) (wt %) Mw exp. no. S0 seed fraction (kg) (water) (water) (kg) PM1 1.1755 125−250 0.00497 40 50 0.065 μm PM2 1.3077 125−250 0.00501 40 55 0.11 μm PM3 1.2330 125−250 0.00497 50 60 0.075 μm PM4 1.0854 125−250 0.00496 20 40 0.1 μm PM5 1.2198 125−250 0.00502 60 68 0.075 μm PM6 1.2160 125−250 0.00993 50 60 0.075 μm PM7 1.2223 90−125 μm 0.00497 50 60 0.075 PM8 1.4396 125−250 0.00495 40 60 0.150 μm PM5R 1.2164 125−250 0.00503 60 68 0.075 μm Figure 3. Measured CLDs from FBRM for typical seeded growth PM8R 1.4396 125−250 0.00502 40 60 0.150 experiment. μm D dx.doi.org/10.1021/ie2020262 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
- 5. Industrial & Engineering Chemistry Research Article Table 2. Growth Rate Parameters Estimated from Desupersaturation Data at Varying Compositions parameter 40% mass water 50% mass water 55% mass water 60% mass water 68% mass water kg 1.10 × 10−4 3.46 × 10−5 4.93 × 10−5 1.86 × 10−4 8.1232 × 10−5 g 1.7531 1.604 1.895 2.239 1.6083 residual 8.53 × 10−5 1.10 × 10−4 1.20 × 10−3 7.43 × 10−4 8.76 × 10−4 313 vessel to generate the initial supersaturation. The operating 314 parameters in Table 1 were chosen to cover the range of 315 interest and at the same time to avoid the occurrence of 316 nucleation. On the basis of this set of experiments, the growth 317 kinetics were evaluated. 318 4.1. Estimation of Growth Kinetics. To determine the 319 growth kinetics of paracetamol in methanol/water solutions, 320 the experimental desupersaturation data were used together 321 with the PBE model and the optimization algorithm described 322 in Section 2.2. An empirical power law expression was 323 employed to express the relationship between supersaturation 324 and growth rate, eq 13. G = kg (ΔC) g (13) 325 where kg is the growth rate constant, ΔC is absolute 326 supersaturation, and g is the growth exponent. The growth 327 rate parameters were calculated as a function of solventt2 328 composition and are listed in Table 2. The power law eq 13 Figure 5. Effect of initial supersaturation on the desupersaturation 329 provides a good fit of the desupersaturation data in all the curves.f4 330 growth experiments as can be seen from Figures 4−7. 4.3. Effect of Seed Mass. The effect of seed mass on the 345 rate of supersaturation decay is shown in Figure 6. It can be 346 f6 Figure 4. Desupersaturation experiment PM1: Experimental and simulated data. Figure 6. Effect of seed mass on the desupersaturation curves. 331 Changing the initial values of the estimated parameters over 332 several orders of magnitude in the optimization procedure seen from the plot that as a result of increasing seed mass, the 347 333 always produced the same results, hence indicating a global supersaturation in solution is consumed at a faster rate. This 348 334 optimum. increased consumption can be explained by the increase in total 349 4.2. Effect of Initial Supersaturation. The effect of initial seed surface area available for crystal growth, from the 350 335 additional seed. It should be noted that crystal growth rate is 351 336 supersaturation on the rate of supersaturation decay is shown in not a function of seed mass. Instead, the effect of seed mass on 352f5 337 Figure 5. It can be observed that generating a higher initial the decay of supersaturation is accounted for in eq 5, using the 353 338 supersaturation results in a faster rate of decay of super- second moment of the seed crystals present. A larger seed mass 354 339 saturation. At approximately 400 s the higher initial will result in a larger value for the second moment and hence 355 340 desupersaturation curve cuts across the lower curve. This is will result in higher decay of supersaturation. 356 341 an expected result as growth rates are a function of 4.4. Effect of Seed Size. The effect of seed size fraction on 357 342 supersaturation and a higher generation of supersaturation or the rate of supersaturation decay is shown in Figure 7. Figure 7 358 f7 343 driving force leads to a higher growth rate and desupersatura- demonstrates that when seeds of a smaller size fraction are 359 344 tion decay. present in solution, a faster rate of desupersaturation decay is 360 E dx.doi.org/10.1021/ie2020262 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
