- Email: [email protected]
Monitoring the particle size and shape in the crystallization of paracetamol from water
chemical engineering research and design 8 8 ( 2 0 1 0 ) 447–454
Contents lists available at ScienceDirect
Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Monitoring the particle size and shape in the crystallization of paracetamol from water Michel Kempkes, Thomas Vetter, Marco Mazzotti ∗ ETH Zurich, Institute of Process Engineering, Sonneggstrasse 3, CH-8092 Zurich, Switzerland
a b s t r a c t In this work, a technique capable of restoring bidimensional particle size distributions from images of the particles in suspension is applied to the seeded cooling crystallization of paracetamol from water. The effects of cooling rate and stirring rate on the final particle size and shape are studied and the average growth rates along different directions of particles are found to be strongly dependend on supersaturation. This observation is in line with previous studies, though in this work it has been established for the first time using populations of particles. The technique was capable of quantifying changes in particle size and shape, indicating particle sizes and shapes that correlated well with observations from electron microscopy images. © 2009 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Crystallization; Imaging; Instrumentation; Particle size; Particle shape; Particulate processes
1.
Introduction
The importance of particle shape is widely acknowledged (Variankaval et al., 2008; Wang et al., 2008, 2007), but the lack of measurement techniques to quantify this important property has severely limited research efforts in this direction. Thus far, particle shape has mainly been characterized in a semi-quantitative manner, by observations from optical or electron microscopic images. Due to the extensive sample preparation required, the conclusions drawn from these images were usually based on a very limited number of particles. Puel et al. (1997) were among the first to characterize particle shape for larger numbers of particles. In their work, microscopic images of crystals were analyzed using optical microscopy and a semi-automatic image analysis routine. The size of the crystals was measured in two dimensions, with the third dimension either assumed equal to one of the other two, or constant. The approach yielded the bidimensional particle size distribution (PSD) of the crystals. This approach was adopted in later works, to model (Briesen, 2006; Oullion et al., 2007b; Puel et al., 2003a) or to monitor crystallization processes (Oullion et al., 2007a; Puel et al., 2003b) where shape varies throughout the particle population. Recently, we presented a technique that allows for the characterization of a 2D PSD (Eggers et al., 2008). The tech-
∗
nique is based on the fully automated analysis of a large set of microscopic images from crystals in suspension. The technique requires minimal sample preparation, gives high quality images of the crystals in suspension and produces results based on a very large number of particles. However, since the crystals are suspended in a flowing liquid, the images and the measurements inferred from them are based on randomly oriented particles. More specifically, what is measured for each observed particle, are the major and minor axis lengths of an ellipse with the same area moment of inertia as the projection of the particle. From a large set of these measurements, the so-called axis length distribution (ALD) can be constructed. The relation between the underlying 2D PSD and the ALD that is measured was established in a previous publication (Kempkes et al., 2008). This measurement model was used in combination with a genetic algorithm to find the underlying 2D PSD (Eggers et al., 2008). It is the goal of this work to apply these techniques to a crystallization process and to demonstrate its capability to quantify variations in particle size and shape due to changes of the operating conditions. In particular, the effects of cooling rate and stirring rate on the 2D PSD of the final product crystals are studied in the seeded batch cooling crystallization of paracetamol from water. The 2D PSDs thus obtained
Corresponding author. Tel.: +41 44 6322456; fax: +41 44 63221141. E-mail address: [email protected] (M. Mazzotti). Received 31 October 2008; Received in revised form 22 July 2009; Accepted 2 September 2009 0263-8762/$ – see front matter © 2009 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.cherd.2009.09.006
448
chemical engineering research and design 8 8 ( 2 0 1 0 ) 447–454
In a typical analysis, about 1 × 104 images are acquired, which contain from about 5 × 104 to 1 × 105 particles. From this large set of individual measurements of major and minor axis lengths, the overall axis length distribution r(a, b) is constructed.
2.2.
Restoration of 2D PSD from ALD
Fig. 1 – Scheme of the experimental setup used to determine the ALD. The suspension to be analyzed is sucked through a narrow flow channel where two windows have been installed. Light from the xenon-stroboscope passes through this channel to an optical system with a digital camera that rapidly acquires images of the crystals in suspension.
Previously, we presented a measurement model capable of a very fast calculation of the ALD for any given 2D PSD (Kempkes et al., 2008). A Monte-Carlo simulation is used to calculate the so-called single particle ALDs rp (a, b; L1 , L2 ) which give the probability of observing a projection with major axis length a and minor axis length b, orginating from a particle with sizes L1 and L2 . Since the ALD for the entire particle population is the sum of these single particle ALDs, weighted by the occurence of these particles, i.e. the 2D PSD, the population ALD can be calculated with the following equation:
are then compared to observations from electron microscopic images.
r(a, b) =
∞
rp (a, b; L1 , L2 )n(L1 , L2 )
0
2. Characterization of a bidimensional particle size distribution In the following we present a brief summary of previously presented techniques that are used in this work. The reader can find in published papers more details about the experimental setup as well as the restoration algorithm (Eggers et al., 2008), and about the measurement model used in the restoration algorithm (Kempkes et al., 2008).
2.1.
