Spontaneous Polymorphic Nucleation of d-Mannitol in Aqueous

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Spontaneous Polymorphic Nucleation of D‑Mannitol in Aqueous Solution Monitored with Raman Spectroscopy and FBRM Weiyi Su,† Hongxun Hao,‡ Brian Glennon,*,† and Mark Barrett† †

Solid State Pharmaceutical Cluster, School of Chemical and Bioprocess Engineering, University College Dublin, Belfield, Dublin 4, Ireland ‡ School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China ABSTRACT: The spontaneous nucleation of D-mannitol polymorphs at different initial concentrations in an aqueous solution was investigated. Two in situ process analytical technology (PAT) tools, Raman spectroscopy and focused beam reflectance measurement (FBRM), were combined to monitor the process, allowing instantaneous detection of polymorphs after nucleation. It was found that the stable β form of mannitol was favored at low initial concentrations, whereas the metastable α form nucleated at high concentrations and the metastable δ polymorph crystallized when the concentration was in the medium level. To help understand this phenomenon, the thermodynamic and kinetic characteristics of different polymorphs were analyzed. The solubility of the two metastable forms was determined by an innovative method with the aid of Raman spectroscopy, whereas the interfacial energy between polymorphs and the bulk solution were obtained from the induction time measurements. Consequently, the critical excess free energy and other critical parameters associated with the nucleation of various polymorphs were calculated. It was concluded that the nucleation of mannitol polymorphs from an aqueous solution depends on both the thermodynamic and kinetic properties, with the importance of each highly dependent on the supersaturation prevailing in the system.

1. INTRODUCTION Nucleation as the first step in the formation of a crystal is critical in determining the final crystal properties. The situation becomes more complicated when polymorphism is involved, which is the ability of a solid material to exist in more than one crystalline form. Generally, the initial nucleation event during a polymorphic crystallization can directly influence the form, purity, and quality of the final polymorph. According to the classic Ostwald’s “Rule of Stages”,1 the solid first nucleated, from the melt or the solution, will be the least stable polymorph. However in recent years, others have found some inverse cases to the rule.2 More and more researchers now accept that Ostwald’s rule is not a universal law but only a possible tendency.3 Polymorphism is very common in active pharmaceutical ingredients (APIs) and different polymorphs may have different physical and chemical properties, such as crystal habit, solubility, functionality, and even bioavailability; therefore, it is important to understand the mechanism of polymorphic nucleation in order to selectively get the desired polymorph in pharmaceuticals. The nucleation of polymorphs theoretically depends on the interactions between the polymorphic clusters and the solute/ solvent molecules. These interactions can certainly vary in different molecular environments, which might be the reason why numerous polymorphs have been observed in different solvents4,5 or at least different solution conditions, such as pH,6 supersaturation,7−9 and even with or without additives.10,11 © 2013 American Chemical Society

Among them, supersaturation as the driving force of nucleation plays a very important role. This paper precisely focused on the influence of supersaturation on the nucleation of polymorphs. D-Mannitol, as a widely used excipient in the formulation of tablets and granulated powders in pharmaceutical industry,12 is chosen to be an example compound. To date, three anhydrous mannitol polymorphs have been reported as well as a hemihydrate13 obtained only in a freeze-drying process, whereas the latter is avoided in this paper. Literature abounds with studies on the polymorphism of anhydrous mannitol, and the differences in nomenclature have led to some confusion regarding the identity of these polymorphs.14−19 Here in this paper the nomenclature by Walter-Levy15 is referred for clarity. Generally, the β form is the thermodynamically stable polymorph of mannitol at room temperature, and the α and δ forms are metastable. As for the nucleation of D-mannitol, most literature focused on the freezing methods, during which it was found that the solvent composition20 as well as the use of additives such as sodium chloride, sodium citrate, and sodium acetate21 had influence on the nucleation of individual polymorphs. Cross-nucleation of the three polymorphs was even observed during the melting crystallization of mannitol with the presence of an additive of 10 wt % polyReceived: February 25, 2013 Revised: October 5, 2013 Published: October 22, 2013 5179