- 6. Industrial & Engineering Chemistry Research Article Figure 7. Effect of seed size on the desupersaturation curves. Figure 8. Experimental and simulated final PSD of run PM2. 361 observed, which can be explained by eq 5. A smaller seed size 362 provides a larger specific surface area for the crystal growth 363 process. Hence the second moment of the seed crystals, m2 will 364 be larger, promoting a faster desupersaturation decay. This 365 effect is analogous to the effect of seed mass, although the effect 366 of seed size on the desupersaturation decay is not as 367 pronounced as the effect of seed mass. This may be due to 368 the fact that there is not a substantial difference between the 369 size fractions employed to produce significantly different 370 results. 371 4. 5. Accuracy of Numerical Model. The technique 372 employed here provides two methods of verifying the accuracy 373 of the numerical model employed in this work. The first is the 374 simulated desupersaturation curves shown in Figures 4−7. It 375 can be seen that a reasonable fit to the desupersaturation data is 376 achieved with a maximum residual calculated using eq 9 of 1.2 377 × 10−3. Residuals for all growth rate estimation experiments are 378 reported in Table 2. All phenomena associated with the effects Figure 9. Experimental and simulated final PSD of run PM3. 379 on crystal growth, such as the effect of initial supersaturation, 380 seed mass, and seed size are captured by the numerical model 4.6. Growth Rate Mechanism. In the previous section 404 381 as can be seen from Figures 4−7. growth kinetics as a function of solvent composition were 405 382 The second method for validating the accuracy of the evaluated via fitting a population balance model to 406 383 numerical model employed involves comparison of the desupersaturation data. These parameters are essential in 407 384 experimental product PSDs with the simulated product PSDs. 385 The particle size distributions for PM2, PM3, and PM4 aref8f9f10 386 plotted in Figures 8, 9, and 10, respectively. It can be readilyf11 387 observed from Figure 11 that the experimental PSD has shifted 388 to larger particle size values. It can be seen that a reasonable 389 prediction is obtained from the numerical model of the 390 simulated PSD. All other experiments conducted within this 391 work were found to be in similar agreement. The numerical 392 model captures the particles in the smaller range quiet well, 393 however in experiment PM3 the experimental PSD is slightly 394 underpredicting the larger particles. Some particle agglomer- 395 ation can be seen in the product PSDs, however Figure 11 396 shows that this agglomeration originates from the seed and thisf12 397 is supported by both Figure 11 and 12 which show PSDs and 398 SEM images of both seed and product PSDs. To some extent 399 this agglomeration may be due to the particles agglomerating 400 on filtration or on storage as the particles appear to absorb 401 moisture quite strongly when present in air. Monitoring the 402 particles during the experiments with FBRM also suggests that Figure 10. Experimental and simulated final PSD of run PM4. 403 no significant agglomeration occurred. F dx.doi.org/10.1021/ie2020262 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
- 7. Industrial & Engineering Chemistry Research Article Figure 13. Growth rate as a function of supersaturation ratio at various Figure 11. Seed PSD together with the experimental final and solvent compositions. simulated PSD of run PM4. interface. Since the concentration of the solute is greater as you 418 leave the interface, solute will diffuse toward the crystal surface. 419 If diffusion of solute from the bulk solution to the crystal 420 surface is rate limiting, growth is diffusion controlled. A model 421 that focuses on the diffusion of solute through the boundary 422 layer is known as the diffusion controlled model. If 423 incorporation into a crystal lattice is the slowest process, 424 growth is surface-integration controlled. To determine which 425 growth mechanism is rate determining we use the following 426 equation: 427 kM G = kd a (c − c*) 3k vρ (14) where M is the molar mass of paracetamol (0.15117 kg/mol), c 428 is the concentration, and c* is the solubility in molar units of 429 mol/m3. This equation requires the mass transfer coefficient, 430 which is calculated using the Sherwood correlation. 