Measurement of ALD
The measurement of the ALD is performed using the setup shown in Fig. 1 where the suspension is pumped through a flow through cell. The cell consists of two metal discs with sapphire windows and openings in the top and the bottom. On one side of each disc, a narrow flow channel is milled out. The discs are pressed together by a set of screws and sealed with an O-ring. A peristaltic pump, located after the cell to avoid damage to the crystals prior to the measurement, pumps the suspension through the setup. On one side of the cell a LX7865 high intensity xenon flash lamp (Hamamatsu Photonics, Japan) and on the opposite side of the cell a Leica Z6-APO optical system equipped with a DFC290 digital camera (Leica Microsystems, Switzerland) are installed. The system is capable of acquiring 10 images per second with a resolution of 1.75 m per pixel and a field of view of 3579 m × 2684 m. The depth of field of the optical system is identical to the depth of the flow channel, thus ensuring that all particles are in focus. This, together with the transmission illumination, guarantees sharp edges and well defined contours of the detected particles. The task of the image analysis routine is facilitated by the high quality of the images. Image analysis consists of a thresholding step, followed by contour closing and region filling. These operations are followed by the measurement of several properties of the detected objects. A set of criteria is formulated that, based on these measurements, aims to allow only good, single crystals to be considered for further analysis. For each of these objects, the major length a and the minor axis b length of an ellipse with equal moments of inertia are calculated.
∞
dL2 0
∞
×
0
dL2
∞
¯ 1 , L2 ) p(L
0
¯ 1 , L2 ) n(L1 , L2 )dL1 p(L
dL1
(1)
where n(L1 , L2 ) is the 2D PSD, whose meaning is that the total number of particles per unit volume of the suspension with characteristic dimensions between L1 and L1 + dL1 , and between L2 and L2 + dL2 is n(L1 , L2 )dL1 dL2 (n has units of m−5 ). The above equation allows for a fast calculation of the ALD for any given 2D PSD. To perform the inverse operation, i.e. the restoration of a 2D PSD from a measured ALD, we developed an algorithm that assumes a 2D PSD, calculates the corresponding ALD, and then minimizes the difference between the measured and the calculated ALD (Eggers et al., 2008). The 2D PSD for which this difference is minimized, is the bidimensional particle size distribution of the sample analyzed in the flow through cell. In this work, the ALD is visualized as a contour plot, with the color indicating the frequency with which a certain combination of major and minor axis lengths was observed. The 2D ˜ 1 , L2 ), PSD is represented as a volume weighted distribution, n(L which is defined in terms of the number weighted distribution, n(L1 , L2 ), as: ˜ 1 , L2 ) = L1 L22 n(L1 , L2 ) n(L
(2)
where n˜ has units of m−2 . This definition accounts for the fact ˜ 1 , L2 ) that the volume of a cuboid particle is L1 L22 . Visualizing n(L instead of n(L1 , L2 ) as a contour plot highlights the features of the larger particles in the crystal population. To facilitate a comparison of the particle shape between different experiments, the distribution of the aspect ratio is also calculated from the restored 2D PSDs. If we define the aspect ratio as follows: A=
L1 L2
(3)
Then the number of particles with an aspect ratio between A and A + dA is defined as:
f (A)dA =
∞
(A+dA)L2
n(L1 , L2 )dL1
dL2 0
AL2
(4)
chemical engineering research and design 8 8 ( 2 0 1 0 ) 447–454
449
Fig. 2 – Approximation of the complex shape of paracetamol crystals by a square cuboidal geometry. Crystal A has L1 = 400 m and L2 = 150 m; crystal B has L1 = 1000 m and L2 = 200 m. The unit bar corresponds to 200 m.
where f (A) is the aspect ratio density distribution (f (A) has units of m−3 ). Similarly to the 2D PSD we want to avoid the masking effect of small, shapeless particles and will therefore mainly be using the volume weighted aspect ratio distribution f˜ (A), which is defined as:
f˜ (A)dA =
(A+dA)L2
˜ 1 , L2 )dL1 n(L
dL2 0
3.
∞
(5)
AL2
Experimental work
Paracetamol (N-(4-hydroxyphenyl)acetamide) crystallized from water forms crystals that, despite the many different faces and rather complex geometry, can rather well be approximated by a square cuboidal geometry. This is illustrated for two paracetamol crystals in Fig. 2, where the length of the cuboids is denoted by L1 and the width and the thickness by L2 . This means that in the (L1 , L2 ) space, the second, more elongated crystal will be positioned further away from the diagonal than the first, more compact crystal. It is known that the growth rates of the crystal faces strongly depend on the supersaturation (Ristic et al., 2001), resulting in rather elongated crystals at low supersaturations and more prismatic crystals at high supersaturations. So far, these observations have been based on a rather small set of crystals. In this work, the previously presented techniques to characterize crystal size and shape for a very large set of crystals are applied to the crystallization of paracetamol, where the effect of operating conditions, in this case cooling rate and stirring rate, on the final 2D PSD is studied. The experiments were conducted in a temperature controlled 2000 mL glass reactor, stirred by a 4-blade glass impeller with 45◦ inclined blades and a diameter of 50
mm (LTS, Switzerland). A suspension of paracetamol (≥98%, Fluka, France) in de-ionized water at 40 ◦ C was equilibrated overnight and filtered off. To the clear solution thus obtained, a mass of 1.3 g of seed crystals per kilogram of solution were added. The seed crystals had been prepared by shock-cooling a saturated solution of paracetamol in ethanol from 50 to 5 ◦ C, which was then filtered and wet-sieved. The sieve fraction from 125 to 180 m were dried and used as seed crystals. An SEM image of the seed crystals, together with the measured ALD and the restored 2D PSD are shown in Fig. 3. After addition of the seed crystals, the suspension was cooled from 40 to 15 ◦ C. At 15 ◦ C, the solution was filtered off and the crystals were washed with ice-cold water and dried. A small amount of crystals was used for electron microscopic analysis. The remainder was added to a large volume of clear iso-propanol solution saturated with paracetamol which was then pumped through the flow through cell for analysis. A total of 1 × 104 images were taken for each sample. The choice of iso-propanol as a transport medium in the flow through cell was motivated by the tendency of paracetamol crystals to form weak agglomerates in water, i.e. an effect that complicates particle measurement and that was not observed in iso-propanol.
3.1.