dx.doi.org/10.1021/cg400304c | Cryst. Growth Des. 2013, 13, 5179−5187

Crystal Growth & Design

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(vinylpyrrolidone) (PVP).22,23 There are only a few publications reporting on the nucleation of mannitol in a solution crystallization process, and most focused on the stable β form.24,25 Trovao et al26 discussed the crystallization of mannitol from acetone−water mixtures, and found that the α form was obtained with the Keggin heteropolyanions [PW12O40]3− or [SiW12O40]4−, whereas the β polymorph was produced in the absence of these polyanions. Cornel et al.19 roughly found different polymorphs could crystallize from aqueous solutions with the change of initial supersaturation, which afterward all transformed to the stable form. There are few literature reports concerning how to obtain various pure polymorphs of mannitol in an aqueous solution, which is the objective of this work. Many PAT tools have been used in the investigation of crystallization and polymorphism, among which FBRM is quite important because of its high sensitivity to particle morphologies. FBRM can generally provide information about the size, shape, and population of particles in real time. In fact, FBRM has been successfully used to monitor the nucleation event and even determine the nucleation mechanism in many cases.27−29 Based on the principle of Raman scattering due to different low-frequency vibrations in a system, Raman spectroscopy is an efficient analytical technique to identify polymorphs.30−33 Furthermore with the use of fiber optic probes, Raman spectroscopy can also online track polymorphs. Specifically, it has been successfully used to provide the real time information during the form transformation of mannitol,34 p-aminobenzoic acid,35 and L-glutamic acid.36,37 In this work, Raman spectroscopy is utilized to in situ detect the type of polymorphs while FBRM is applied to detect the nucleation as well as measure the induction time during spontaneous nucleation. The combination of Raman spectroscopy and FBRM is quite suitable for the nucleation study of mannitol polymorphs compared to other analytical tools. First, because the crystal shape of different polymorphs is similar, it is impossible to distinguish them only by images, say PVM (particle vision measurement) or microscope. Second, any offline polymorph identification, like XRD (X-ray diffraction) or solid IR (Infrared spectroscopy), etc., is inapplicable in this case because of the possible transformation mechanism from the metastable to the stable form of mannitol right after the nucleation according to literatures.19,34,38 Raman spectroscopy makes itself a perfect tool to deal with these two problems by efficiently distinguishing different polymorphs in real time. At last, although a turbidity meter can also be used to detect the nucleation event as FBRM, it is incompatible with Raman spectroscopy because light scattering and absorption can interfere with each other resulting distorted spectral information.39 Hereby in this paper Raman spectroscopy and FBRM are jointly used to track the spontaneous nucleation of mannitol polymorphs.

polymorphs were checked by XRD and differential scanning calorimetry (DSC) as described previously.40 Ethanol (99.5%) in analytical grade was also supplied by Sigma Aldrich Co. (UK). Deionized water was used throughout. 2.2. Apparatus. A Kaiser Raman RXN2 system was used in this study. With the excitation wavelength at 785 nm, the observed spectral range of this system was from 100 to 1890 cm−1. The spectral resolution was 5 cm−1 on average. The fiber-coupled probe optic technology was applied in the RXN2 analyzer. Generally, the noncontact PhAT probe was used off-line to collect the spectra of the isolated solid materials while the MR probe was utilized as an immersion optic to gain online polymorphic information with an exposure time of 45 s. The iControl Raman software (Mettler-Toledo) was employed with the RXN2 system, which handily worked with the instrument configuration, data acquisition, as well as data analysis. The Mettler-Toledo FBRM probe (model S 400) was applied to detect spontaneous nucleation. A sample measurement duration of 10 s was set for all runs. The change of the count rate of full chord size particles read by FBRM were used to indicate nucleation. Similarly, the iControl FBRM software (Mettler-Toledo) was applied to collect and analyze the data. 2.3. Spontaneous Nucleation and Induction Time. The spontaneous nucleation of mannitol was performed in a 100-mL Easymax reactor (Mettler-Toledo) with a four-blade metal impeller. The solution of mannitol at desired concentration was first prepared in 100 g of water, which was stirred at 350 rpm for half an hour when it was 5 °C higher than the equilibrium temperature in order to ensure complete dissolution. The temperature was then dropped 5 °C to create a saturated solution, which was hold for another half an hour before being fast cooled to the desired temperature (5 or 10 °C for all runs) at a rate of 2 K/min. At the same time, FBRM and Raman spectroscopy began to track the process with the former to detect the nucleation and measure the induction time and the latter to distinguish the crystallized polymorph. The induction time here is defined as the time elapsing from the creation of the supersaturated state to the threshold of nucleation, which was illustrated by the sudden change in the FBRM count rate (full chord size 1−1000 μm). Each run was repeated at least three times to confirm the polymorph and the average induction time was determined for further use. 2.4. Solubility Measurement. The solubility of the metastable δ and α forms were innovatively measured by a gravimetric method with the aid of Raman spectroscopy. First, a saturated solution of the stable β form of mannitol was made in a 100-mL Easymax reactor at a constant temperature. Sufficient δ or α form was then added to this solution in order to form a suspension with the solution saturated in the corresponding metastable form. Raman spectroscopy was utilized in situ to confirm the existence and purity of the correct metastable polymorph throughout as well as determine the time to transform this metastable form. The experiment was then repeated and a sample of the solution was taken by a syringe and a pore filter right before the transformation occurred. The concentration of the sample was determined gravimetrically afterward as the solubility of the metastable mannitol polymorph at the corresponding temperature.