431 ⎛ ⎛ εL4 ⎞1/5 ⎞ D⎜ 1/3⎟ kd = ⎜2 + 0.8⎜ 3 ⎟ Sc ⎟ ⎜ ⎟ L ⎝ ⎝ ν ⎠ ⎠ (15) where D is the diffusivity or diffusion coefficient, L is the crystal 432 size, ε is the average power input, υ is the kinematic viscosity, 433 and Sc is the Schmidt number (Sc = υ/D). Since the solvent 434 composition in this work is dynamic, the variation in the 435 density of the solution is considered through 436 1 ρsolution = mfrac w /ρw + (1 − mfrac w)/ρm (16) Figure 12. SEM image of (A) seed and (B) product crystals from run PM4. where Mfracw is the mass fraction of water and ρw and ρm are 437 the densities of water and methanol, respectively. This results in 438 408 developing a numerical model to optimize an antisolvent dynamic viscosity as a function of solvent composition. The 439f13 409 crystallization process. Table 2 and Figure 13 show that solvent diffusion coefficient, D, can be evaluated using the Stokes− 440 410 composition has a significant impact on the growth rates. In Einstein equation as follows: 441 411 this section, we attempt to further investigate the underlying kT 412 mechanisms of the effect of solvent on the growth rates D= 3πμdm (17) 413 observed in Section 4.1. −23 414 Goals of crystal growth theory are to determine the source of where k is the Boltzmann constant (1.38065 × 10 J/K), T is 442 415 steps and the rate controlling step for crystal growth. As a the temperature in Kelvin, and μ is the dynamic viscosity of the 443 416 crystal grows from a supersaturated solution, the solute fluid. Because all values of viscosity are calculated as a function 444 417 concentration is depleted in the region of the crystal−solution of solvent composition a case study of a water mass fraction of 445 G dx.doi.org/10.1021/ie2020262 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
- 8. Industrial & Engineering Chemistry Research Article 446 0.4 will be used for demonstration purposes. The dynamic 447 viscosity of the fluid at a water mass fraction of 0.4 is (6.45008 448 × 10−4 kg/m s @ 25 °C). The molecular diameter, dm in the 449 above expression is evaluated as follows: 1 dm = 3 ccNA (18) 450 where cc is the molar density of the paracetamol (8.8113 kmol/ 451 m3), and NA is Avogadro’s constant (6.022 × 1026 1/kmol). 452 This results in a value of 5.733 × 10−10 m for the molecular 453 diameter of paracetamol crystals. For stirred tanks, the average 454 power input, ε, can be evaluated using: NPvs3ds5 ε= V (19) 455 where Np is the Power number of the impeller, vs is the stirrer Figure 15. Diffusion growth rates and experimental growth rates as a 456 speed (250 rpm), ds is the stirrer diameter (0.06 m), and V is function of solvent composition at a constant supersaturation of 1.2. 457 the solution volume (0.0004 m3). For the downward-pumping, 458 four-blade, 45° pitched blade impeller used in this work, a generated at this point of the solubility curve, which in turn 482 459 Power number of 1.08 has been estimated previously by can increase the experimental error. It is difficult to obtain 483 460 Chapple et al.18 This results in an average power input of reproducible data in this region of the solubility curve due to a 484 461 0.1493 W/kg for the LabMax reactor. Using the above values, 462 for an average particle size, L, of 2 × 10−4 m and a water mass low driving force. The data in Figure 15 are also calculated for a 485 463 fraction of 0.4 at 25 °C, eq 15 yields a value of 1.23 × 10−5 m/s constant supersaturation of 1.2 which is outside the super- 486 464 for the mass transfer coefficient, kd, for this solution system. saturation range generated in the experiment carried out to 487 465 The values of kd as a function of solvent composition are shown estimate growth rates for a water mass fraction above 0.68. The 488f14 466 in Figure 14. reduction in both diffusion limited growth rates and the 489 experimental growth rates is approximately proportional by a 490 factor of 2. The slope of both growth rates as a function of 491 water mass fraction is −1 × 10−7 m/s from water mass fractions 492 of 0.4−0.6. The discrepancy between the experimental growth 493 rates and the diffusion limited growths can be attributed to a 494 reduction in the solubility gradient, higher solution viscosities, 495 selective adsorption of solvent molecules at specific surface sites 496 due to strong interactions between solute and solvent 497 molecules, and the influence of the solvent on the surface 498 roughening. These mechanisms are discussed in more detail in 499 the following section. 500 4.7.1. Effect of Solvent Composition. Selective 501 Adsorption and Surface Roughening. The role played by 502 the solvent in enhancing or inhibiting crystal growth is not clear 503 at present.18 According to the existing literature, the solvent 504 may contribute to decreasing growth rate due to a selective 505 adsorption of solvent molecules or may enhance face growth 506 Figure 14. Mass transfer coefficient kd calculated from eq 15 as a rate by causing a reduction in the interfacial tension.19−21 The 507 function of solvent composition. first mechanism has been attributed to a selective adsorption of 508 solvent molecules at specific surface sites due to strong 509 467 The knowledge of kd provides the possibility of calculating 468 the diffusion growth rates as a function of solvent