Effect of cooling rate
In the first set of experiments, the effect of cooling rate on the final particle size and shape was studied. To this end, the seeded solution was linearly cooled from 40 to 15 ◦ C at cooling rates of 10, 5, 1.5 and 0.5 ◦ C/h, while stirring at 250 rpm; the experiments lasted 2.5, 5, 16.5 and 50 h, respectively. The results of these experiments and of the analysis outlined above are shown in Fig. 4.
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chemical engineering research and design 8 8 ( 2 0 1 0 ) 447–454
Fig. 3 – An SEM image of the seed crystals used in all experiments (a) the ALD measured by the flow through cell (b) and the volume weighted 2D PSD that was restored from the ALD (c). The 2D PSD is shown in a log–log plot, where the location of the highest peak is indicated by the dashed lines. The unit bar in the SEM image corresponds to 200 m.
3.2.
Effect of stirring rate
The aim of the second series of experiments was to study the effect of the stirring rate on the final particle size and shape. Since the effect of increased stirring rate and therefore enhanced abrasion and breakage phenomena would be most pronounced with elongated crystals, a cooling rate of 0.5 ◦ C/h was applied. Stirring rates of 250, 500 and 1000 rpm were used. The effect of stirring rate on particle size and shape is illustrated in Fig. 5a–c.
3.3.
Combined experiment
A third type of experiment was performed where the seeded solution was cooled with a cooling rate of 0.5 ◦ C/h and a stirring rate of 250 rpm to produce a suspension of elongated crystals same as those in Figs. 4a and 5a. This suspension was then stirred at 1000 rpm for 50 h. The results of this experiment are shown in Fig. 5d.
common particle size of the seed crystals, both corresponding to the locations of the highest peaks in the 2D PSDs as indicated in the corresponding Figs. 3 and 4. For this analysis only the bigger particles are considered if the 2D PSD is bimodal. In Fig. 7 the total extents of growth in both characteristic dimensions, Li , are compared with each other for different cooling rates. Dividing the total amounts of growth by the duration of the experiment yields the average growth rates ¯ i , also shown in Fig. 7b. It is readily seen in both directions, G that the seed crystals experience very different growth rates when different cooling rates are applied. More importantly, ¯ 1 /G ¯ 2 , is strongly the ratio between the average growth rates, G influenced by the cooling rate, as can be seen in Fig. 7b. Considering the cooling rate to be a proxy of the supersaturation, i.e. faster cooling results in a higher average level of supersaturation, the observed relation between cooling rate and growth rates is well consistent with earlier reports (Ristic et al., 2001).
4.2.
4.
Discussion
4.1.
Effect of cooling rate
With reference to Fig. 4 one can readily observe that slower cooling, corresponding to lower average levels of supersaturation, results in more elongated crystals. A qualitative indication of this trend is given by the SEM images and is confirmed and quantified by the measured ALDs (second column of Fig. 4) and by the 2D PSDs that were restored from the ALDs (third column of Fig. 4). It should be stressed that contrary to observations from SEM images, where only a handful of particles is shown, the ALDs and PSDs are based on thousands of particles and can therefore be used to make quantitative statements about the changes of crystal size and shape during crystallization. To facilitate an analysis of the effect of the cooling rate on the particle shape, the volume weighted distributions of aspect ratio f˜ (A) are plotted in Fig. 6. This shows that, the lower the cooling rate hence the lower the average level of supersaturation, the higher the aspect ratio. The total amount of growth in the L1 and the L2 directions can be estimated by comparing the most common particle size of the product crystals with the most
Effect of stirring rate
The effect of changing stirring rate at constant low cooling rate (0.5 ◦ C/h) is illustrated in Fig. 5a–c. For the sake of comparison Fig. 5a reports the same experiment at 250 rpm already shown in Fig. 4a, yielding elongated crystals with an aspect ratio of about 4. The main effect is that the aspect ratio decreases as the stirring rate increases, namely it is between 2 and 3 at 500 rpm and about 1 at 1000 rpm. The particles obtained in the last experiment are remarkably rounded and homogeneous in size. The volume weighted distributions of aspect ratios plotted in Fig. 8 for these three experiments demonstrate quantitatively the same trend. Under the action of high stirring rates growing crystals do not have the possibility to develop an elongated shape as it is the case at low stirring rate. This might be due to particle abrasion or to secondary nucleation, both phenomena being certainly favored at high stirring rates. At least in the case of the experiment at the highest stirring rate shown in Fig. 5c, we tend to favor abrasion because of the rounded shape of the final particles and of the scarcity of fines in the final distribution. It is worth noting that we consider abrasion and fragmentation as two different types of breakage phenomena. In the
chemical engineering research and design 8 8 ( 2 0 1 0 ) 447–454
451
Fig. 4 – Effect of cooling rate on the size and shape of the final crystals. In the left column the SEM images are shown, in the middle column the measured ALD is shown and in the right column the volume weighted, restored 2D PSDs are shown in a log–log plot. The highest peaks of the large particles in the PSDs are indicated with the dashed lines. The unit bar in the SEM images corresponds to 200 m. The stirring rate was 250 rpm in all experiments. Cooling rates were: (a) 0.5, (b) 1.5, (c) 5 and (d) 10 ◦ C/h.
452
chemical engineering research and design 8 8 ( 2 0 1 0 ) 447–454
Fig. 5 – Effect of stirring rate on the size and shape of the final crystals. In the left column the SEM images are shown, in the middle column the measured ALD is shown and in the right column the volume weighted, restored 2D PSDs are shown in a log–log plot. The unit bar in the SEM images corresponds to 200 m. The cooling rate was 0.5 ◦ C/h in all experiments. Stirring rates: (a) 250 (this is the same experiment shown in Fig. 4a; (b) 500; (c) 1000 rpm; (d) combined experiment (see Section 3.3 for a detailed description).
chemical engineering research and design 8 8 ( 2 0 1 0 ) 447–454
453
Fig. 6 – The volume weighted aspect ratio distributions f˜ (A) of the particle obtained at different cooling rates.