3. RESULTS AND DISCUSSION 3.1. Tracking Polymorphic Spontaneous Nucleation by Raman Spectroscopy and FBRM. Raman spectroscopy was initially used to identify the polymorphs of mannitol in solid, and the spectra of the three pure forms (confirmed by XRD) are shown in Figure 1. The details of these Raman spectra have been discussed previously.40 Referring to Figure 1, the distinct Raman shift at 1355 cm−1 only appears in the spectrum of the α form, and the δ from has a unique peak at 1054 cm−1, whereas an intense peak at 1233 cm−1 can be used to track the β form. Thus the three peaks (as indicated by the arrows in Figure 1) are considered as the Raman shifts characteristic of the corresponding polymorphs in this paper.

2. EXPERIMENTAL SECTION 2.1. Materials. The D-mannitol (1,2,3,4,5,6-hexanehexol, 99%) purchased from Sigma Aldrich Co. (UK) was tested as the stable β form by X-ray powder diffraction (XRD) and Raman spectroscopy. The α and δ forms of mannitol were prepared as described previously.40 Typically, the α form was obtained by fast cooling a saturated mannitol solution in a 70 wt % ethanol aqueous solution from 50 to −5 °C, whereas the δ form was produced by a reverse antisolvent crystallization with adding of the saturated mannitol solution into cold ethanol at −5 °C. The products were both filtered and then dried in vacuum at 40 °C for 24 h. The purities of these 5180



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Figure 1. Raman spectra of the three D-mannitol polymorphs.

With the base of these characteristic peaks, Raman spectroscopy was applied to track the spontaneous nucleation of mannitol at different initial concentrations in water at 10 °C along with FBRM. The trends in FBRM total counts and Raman intensities of these characteristic peaks during the nucleation at three initial concentrations are shown in Figure 2. It is worth noting that the peak intensity in this paper is defined as the peak height in a valid wavelength range (approximately ±2 cm−1, depending on the width of a particular peak) to the two-point baseline around that peak. According to Figure 2, on one hand, the sudden change in the FBRM count rate (full chord size 1−1000 μm) indicates the occurrence of spontaneous nucleation. On the other hand, it is apparent that different polymorphs were obtained at different initial concentrations reading by Raman spectroscopy. The concentration used in this paper is expressed as the mole fraction of the solute with respect to the solution, nsolute/(nsolute + nsolvent). From Figure 2, it can be seen that the α form was produced at high initial concentration (mole fraction of 0.0521), the β form appeared when the initial concentration was low (mole fraction of 0.0237) while the δ form nucleated in the medium region (mole fraction of 0.0324). It should be noted that due to the level of nucleation occurring, the viscosity of the suspension increases significantly especially when the initial concentration is high. As a result, the system is difficult to agitate, so that reliable measurement of the persistence of the metastable forms might be problematic. While comparing the two PAT tools, it is clear that the change of Raman intensity lags somewhat behind the FBRM in Figure 2. The reason should be the slightly lower sensitivity of Raman spectroscopy especially compared with FBRM. The low sensitivity is a common issue in any analysis related to the Raman effect due to the low proportion of inelastic Raman scattering to elastic Rayleigh scattering although it has been somehow improved in modern instruments. To visualize this effect, we examined the detection limit of Raman spectroscopy for the β form of mannitol. The solid β mannitol obtained from the spontaneous nucleation process was added into its saturated solution in discrete small amounts with the Raman spectrum being collected after each addition. The Raman spectra with different suspension densities (ratio of the amount of solid to the saturated solution) are illustrated in Figure 3, whereas the intensities of three characteristic peaks during the experiment are shown in Figure 4.