composition. interactions between solute and solvent molecules.20−22 The 510 469 Diffusion limited growth rates calculated from eq 14 are plotted second mechanism referred to here as the interfacial energy 511f15 470 in Figure 15. Over the range of solvent compositions studied, effect, is related to the influence of the solvent on the surface 512 471 the experimental growth rates were found to be lower than the roughening which under certain circumstances may induce a 513 472 diffusion limited growth rates, predicted from eq 14. Therefore, change in the growth mechanism.23−25 Davey and co-workers 514 473 surface integration of the solute is deemed to be the rate provide a good example of the interfacial effect of the solvent 515 474 limiting step of the growth mechanism. Figure 15 shows that as on crystal interface. They reported on the growth kinetics of 516 475 the mass fraction of water increases, a reduction in the hexamethylene tetramine (HMT) crystallized from different 517 476 experimental growth rates and the diffusion limited growth solvents and solvent mixtures.23−27 It was reported that the 518 477 rates is observed. With the exception of water mass fraction of growth rate of the (110) face increased faster when water or 519 478 0.68, it can be seen that the experimental growth rates reduce at water/acetone mixtures replaced ethanol as the solvent. 520 479 the same rate as the diffusion limited growth rates. This Decreasing surface diffusion and a direct integration to the 521 480 increase at mass fractions of 0.68 may be due to some crystal lattice were connected to a change in the growth 522 481 experimental error as very little supersaturation can be mechanism. The observed effect was attributed to favorable 523 H dx.doi.org/10.1021/ie2020262 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
- 9. Industrial & Engineering Chemistry Research Article 524 interactions between the solute and the solvent at increasing supersaturation, seed mass, and seed size have been investigated 563 525 solubility. and the numerical model has been shown to capture these 564 526 4.7.2. Solubility Gradient. It has been shown that at higher phenomena with good accuracy. With regard to the effect of 565 527 solubilities more favorable interactions occur between the initial supersaturation, faster desupersaturation decay and hence 566 528 solute and solvent or in the case studied here lower solubilities crystal growth rate was observed with higher supersaturations 567 529 leading to unfavorable interactions. The solubility gradient may due to a larger driving force. A faster desupersaturation decay 568 530 also have an impact as the gradient is reduced with higher water was observed for cases where a larger seed mass was used. This 569 531 mass fractions leading to a reduced driving force and hence increased consumption can be explained by the increase in total 570 532 reduced crystal growth. Desupersaturation experiments gen- seed surface area available for crystal growth, from the 571 533 erally involve adding a known amount of antisolvent into the additional seed. A similar observation was made when seeds 572 534 reactor and generating a specific supersaturation, followed by of a smaller size fraction were used. A smaller seed size provides 573 535 seeding and subsequent growth. However as the water mass a larger specific surface area for the crystal growth process. 574 536 fraction tends to one the gradient of the solubility with respect Hence the second moment of the seed crystals, m2 will be 575f16 537 to the water mass fraction reduces. Figure 16 illustrates that the larger, promoting a faster desupersaturation decay. Further- 576 more the role of the solvent has shown to have a significant 577 impact on the crystal growth rate. Diffusion growth rates have 578 been calculated in order to provide detail about the growth 579 mechanism. With the aid of the growth mechanism a detailed 580 discussion on how solvent composition affects growth rates is 581 outlined. The effects of solvent composition are split into four 582 different phenomena and the growth mechanism is utilized to 583 determine which one is the most probable. The phenomena are 584 named surface roughing, selective absorption, solubility 585 gradient, and increasing viscosity due to higher water mass 586 fractions. This work offers a successful methodology for the 587 quick determination of crystal growth parameters for use in 588 modeling and optimizing particulate systems and also highlights 589 that investigating the crystal growth mechanism can offer new 590 insights into understanding the role of the solvent in affecting 591 crystal growth kinetics. 