Fig. 8 – The volume weighted aspect ratio distributions f˜ (A) of the particles obtained at different stirring rates.
former case the breakage event leads to two particles, one of which is much larger than the other, i.e. of a size very similar to that of the original particle. In the latter case the breakage event fragments the original particle in two smaller particles of similar sizes. Rounded off crystals, which are homogeneous in size, should more likely be formed by abrasion than by fragmentation. We consider abrasion the more likely mechanism for crystals that are growing from prismatic seeds and never develop an elongated shape. Elongated particles on the contrary are expected to be more prone to fragmentation. The next, combined experiment is aimed at shedding light on this issue.
ratio distribution is plotted in Fig. 8. All the experimental evidence indicates that such properties are intermediate to those of the particles grown at 0.5 ◦ C/h under stirring at 250 rpm and at 1000 rpm. Remarkably, the particles formed in the combined experiment seem to exhibit a bi-modality in the aspect ratio distribution. We conceptualize these results by considering how the final population of crystals that we observe (see Figs. 5d and 8) develop. First the seeds shown in Fig. 3 grow at low cooling rate and low stirring rate to form elongated crystals that we assume to be very similar to those shown in Fig. 4a (or 5a), having the aspect ratio distribution plotted as thick solid line in Fig. 8 that exhibits a mode at an aspect ratio of about 4. The low suspension density of paracetamol in water created by cooling from 40 to 15 ◦ C prohibits a direct characterization of these intermediate crystals from the same batch, but we are confident that their properties are as described because we have in
4.3.
Combined experiment
The properties of the product particles obtained in the combined experiment are shown in Fig. 5d, whereas their aspect
Fig. 7 – Comparison of the total amount of growth in the two directions (a) and of the average growth rates (b) at different cooling rates. The locations of the peaks used to determine the total amounts of growth are indicated in the PSDs in Fig. 4.
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chemical engineering research and design 8 8 ( 2 0 1 0 ) 447–454
fact repeated the slow cooling, slow stirring experiment a few times, always obtaining elongated particles. The suspension of these elongated crystals is then stirred at 1000 rpm, i.e. very fast, for 50 more hours, i.e. for a time as long as the duration of the cooling phase itself. During this phase of the experiment the solution is saturated, i.e. there is no driving force to trigger significant secondary nucleation events. We expect that during this phase not only abrasion but also fragmentation occur, due to the large aspect ratio of the initial particles. If this is the case, and considering that fragmentation per se cannot yield a narrow aspect ratio distribution due to its intrinsic stochastic nature, the characteristics of the final particles, particularly the bimodal aspect ratio distribution with mode values of about 1 and about 2, are not surprising. To be more specific, all particles have rounded edges and vertices due to intense abrasion (as in the experiment shown in Fig. 5c). Moreover, low aspect ratio particles look like those in Fig. 5c as they originate from fragments formed rather soon during the stirring second phase of the experiment. Large aspect ratio particles are those that are fragmented later or that are not fragmented at all, but only abraded during stirring; they are rather large in fact.
5.
Conclusions
The effects of two important operating conditions, i.e. the cooling rate and the stirring rate, on the shape of a population of paracetamol crystals grown by cooling were studied. To this end, a microscopy imaging technique was used to acquire the length and width of a statiscally relevant number of particles. These data were then processed by an algorithm to yield the bidimensional particle size distribution of the population. The effect of the cooling rate and of the stirring rate on the particle shape could clearly be observed and measured quantitatively. A lower cooling rate and hence a lower average level of supersaturation was found to increase the ratio of average growth rates, thus yielding more elongated crystals. These observations are in line with findings of other researchers. The effect of an increased stirring rate could also clearly be seen, with increased stirring resulting in more rounded off and less elongated particles. To discriminate the effects of abrasion and fragmentation from secondary nucleation, a combined experiment was performed, where fast stirring was only applied in the absence of supersaturation, i.e. when growth of the particles upon cooling was completed. The experiments presented in this work demonstrate the capability of the 2D PSD restoration technique to monitor particle shape for particle populations in suspension. Considering the difficulties commonly encountered in measuring the shape of a statiscally meaningful number of particles, the technique applied in this work could prove of great use in monitoring and studying of crystallization processes. The
quantitative knowledge of the 2D PSD gained with the presented technique can be used to estimate crystallization kinetics in more than one characteristic dimension. Determining the dependence of such kinetics on the operating conditions, i.e. supersaturation, temperature and stirring rate, could be the basis for a process model to predict and control both size and shape of growing crystals.