Figure 2. Profile of Raman intensity of the three characteristic peaks (1355 cm−1 for the α, 1233 cm−1 for the β, and 1054 cm−1 for the δ) and FBRM total counts (size 1−1000 μm) in spontaneous nucleation at different initial mole fractions, c, at 10 °C, (a) c = 0.0521, (b) c = 0.0324, (c) c = 0.0237.

The Raman intensity in this work is defined as the peak height to the two-point baseline. It is worth noting that the absolute Raman peak position could vary slightly. As shown in Figure 3, the peak at 1233 cm−1 from the spectrum for the solid β form shifted to the left or right at different suspension densities in a narrow range. This is due to the accuracy of the instrument and potential changes in the microenvironment during each determination. However, it will not affect the use of this peak for the specific polymorph as there are no other 5181



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3.2. Solubility. With the advantage of the two PAT tools, it is obvious to find that different initial concentrations can produce different polymorphs of D-mannitol in aqueous solution according to Figure 2. In order to have a clear perspective on this phenomenon, the thermodynamic and kinetic characteristics of these polymorphs are investigated. Crucially, the solubility is required. The solubility data of the stable β form of mannitol has been reported in literatures.12,41 There is, however, little information on the solubility of the metastable polymorphs, probably because of their tendency to transform to the stable form in water at various temperatures and supersaturations.34,42 In this paper, Raman spectroscopy is innovatively used to assist the solubility determination of these metastable polymorphs. The equilibrated solution of the metastable polymorphs were prepared as described in the Experimental Section using a gravimetric determination. Figure 5 shows the Raman intensity

Figure 3. Variation in the Raman intensity with different suspension densities of β mannitol in saturated solution (emphasized frame: valid range of peak 1233 cm−1 to stand for the β form).

Figure 4. Variation in the Raman intensity of the three characteristic peaks with different suspension densities of β mannitol.

Figure 5. Raman intensity of the characteristic polymorph peaks (1355 cm−1 for the α, 1233 cm−1 for the β, and 1054 cm−1 for the δ) as the addition of α mannitol during the preparation of the saturated solution with respect to the α form in water at 20 °C.

Raman peaks in the selected range in Figure 3, according to the spectra in Figure 1. In fact, the slight shift of peaks is common in any spectroscopic analytical tools, like IR and even XRD. According to Figures 3 and 4, the slurry with a suspension density of approximately 0.74% is seen to show the solid peak of the β form (1233 cm−1) clearly, which is considered as the detection limit of the Raman spectroscopy used in this work. At no point, are either α and δ forms erroneously detected when only the β form is present. Because the detection limit is instrument related, it should be the same to the α and δ forms of mannitol. In an rapid nucleation event, as in Figure 2a, the Raman intensity rapidly reached its maximum value. But at the low initial concentration reported in Figure 2c, it took almost 15 min for Raman spectroscopy to indicate the presence of solid after the occurrence of nucleation read by FBRM. The relatively low sensitivity makes Raman spectroscopy a less robust technique to detect nucleation, compared to FBRM. For this reason, the induction time measurements in this work rely on FBRM. Despite this, Raman spectroscopy is still a highly effective real-time in-line tool for polymorphic nucleation monitoring, eliminating the need for unreliable sampling and associated preparation prior to off-line analysis.