592 Figure 16. Antisolvent free solubility gradient as a function of water ■ AUTHOR INFORMATION Corresponding Author 593 594 mass fraction. *Tel.: 00 353 61 213134. Fax: 00 353 61 202944. E-mail: 595 clifford.ociardha@ul.ie. 596 538 driving force is reduced when starting from 0.6 in comparison Notes 597 539 to starting and generating a supersaturation from 0.4. Hence The authors declare no competing financial interest. 598 ■ 540 the driving force is reduced resulting in a reduced mass transfer, 541 solute integration, and subsequent crystal growth rate. ACKNOWLEDGMENTS 599 542 4.7.3. Viscosity. One other reason could be due to the 543 increased viscosity of the fluid inhibiting mass transfer of the This research has been conducted as part of the Solid State 600 544 solute from solution to the crystal face thereby reducing the Pharmaceuticals Cluster (SSPC) and funded by Science 601 Foundation Ireland (SFI). 602 ■ 545 crystal growth rate. Figure 15 shows that at higher water mass 546 fractions a reduction in mass transfer is observed. The mass 547 transfer coefficient is a function of dynamic viscosity as can be NOMENCLATURE 603 548 seen from eq 15, therefore higher water mass fractions lead to B = Nucleation rate (no./kg methanol s) 604 549 higher densities and viscosities leading to inhibited mass C = Concentration (kg/kg methanol) 605 550 transfer of solute. This mechanism along with the effect of the C* = Equilibrium concentration (solubility) (kg/kg 606 551 solubility gradient appears to be the most likely mechanism as methanol) 607 552 the decrease in the experimental growth rates is largely D = Diffusivity (m2/s) 608 553 proportional to the diffusion limited growth rates. G = Growth rate (m/s) 609 K = Boltzmann’s constant (J/K) 610 5. CONCLUSIONS L = Particle size (m) 611 M = Molar mass (kg/kmol) 612 554 Growth kinetics as a function of solvent composition have been Np = Power number (-) 613 555 determined based on seeded isothermal batch desupersatura- NA = Avogadro Constant (no./kmol) 614 556 tion experiments. A population balance model combined with a R = Gas constant (J/kmol K) 615 557 parameter estimation procedure have been utilized to obtain Sc = Schmidt number (-) 616 558 growth rate parameters from desupersaturation data. The Stsim = Simulated supersaturation ratio (-) 617 559 method takes advantage of two online PAT technologies to Stexp = Experimental supersaturation ratio 618 560 measure solution concentration and to ensure negligible T = Temperature (K) 619 561 nucleation occurs. The method has been shown to predict V = Solution volume (m3) 620 562 experimental data with good accuracy. The effects of initial cc = Molar density (kmol/m3) 621 I dx.doi.org/10.1021/ie2020262 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
- 10. Industrial & Engineering Chemistry Research Article622 dm = Molecular diameter (m) cetamol in methanol/water solutions. J. Cryst. Growth 2011, 328, 50− 687623 ds = Stirrer diameter (m) 57. 688624 g = Growth order (-) (15) Brittain, H. G., Ed. Polymorphism in Pharmaceutical Solids; 689625 ka = Surface area shape factor (-) Marcel Dekker Inc.: New York, 1999. 690 (16) Hutton, K. Mathematical modelling of gibbsite precipitation, 691626 kd = Mass transfer coefficient (m/s) Ph.D. Thesis, University of Limerick, Ireland, 2009. 692627 kg = Growth rate constant (m/s) (17) Lewiner, F.; Klein, J. P.; Puel, F.; Févotte, G. On-line ATR-FTIR 693628 kv = Volume shape factor (-) measurement of supersaturation during solution crystallization 694629 mf rac = Mass fraction (-) processes. Calibration and applications on three solute/solvent 695630 mk = kth Moment of particle size distribution (mk) systems. Chem. Eng. Sci. 2001, 56, 2069−2084. 696631 n = Population density (no./m4) (18) Chapple, D.; Kresta, S. M.; Wall, A.; Afacan, A. The effect of 697632 vs = Stirrer speed (no./s) impeller and tank geometry on power number for a pitched blade 698633 ε = Average power input (W/kg) turbine. Trans. IChemE 2002, 80 (A), 364−372. 699634 μ = Dynamic viscosity (kg/m s) (19) Lahav, M.; Leiserowitz, L. The effect of solvent on crystal 700635 π = Pi (-) growth and morphology. J. Chem. Eng. Sci. 2001, 56 (7), 2245−2253. 701 (20) Berkovitch-Yellin, Z.; Van Mil, J.; Addadi, L.; Idelson, M.; 702636 ρc = Crystal density (kg/m3) Lahav, M.; Leiseroweitz, L Crystal morphology engineering by ″tailor- 703637 υ = Kinematic viscosity (m2/s) made″ inhibitors; A new probe to fine intermolecular interactions. J. 704638 ρsoln = Solution density (kg/m3) Am. Chem. Soc. 1985, 107, 3111. 705639 ρw = Water density (kg/m3) (21) Mersmann, A., Ed. 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