References Briesen, H., 2006, Simulation of crystal size and shape by means of a reduced two-dimensional population balance model. Chemical Engineering Science, 61(1): 104–112. Eggers, J., Kempkes, M. and Mazzotti, M., 2008, Measurement of size and shape distributions of particles through image analysis. Chemical Engineering Science, 63(22): 5513–5521. Kempkes, M., Eggers, J. and Mazzotti, M., 2008, Measurement of particle size and shape by FBRM and in situ microscopy. Chemical Engineering Science, 63(19): 4656–4675. Oullion, M., Puel, F., Févotte, G., Righini, S. and Carvin, P., 2007, Industrial batch crystallization of a plate-like organic product. In situ monitoring and 2D-CSD modelling. Part 1: experimental study. Chemical Engineering Science, 62(3): 820–832. Oullion, M., Puel, F., Févotte, G., Righini, S. and Carvin, P., 2007, Industrial batch crystallization of a plate-like organic product. In situ monitoring and 2D-CSD modelling. Part 2: kinetic modelling and identification. Chemical Engineering Science, 62(3): 833–845. Puel, F., Marchal, P. and Klein, J., 1997, Habit transient analysis in industrial crystallization using two dimensional crystal sizing technique. Chemical Engineering Research & Design, 75(A2): 193–205. Puel, F., Févotte, G. and Klein, J.P., 2003, Simulation and analysis of industrial crystallization processes through multidimensional population balance equations. Part 1: a resolution algorithm based on the method of classes. Chemical Engineering Science, 58(16): 3715–3727. Puel, F., Févotte, G. and Klein, J.P., 2003, Simulation and analysis of industrial crystallization processes through multidimensional population balance equations. Part 2: a study of semi-batch crystallization. Chemical Engineering Science, 58(16): 3729–3740. Ristic, R.I., Finnie, S., Sheen, D.B. and Sherwood, J.N., 2001, Macroand micromorphology of monoclinic paracetamol grown from pure aqueous solution. Journal of Physical Chemistry B, 105: 9057–9066. Variankaval, N., Cote, A.S. and Doherty, M.F., 2008, From form to function: crystallization of active pharmaceutical ingredients. AIChE Journal, 54(7): 1682–1688. Wang, X.Z., Calderon de Anda, J. and Roberts, K.J., 2007, Real-time measurement of the growth rates of individual crystal facets using imaging and image analysis: a feasibility on needle-shaped crystals of l-glutamic acid. Chemical Engineering Research & Design, 85A: 921–927. Wang, X.Z., Roberts, K.J. and Ma, C., 2008, Crystal growth measurement using 2D and 3D imaging and the perspectives for shape control. Chemical Engineering Science, 63(5): 1173–1184.
Contents lists available at ScienceDirect
Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Monitoring the particle size and shape in the crystallization of paracetamol from water Michel Kempkes, Thomas Vetter, Marco Mazzotti ∗ ETH Zurich, Institute of Process Engineering, Sonneggstrasse 3, CH-8092 Zurich, Switzerland
a b s t r a c t In this work, a technique capable of restoring bidimensional particle size distributions from images of the particles in suspension is applied to the seeded cooling crystallization of paracetamol from water. The effects of cooling rate and stirring rate on the final particle size and shape are studied and the average growth rates along different directions of particles are found to be strongly dependend on supersaturation. This observation is in line with previous studies, though in this work it has been established for the first time using populations of particles. The technique was capable of quantifying changes in particle size and shape, indicating particle sizes and shapes that correlated well with observations from electron microscopy images. © 2009 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Crystallization; Imaging; Instrumentation; Particle size; Particle shape; Particulate processes
1.
Introduction
The importance of particle shape is widely acknowledged (Variankaval et al., 2008; Wang et al., 2008, 2007), but the lack of measurement techniques to quantify this important property has severely limited research efforts in this direction. Thus far, particle shape has mainly been characterized in a semi-quantitative manner, by observations from optical or electron microscopic images. Due to the extensive sample preparation required, the conclusions drawn from these images were usually based on a very limited number of particles. Puel et al. (1997) were among the first to characterize particle shape for larger numbers of particles. In their work, microscopic images of crystals were analyzed using optical microscopy and a semi-automatic image analysis routine. The size of the crystals was measured in two dimensions, with the third dimension either assumed equal to one of the other two, or constant. The approach yielded the bidimensional particle size distribution (PSD) of the crystals. This approach was adopted in later works, to model (Briesen, 2006; Oullion et al., 2007b; Puel et al., 2003a) or to monitor crystallization processes (Oullion et al., 2007a; Puel et al., 2003b) where shape varies throughout the particle population. Recently, we presented a technique that allows for the characterization of a 2D PSD (Eggers et al., 2008). The tech-
∗
nique is based on the fully automated analysis of a large set of microscopic images from crystals in suspension. The technique requires minimal sample preparation, gives high quality images of the crystals in suspension and produces results based on a very large number of particles. However, since the crystals are suspended in a flowing liquid, the images and the measurements inferred from them are based on randomly oriented particles. More specifically, what is measured for each observed particle, are the major and minor axis lengths of an ellipse with the same area moment of inertia as the projection of the particle. From a large set of these measurements, the so-called axis length distribution (ALD) can be constructed. The relation between the underlying 2D PSD and the ALD that is measured was established in a previous publication (Kempkes et al., 2008). This measurement model was used in combination with a genetic algorithm to find the underlying 2D PSD (Eggers et al., 2008). It is the goal of this work to apply these techniques to a crystallization process and to demonstrate its capability to quantify variations in particle size and shape due to changes of the operating conditions. In particular, the effects of cooling rate and stirring rate on the 2D PSD of the final product crystals are studied in the seeded batch cooling crystallization of paracetamol from water. The 2D PSDs thus obtained
Corresponding author. Tel.: +41 44 6322456; fax: +41 44 63221141. E-mail address: [email protected] (M. Mazzotti). Received 31 October 2008; Received in revised form 22 July 2009; Accepted 2 September 2009 0263-8762/$ – see front matter © 2009 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.cherd.2009.09.006
448
chemical engineering research and design 8 8 ( 2 0 1 0 ) 447–454
In a typical analysis, about 1 × 104 images are acquired, which contain from about 5 × 104 to 1 × 105 particles. From this large set of individual measurements of major and minor axis lengths, the overall axis length distribution r(a, b) is constructed.
2.2.
Restoration of 2D PSD from ALD
Fig. 1 – Scheme of the experimental setup used to determine the ALD. The suspension to be analyzed is sucked through a narrow flow channel where two windows have been installed. Light from the xenon-stroboscope passes through this channel to an optical system with a digital camera that rapidly acquires images of the crystals in suspension.