of the three characteristic peaks during the preparation of the saturated solution with respect to the α form in water at 20 °C. According to Figure 5, the intensity of the characteristic α peak initially increases slowly as the α form rapidly dissolves because of its higher solubility than the stable β form. As the α form continued to be added to the system, the rate of dissolution is seen to decrease since the dissolved concentration approaches equilibrium with respect to the α form. The addition of material was stopped when the α peak was sufficiently higher than the baseline according to Raman spectroscopy. The suspension was then held for a sufficiently long time to ensure equilibrium, which can be revealed by the approximately constant intensity of the α peak indicating no more solid dissolved as shown in Figure 5. Subsequently, a sample of the clear solution was taken before a polymorphic transformation of the metastable α form denoted by an intensity drop of its characteristic Raman peak.34 The sample concentration was then measured gravimetrically, which was considered to be the solubility of the α form in water at 20 °C. The solubility of the α and δ forms of mannitol at various temperatures were determined in the same way. The data are summarized in Table 1 and Figure 6 with a comparison to the solubility data of the β form from the literature.12 It is clear that the solubility values are always δ > α > β within the 5182



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Table 1. Solubility of the α and δ forms of Mannitol in Mole Fraction of the Solute to Solution T (K) form α T (K) form δ

278.15 0.0141 278.15 0.0160

283.15 0.0168 284.65 0.0198

288.15 0.0187 291.15 0.0232

293.15 0.0227 298.15 0.0286

temperature range examined in this work as shown in Figure 6. This is consistent with their known relative stabilities as the stable form always has the lowest solubility while the most unstable form has the highest. The same solubility order of the three polymorphs had also been mentioned in the literature.19 3.3. Induction Time and Interfacial Energy. In addition to the thermodynamic solubility, the kinetic factors (as indicated by the interfacial energy) may also influence polymorph nucleation. The interfacial energy between the crystal and the bulk solution is generally regarded as the disruption of intermolecular bonds when a new crystal surface is created. In this work, the interfacial energies of different mannitol polymorphs are investigated to provide an insight into their kinetic tendency to nucleate. Typically, the direct measurement of the interfacial energy is difficult. The widely accepted experimental method is by means of measuring the induction time (t ind) at various supersaturations in a crystallization process. Generally the induction time can be considered as a measure of the metastability of a supersaturated phase before a new phase can form. So it reflects the nucleation rate reciprocally (tind ∝ 1/J). The relationship between the induction time and the supersaturation in a spontaneous nucleation process can be described by the following equations43

m=

308.15 0.0325

313.15 0.0373

Table 2. Induction Time of Different Mannitol Polymorphs at Various Initial Concentrations along with the Supersaturation with Respect to Corresponding Forms at 10 °C in Water initial concentration

supersaturation

tind (min)

form

0.0490 0.0445 0.0418 0.0380 0.0357 0.0325 0.0305 0.0296 0.0293 0.0246 0.0239 0.0237 0.0234

2.92

2

2.22 2.02 1.90 1.73 1.62 1.57

30 35 40.3 60.4 83.4 99

α α/δa δ δ δ δ δ δ δ/βa β β β β

1.31 1.27 1.26 1.24

370 643 713 885

a Different polymorphs or their mixtures were obtained when repeating the experiments.

(1)

The data in Table 2 are then analyzed based on eq 1, and the relationship between the induction time (ln tind) and the supersaturation (1/(ln s)2) for both the δ and β forms of mannitol are shown in Figure 7. The rising trend of ln tind with the increase in (1/(ln s)2) is quite clear for both polymorphs. The linear regressions of these data points also reveal good correlations with R2 of 0.9958 and 0.9965 for the δ and β forms, respectively. It is apparent that the slop of the straight line obtained for the δ form is smaller than that of β mannitol, which probably illustrates a smaller interfacial energy of the δ form. To confirm this, we need to be determine the molecular properties, especially the volume and area shape factors.

4fs,3i γ 3vi 2 27f v,2 i k3T 3

303.15 0.0284

nucleation of the α form at the desired temperature (10 °C as illustrated in Figure 2) needs an extremely high initial concentration that is difficult to control, here only the interfacial energy of the β and δ forms of mannitol have been determined to discuss how they affect the polymorph nucleation. The induction time was measured by FBRM during the spontaneous nucleation as described in the Experimental Section. Because the δ and β forms can nucleate at different initial concentrations according to Figure 2, the induction time was analyzed separately for the two polymorphs. During the spontaneous nucleation, once the form information was confirmed by Raman spectroscopy, it is feasible to calculate the exact supersaturation based on the initial concentration and solubility of the corresponding polymorph. In this way, the induction times at different supersaturations were obtained for both forms at 10 °C, and the results are shown in Table 2. It is worth noting that the experiment at each initial concentration was repeated three times, and the average induction time was used for the interfacial energy calculation.

Figure 6. Solubility of the three polymorphs of mannitol in mole fraction (the data of the β form is from the literature12).

ln t ind = K + m(ln si)−2

298.15 0.0248 305.15 0.0327

(2)

where K is the intercept and m is the slope of the linear line ln tind ∼ (ln s)−2, fs and f v are the area and volume shape factors, γ is the interfacial energy, v is the molecular volume, k is the Boltzmann constant, T is temperature, s is supersaturation, and i indicates different polymorphs. Thus once the induction times at different supersaturations and the molecular properties are obtained the interfacial energy can be calculated. Because the 5183



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The area and volume shape factors were then estimated for each individual particle, and the average of 50 particles of each form with associated standard deviations, is shown in Table 3. Table 3. Area Shape Factors (fs) and the Volume Shape Factors (f v) of the δ and β Forms of Mannitol in Aqueous Solution at 10 °C polymorph

fs

standard deviation of fs

fv

standard deviation of f v

delta (δ) beta (β)

37.5 29.6

4.7 3.8

8.9 6.9

1.2 1.0

There are only slight differences between each form. It is also observed that the shape factor remains constant over the course of the process even though the size varied somehow. With the slopes in Figure 7, the shape factors in Table 3, and eqs 1 and 2, the interfacial energies of the δ and β forms of mannitol at 10 °C were calculated and displayed in Table 4.

Figure 7. Induction time (tind) of the δ and β forms at different supersaturations (s) at 10 °C in water with the linear regressions between ln tind and 1/(ln s)2.

Table 4. Interfacial Energy of Mannitol Polymorphs Obtained by the Experiments in This Work and the Theoretical Equations44−46

The shape factors of the two polymorphs were determined microscopically. Because the crystals of the δ and β forms are needle- or rod-shaped, as the SEM images in Figure 8 (top) show, it is reasonable to consider them as rods, in which the width and height are the same while the length is evidently larger than those. With this simplification, almost 50 individual particles of each polymorph obtained from the nucleation experiments at different initial concentrations were measured the length and width under an optical microscope, and some examples are shown in Figure 8 (bottom).

interfacial energy (mJ/m2)

this work

delta (δ) beta (β)

1.78 3.23

Mersmann44 Christoffersen45 9.79 11.43

6.68 7.79

Sangwal46 10.01 10.48

Some theoretical equations given by Mersmann,44 Christoffersen,45 and Sangwal46 are used to predict the interfacial

Figure 8. Morphology of the δ and β forms of mannitol: top, by scanning electron microscope (SEM); bottom, by optical microscope. 5184