Previously, we presented a measurement model capable of a very fast calculation of the ALD for any given 2D PSD (Kempkes et al., 2008). A Monte-Carlo simulation is used to calculate the so-called single particle ALDs rp (a, b; L1 , L2 ) which give the probability of observing a projection with major axis length a and minor axis length b, orginating from a particle with sizes L1 and L2 . Since the ALD for the entire particle population is the sum of these single particle ALDs, weighted by the occurence of these particles, i.e. the 2D PSD, the population ALD can be calculated with the following equation:
are then compared to observations from electron microscopic images.
r(a, b) =
∞
rp (a, b; L1 , L2 )n(L1 , L2 )
0
2. Characterization of a bidimensional particle size distribution In the following we present a brief summary of previously presented techniques that are used in this work. The reader can find in published papers more details about the experimental setup as well as the restoration algorithm (Eggers et al., 2008), and about the measurement model used in the restoration algorithm (Kempkes et al., 2008).
2.1.
Measurement of ALD
The measurement of the ALD is performed using the setup shown in Fig. 1 where the suspension is pumped through a flow through cell. The cell consists of two metal discs with sapphire windows and openings in the top and the bottom. On one side of each disc, a narrow flow channel is milled out. The discs are pressed together by a set of screws and sealed with an O-ring. A peristaltic pump, located after the cell to avoid damage to the crystals prior to the measurement, pumps the suspension through the setup. On one side of the cell a LX7865 high intensity xenon flash lamp (Hamamatsu Photonics, Japan) and on the opposite side of the cell a Leica Z6-APO optical system equipped with a DFC290 digital camera (Leica Microsystems, Switzerland) are installed. The system is capable of acquiring 10 images per second with a resolution of 1.75 m per pixel and a field of view of 3579 m × 2684 m. The depth of field of the optical system is identical to the depth of the flow channel, thus ensuring that all particles are in focus. This, together with the transmission illumination, guarantees sharp edges and well defined contours of the detected particles. The task of the image analysis routine is facilitated by the high quality of the images. Image analysis consists of a thresholding step, followed by contour closing and region filling. These operations are followed by the measurement of several properties of the detected objects. A set of criteria is formulated that, based on these measurements, aims to allow only good, single crystals to be considered for further analysis. For each of these objects, the major length a and the minor axis b length of an ellipse with equal moments of inertia are calculated.
∞
dL2 0
∞
×
0
dL2
∞
¯ 1 , L2 ) p(L
0
¯ 1 , L2 ) n(L1 , L2 )dL1 p(L
dL1
(1)
where n(L1 , L2 ) is the 2D PSD, whose meaning is that the total number of particles per unit volume of the suspension with characteristic dimensions between L1 and L1 + dL1 , and between L2 and L2 + dL2 is n(L1 , L2 )dL1 dL2 (n has units of m−5 ). The above equation allows for a fast calculation of the ALD for any given 2D PSD. To perform the inverse operation, i.e. the restoration of a 2D PSD from a measured ALD, we developed an algorithm that assumes a 2D PSD, calculates the corresponding ALD, and then minimizes the difference between the measured and the calculated ALD (Eggers et al., 2008). The 2D PSD for which this difference is minimized, is the bidimensional particle size distribution of the sample analyzed in the flow through cell. In this work, the ALD is visualized as a contour plot, with the color indicating the frequency with which a certain combination of major and minor axis lengths was observed. The 2D ˜ 1 , L2 ), PSD is represented as a volume weighted distribution, n(L which is defined in terms of the number weighted distribution, n(L1 , L2 ), as: ˜ 1 , L2 ) = L1 L22 n(L1 , L2 ) n(L
(2)
where n˜ has units of m−2 . This definition accounts for the fact ˜ 1 , L2 ) that the volume of a cuboid particle is L1 L22 . Visualizing n(L instead of n(L1 , L2 ) as a contour plot highlights the features of the larger particles in the crystal population. To facilitate a comparison of the particle shape between different experiments, the distribution of the aspect ratio is also calculated from the restored 2D PSDs. If we define the aspect ratio as follows: A=
L1 L2
(3)
Then the number of particles with an aspect ratio between A and A + dA is defined as:
f (A)dA =
∞
(A+dA)L2
n(L1 , L2 )dL1
dL2 0
AL2
(4)
chemical engineering research and design 8 8 ( 2 0 1 0 ) 447–454
449
Fig. 2 – Approximation of the complex shape of paracetamol crystals by a square cuboidal geometry. Crystal A has L1 = 400 m and L2 = 150 m; crystal B has L1 = 1000 m and L2 = 200 m. The unit bar corresponds to 200 m.
where f (A) is the aspect ratio density distribution (f (A) has units of m−3 ). Similarly to the 2D PSD we want to avoid the masking effect of small, shapeless particles and will therefore mainly be using the volume weighted aspect ratio distribution f˜ (A), which is defined as:
f˜ (A)dA =
(A+dA)L2
˜ 1 , L2 )dL1 n(L
dL2 0
3.