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energy of these polymorphs, and the results are shown in Table 4 as well. Obviously in Table 4, the interfacial energies of the δ and β forms obtained in this work were both lower than the predicted values. The reason should be that the three theoretical predictions were originally derived for inorganic compounds which usually have larger surface energies than organics.47 The same deviation was also found in other organic materials, as with the case of paracetamol,48 the experimental interfacial energies (1.4 and 2.8 mJ/m2 in different solvents) were about an order of magnitude lower than those predicted by the equation provided by Mersmann44 (10−15 mJ/m2). Despite the difference, both the experimental and theoretical data in Table 4 indicate that the interfacial energy of the δ form is smaller than that of the β form at 10 °C. Bennema49 has demonstrated in a crystallization process that the interfacial energy between a solid and its saturated solution was a linear function of logarithm of its equilibrium solubility, whereas the higher the solubility, the lower the interfacial energy. This rule should also work on polymorphs because the more soluble metastable δ mannitol possesses a lower interfacial energy than the stable β polymorph as shown in Table 4. Similarly, this phenomenon has been observed on eflucimibe polymorphs.50 Consequently, with a lower interfacial energy, the metastable δ form is more kinetically favored than the stable β form of mannitol. 3.4. Impact of the Initial Concentration on Polymorphic Nucleation. Both Figure 2 and Table 2 reveal that the initial concentration shows great influence on the nucleation of mannitol polymorphs. Particularly in Table 2, it is apparent that there are two regions of concentration, one of which (from 0.0296 to 0.0418) consistently delivered the δ form of mannitol, whereas in the other region (from 0.0234 to 0.0246) the β form was always obtained spontaneously. At intermediate concentrations (like 0.0293), different polymorphs (δ or β), or occasionally their mixtures were obtained. It is worth noting that each run in Table 2 was repeated at least 3 times. The phenomenon that different supersaturation levels can produce different polymorphs has also been observed on other polymorphic compounds.50 In an effort to explain how the initial concentration affects the polymorphic nucleation of mannitol, further experiments were performed at various concentrations and temperatures. The results are displayed in Figure 9 with a comparison to the solubility curves of the three polymorphs. Similar phenomenon was observed at 5 °C that different initial concentration regions produced different polymorphs of mannitol. As illustrated in Figure 9, on one hand, it is obvious that all of the experiments were performed in the supersaturated zone for each polymorph. On the other hand, it is quite interesting to find that the nucleation sequence is α, δ, β as the concentration is decreased, whereas the solubility order is always δ > α > β at the temperature examined in this paper. The inconsistence between the nucleation order and the solubility order reveals that the spontaneous nucleation of mannitol polymorphs is not only dependent on the thermodynamic properties but also the kinetic factors. Hereby some nucleation parameters at 10 °C were calculated in order to compare the nucleation of mannitol polymorphs based on the thermodynamic and kinetic properties. Among them, the most important is the critical excess free energy (ΔGi*), which can be expressed as the following

Figure 9. Polymorphic nucleation results of mannitol (open symbols, labeled as “Nucleation”) at different initial concentrations and temperatures shown with the solubility curves of the three polymorphs (solid symbols, labeled as “Solubility”).

ΔGi* =

4fs,3i γi3vi2 27f v,2 i k 2T 2(ln si)2

(3)

with i indicating different polymorphs. ΔGi* is typically the required energy for the solute to form a critical nucleus, which can mainly be expressed by the interfacial energy (γ) and the supersaturation (s) according to eq 3. In addition to this, other properties of the critical nucleus, such as the critical radius (r*) and the critical number of molecules forming a nucleus (n*) can also be related to the interfacial energy and the supersaturation following equations below r* = −

n* =

fs γ 3fv ΔGv

=

fs γv 3fv kT ln s

(4)

8fv r *3 v

(5)

Thereby the influence of the thermodynamic and kinetic properties on nucleation is specified as the supersaturation and interfacial energy. Generally, a low interfacial energy and a high supersaturation can give a low critical excess free energy and a small size of critical nuclei permitting an easy nucleation according to eqs 3−5. Because the δ form of mannitol has a lower interfacial energy as shown in Table 4, while the β form has a higher supersaturation in any initial concentration because of its lower solubility, it seems that the competition between the interfacial energy and supersaturation is determining which polymorph nucleates first. The nucleation parameters (ΔG*, r*, and n*) at different initial concentrations at 10 °C were calculated by eqs 3 to 5, and the results are shown in Table 5. As illustrated in Table 5, on one hand, it is apparent that when the initial concentration was higher than 0.0305, the critical excess free energy forming the δ form nuclei was lower than that of the β form. The same trend was also observed on the critical radius and the critical molecular number of the nucleus with both showing similar or lower values for the δ form. It indicates that the nuclei of the δ form, which is kinetically favored, are able to crystallize from the solution easier and faster than the β form in these conditions. In other 5185



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Table 5. Nucleation Properties of Two Mannitol Polymorphs at 10 °Ca

a

initial mole concentration

sδ

sβ

ΔG*δ (× 103 J/mol)

ΔG*β (× 103 J/mol)

r*δ (× 10−10 m)

r*β (× 10−10 m)

n*δ

n*β

0.0418 0.0380 0.0357 0.0325 0.0305 0.0246 0.0239 0.0237 0.0234

2.22 2.02 1.90 1.73 1.62 1.31 1.27 1.26 1.24

3.16 2.87 2.70 2.46 2.31 1.86 1.81 1.79 1.77

1.37 1.76 2.12 2.92 3.73 12.07 15.31 16.44 18.43

3.12 3.82 4.32 5.27 6.09 11.02 12.17 12.52 13.09

1.60 1.81 1.99 2.33 2.67 4.74 5.34 5.54 5.86

2.05 2.23 2.37 2.62 2.82 3.79 3.98 4.04 4.13

2 3 3 5 7 39 55 61 73

3 4 4 5 7 16 18 19 20

The subscripts δ and β refer to the polymorph δ and β forms, respectively, whereas s stands for the supersaturation.