∞
(5)
AL2
Experimental work
Paracetamol (N-(4-hydroxyphenyl)acetamide) crystallized from water forms crystals that, despite the many different faces and rather complex geometry, can rather well be approximated by a square cuboidal geometry. This is illustrated for two paracetamol crystals in Fig. 2, where the length of the cuboids is denoted by L1 and the width and the thickness by L2 . This means that in the (L1 , L2 ) space, the second, more elongated crystal will be positioned further away from the diagonal than the first, more compact crystal. It is known that the growth rates of the crystal faces strongly depend on the supersaturation (Ristic et al., 2001), resulting in rather elongated crystals at low supersaturations and more prismatic crystals at high supersaturations. So far, these observations have been based on a rather small set of crystals. In this work, the previously presented techniques to characterize crystal size and shape for a very large set of crystals are applied to the crystallization of paracetamol, where the effect of operating conditions, in this case cooling rate and stirring rate, on the final 2D PSD is studied. The experiments were conducted in a temperature controlled 2000 mL glass reactor, stirred by a 4-blade glass impeller with 45◦ inclined blades and a diameter of 50
mm (LTS, Switzerland). A suspension of paracetamol (≥98%, Fluka, France) in de-ionized water at 40 ◦ C was equilibrated overnight and filtered off. To the clear solution thus obtained, a mass of 1.3 g of seed crystals per kilogram of solution were added. The seed crystals had been prepared by shock-cooling a saturated solution of paracetamol in ethanol from 50 to 5 ◦ C, which was then filtered and wet-sieved. The sieve fraction from 125 to 180 m were dried and used as seed crystals. An SEM image of the seed crystals, together with the measured ALD and the restored 2D PSD are shown in Fig. 3. After addition of the seed crystals, the suspension was cooled from 40 to 15 ◦ C. At 15 ◦ C, the solution was filtered off and the crystals were washed with ice-cold water and dried. A small amount of crystals was used for electron microscopic analysis. The remainder was added to a large volume of clear iso-propanol solution saturated with paracetamol which was then pumped through the flow through cell for analysis. A total of 1 × 104 images were taken for each sample. The choice of iso-propanol as a transport medium in the flow through cell was motivated by the tendency of paracetamol crystals to form weak agglomerates in water, i.e. an effect that complicates particle measurement and that was not observed in iso-propanol.
3.1.
Effect of cooling rate
In the first set of experiments, the effect of cooling rate on the final particle size and shape was studied. To this end, the seeded solution was linearly cooled from 40 to 15 ◦ C at cooling rates of 10, 5, 1.5 and 0.5 ◦ C/h, while stirring at 250 rpm; the experiments lasted 2.5, 5, 16.5 and 50 h, respectively. The results of these experiments and of the analysis outlined above are shown in Fig. 4.
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Fig. 3 – An SEM image of the seed crystals used in all experiments (a) the ALD measured by the flow through cell (b) and the volume weighted 2D PSD that was restored from the ALD (c). The 2D PSD is shown in a log–log plot, where the location of the highest peak is indicated by the dashed lines. The unit bar in the SEM image corresponds to 200 m.
3.2.
Effect of stirring rate
The aim of the second series of experiments was to study the effect of the stirring rate on the final particle size and shape. Since the effect of increased stirring rate and therefore enhanced abrasion and breakage phenomena would be most pronounced with elongated crystals, a cooling rate of 0.5 ◦ C/h was applied. Stirring rates of 250, 500 and 1000 rpm were used. The effect of stirring rate on particle size and shape is illustrated in Fig. 5a–c.
3.3.
Combined experiment
A third type of experiment was performed where the seeded solution was cooled with a cooling rate of 0.5 ◦ C/h and a stirring rate of 250 rpm to produce a suspension of elongated crystals same as those in Figs. 4a and 5a. This suspension was then stirred at 1000 rpm for 50 h. The results of this experiment are shown in Fig. 5d.
common particle size of the seed crystals, both corresponding to the locations of the highest peaks in the 2D PSDs as indicated in the corresponding Figs. 3 and 4. For this analysis only the bigger particles are considered if the 2D PSD is bimodal. In Fig. 7 the total extents of growth in both characteristic dimensions, Li , are compared with each other for different cooling rates. Dividing the total amounts of growth by the duration of the experiment yields the average growth rates ¯ i , also shown in Fig. 7b. It is readily seen in both directions, G that the seed crystals experience very different growth rates when different cooling rates are applied. More importantly, ¯ 1 /G ¯ 2 , is strongly the ratio between the average growth rates, G influenced by the cooling rate, as can be seen in Fig. 7b. Considering the cooling rate to be a proxy of the supersaturation, i.e. faster cooling results in a higher average level of supersaturation, the observed relation between cooling rate and growth rates is well consistent with earlier reports (Ristic et al., 2001).
4.2.
4.
Discussion
4.1.
Effect of cooling rate
With reference to Fig. 4 one can readily observe that slower cooling, corresponding to lower average levels of supersaturation, results in more elongated crystals. A qualitative indication of this trend is given by the SEM images and is confirmed and quantified by the measured ALDs (second column of Fig. 4) and by the 2D PSDs that were restored from the ALDs (third column of Fig. 4). It should be stressed that contrary to observations from SEM images, where only a handful of particles is shown, the ALDs and PSDs are based on thousands of particles and can therefore be used to make quantitative statements about the changes of crystal size and shape during crystallization. To facilitate an analysis of the effect of the cooling rate on the particle shape, the volume weighted distributions of aspect ratio f˜ (A) are plotted in Fig. 6. This shows that, the lower the cooling rate hence the lower the average level of supersaturation, the higher the aspect ratio. The total amount of growth in the L1 and the L2 directions can be estimated by comparing the most common particle size of the product crystals with the most
Effect of stirring rate
The effect of changing stirring rate at constant low cooling rate (0.5 ◦ C/h) is illustrated in Fig. 5a–c. For the sake of comparison Fig. 5a reports the same experiment at 250 rpm already shown in Fig. 4a, yielding elongated crystals with an aspect ratio of about 4. The main effect is that the aspect ratio decreases as the stirring rate increases, namely it is between 2 and 3 at 500 rpm and about 1 at 1000 rpm. The particles obtained in the last experiment are remarkably rounded and homogeneous in size. The volume weighted distributions of aspect ratios plotted in Fig. 8 for these three experiments demonstrate quantitatively the same trend. Under the action of high stirring rates growing crystals do not have the possibility to develop an elongated shape as it is the case at low stirring rate. This might be due to particle abrasion or to secondary nucleation, both phenomena being certainly favored at high stirring rates. At least in the case of the experiment at the highest stirring rate shown in Fig. 5c, we tend to favor abrasion because of the rounded shape of the final particles and of the scarcity of fines in the final distribution. It is worth noting that we consider abrasion and fragmentation as two different types of breakage phenomena. In the
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Fig. 4 – Effect of cooling rate on the size and shape of the final crystals. In the left column the SEM images are shown, in the middle column the measured ALD is shown and in the right column the volume weighted, restored 2D PSDs are shown in a log–log plot. The highest peaks of the large particles in the PSDs are indicated with the dashed lines. The unit bar in the SEM images corresponds to 200 m. The stirring rate was 250 rpm in all experiments. Cooling rates were: (a) 0.5, (b) 1.5, (c) 5 and (d) 10 ◦ C/h.