properties of the critical nucleus were calculated to compare the nucleation of the δ and β form of mannitol, and the mechanism of this influence was found to be based on the competition between the thermodynamic and kinetic properties of these forms. Specifically, when the initial concentration was high, the kinetic parameters played a more important role than the thermodynamic properties, which made the metastable δ form easier to nucleate. Conversely, the thermodynamically favored stable β form tended to crystallize first when the initial concentration was low. The ability of Raman spectroscopy combined with FBRM to monitor the spontaneous nucleation of polymorphs was also demonstrated during the study. In addition, Raman spectroscopy was also innovatively used to determine the solubility of the two metastable forms of mannitol, whereas FBRM was successfully applied to measure the induction times at different supersaturations, which were then used to calculate the interfacial energies of the δ and β forms.

words, the kinetic properties play a more important role than the thermodynamic properties at high initial concentrations (from 0.0325 to 0.0418). In fact, although the δ form of mannitol is not the thermodynamically stable one, it has been shown to have considerable kinetic stability in the literature.17 On the other hand, when the concentration was lower than 0.0246 in Table 5, both the critical free energy and the size of the critical nucleus indicate that the β form of mannitol is easier to form than the δ form, explaining why the β form crystallized spontaneously within the low initial concentration region (from 0.0234 to 0.0246) as shown in Figure 9. This suggests that the supersaturation is the dominant factor compared with the interfacial energy in this region. The values highlighted in italics in Table 5 indicate lower critical excess free energy values, smaller radius, and molecular number of the critical nucleus for either the δ or β form at certain concentrations, leading to the preferential nucleation of this polymorph at those conditions. Therefore, the competition between the kinetics and thermodynamics determines the nucleation behavior of the δ and β forms of mannitol, which results in different concentration regions inducing different polymorphs during the spontaneous nucleation process. Thus it is feasible to get either the pure δ or β form of mannitol by simply choosing the appropriate initial concentration to nucleate and also isolating the polymorph afterward to avoid any form transition.34,42 In this way, controlling to get the desired polymorphs can be fulfilled. Care has to be taken on some intermediate concentrations (like 0.0293 in Table 2), where different polymorphs (δ or β) or occasionally their mixtures are obtained. These concentrations should be in the region where the thermodynamic and kinetic properties match each other in strength. That is why the nucleation properties in this region are fluctuant between the two polymorphs, which are not shown in Table 5 for a clear description. Obviously this region should be avoided for the preparation of any pure polymorph. Additionally, since it is difficult to maintain very high initial concentrations at low temperature (5 or 10 °C in this paper), the α form cannot be guaranteed to nucleate. Hence the spontaneous nucleation in water is not a robust method to prepare the α form of mannitol.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +353-1-716-1954. Fax: + 353-1-716-1177. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the assistance of Kaiser Optical Co. Ltd. This material is based on works supported by the Science Foundation Ireland under Grant 07/SRC/B1158.

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4. CONCLUSIONS The effect of the initial concentration on the spontaneous nucleation of D-mannitol polymorphs in aqueous solution was investigated with the aid of two in situ PAT tools, Raman spectroscopy and FBRM. It was found that the polymorphs nucleated from the aqueous solution were β, then δ, then α forms of mannitol as the initial concentration was increased at constant temperature. The critical excess free energy and other

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NOMENCLATURE J nucleation rate (#/(m2 s)) M molar mass of a substance (kg kmol−1) k Boltzmann constant (1.38 × 10−23 m2 kg s−2 K−1) fs area shape factor f v volume shape factor tind induction time (min) v molecular volume (m3) s supersaturation (c/c*) γ interfacial energy (J m−2) r* radius of the critical nucleus n* number of molecules in a critical nucleus X mole fraction solubility n amount of material in mole REFERENCES

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Spontaneous Polymorphic Nucleation of d-Mannitol in Aqueous

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