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Fig. 5 – Effect of stirring rate on the size and shape of the final crystals. In the left column the SEM images are shown, in the middle column the measured ALD is shown and in the right column the volume weighted, restored 2D PSDs are shown in a log–log plot. The unit bar in the SEM images corresponds to 200 m. The cooling rate was 0.5 ◦ C/h in all experiments. Stirring rates: (a) 250 (this is the same experiment shown in Fig. 4a; (b) 500; (c) 1000 rpm; (d) combined experiment (see Section 3.3 for a detailed description).
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Fig. 6 – The volume weighted aspect ratio distributions f˜ (A) of the particle obtained at different cooling rates.
Fig. 8 – The volume weighted aspect ratio distributions f˜ (A) of the particles obtained at different stirring rates.
former case the breakage event leads to two particles, one of which is much larger than the other, i.e. of a size very similar to that of the original particle. In the latter case the breakage event fragments the original particle in two smaller particles of similar sizes. Rounded off crystals, which are homogeneous in size, should more likely be formed by abrasion than by fragmentation. We consider abrasion the more likely mechanism for crystals that are growing from prismatic seeds and never develop an elongated shape. Elongated particles on the contrary are expected to be more prone to fragmentation. The next, combined experiment is aimed at shedding light on this issue.
ratio distribution is plotted in Fig. 8. All the experimental evidence indicates that such properties are intermediate to those of the particles grown at 0.5 ◦ C/h under stirring at 250 rpm and at 1000 rpm. Remarkably, the particles formed in the combined experiment seem to exhibit a bi-modality in the aspect ratio distribution. We conceptualize these results by considering how the final population of crystals that we observe (see Figs. 5d and 8) develop. First the seeds shown in Fig. 3 grow at low cooling rate and low stirring rate to form elongated crystals that we assume to be very similar to those shown in Fig. 4a (or 5a), having the aspect ratio distribution plotted as thick solid line in Fig. 8 that exhibits a mode at an aspect ratio of about 4. The low suspension density of paracetamol in water created by cooling from 40 to 15 ◦ C prohibits a direct characterization of these intermediate crystals from the same batch, but we are confident that their properties are as described because we have in
4.3.
Combined experiment
The properties of the product particles obtained in the combined experiment are shown in Fig. 5d, whereas their aspect
Fig. 7 – Comparison of the total amount of growth in the two directions (a) and of the average growth rates (b) at different cooling rates. The locations of the peaks used to determine the total amounts of growth are indicated in the PSDs in Fig. 4.
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fact repeated the slow cooling, slow stirring experiment a few times, always obtaining elongated particles. The suspension of these elongated crystals is then stirred at 1000 rpm, i.e. very fast, for 50 more hours, i.e. for a time as long as the duration of the cooling phase itself. During this phase of the experiment the solution is saturated, i.e. there is no driving force to trigger significant secondary nucleation events. We expect that during this phase not only abrasion but also fragmentation occur, due to the large aspect ratio of the initial particles. If this is the case, and considering that fragmentation per se cannot yield a narrow aspect ratio distribution due to its intrinsic stochastic nature, the characteristics of the final particles, particularly the bimodal aspect ratio distribution with mode values of about 1 and about 2, are not surprising. To be more specific, all particles have rounded edges and vertices due to intense abrasion (as in the experiment shown in Fig. 5c). Moreover, low aspect ratio particles look like those in Fig. 5c as they originate from fragments formed rather soon during the stirring second phase of the experiment. Large aspect ratio particles are those that are fragmented later or that are not fragmented at all, but only abraded during stirring; they are rather large in fact.
5.
Conclusions
The effects of two important operating conditions, i.e. the cooling rate and the stirring rate, on the shape of a population of paracetamol crystals grown by cooling were studied. To this end, a microscopy imaging technique was used to acquire the length and width of a statiscally relevant number of particles. These data were then processed by an algorithm to yield the bidimensional particle size distribution of the population. The effect of the cooling rate and of the stirring rate on the particle shape could clearly be observed and measured quantitatively. A lower cooling rate and hence a lower average level of supersaturation was found to increase the ratio of average growth rates, thus yielding more elongated crystals. These observations are in line with findings of other researchers. The effect of an increased stirring rate could also clearly be seen, with increased stirring resulting in more rounded off and less elongated particles. To discriminate the effects of abrasion and fragmentation from secondary nucleation, a combined experiment was performed, where fast stirring was only applied in the absence of supersaturation, i.e. when growth of the particles upon cooling was completed. The experiments presented in this work demonstrate the capability of the 2D PSD restoration technique to monitor particle shape for particle populations in suspension. Considering the difficulties commonly encountered in measuring the shape of a statiscally meaningful number of particles, the technique applied in this work could prove of great use in monitoring and studying of crystallization processes. The
quantitative knowledge of the 2D PSD gained with the presented technique can be used to estimate crystallization kinetics in more than one characteristic dimension. Determining the dependence of such kinetics on the operating conditions, i.e. supersaturation, temperature and stirring rate, could be the basis for a process model to predict and control both size and shape of growing crystals.
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