Antisolvent Crystallization of Erythromycin ... - ACS Publications

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Antisolvent Crystallization of Erythromycin Ethylsuccinate in the Presence of Liquid−Liquid Phase Separation Xiang Li,† Qiuxiang Yin,†,‡ Meijin Zhang,†,‡ Baohong Hou,†,‡ Ying Bao,†,‡ Junbo Gong,†,‡ Hongxun Hao,†,‡ Yongli Wang,†,‡ Jingkang Wang,†,‡ and Zhao Wang*,†,‡ †

School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin University, and Collaborative Innovation Center of Chemical Science and Chemical Engineering, Tianjin 300072, People’s Republic of China

‡

ABSTRACT: The nucleation point of erythromycin ethylsuccinate crystallization with liquid−liquid phase separation, also called oiling-out, was determined through nucleation analysis. To achieve successful monitoring of nucleation events, focused beam reflectance measurements were performed during antisolvent crystallization. The induction time of the oiling-out system was determined and correlated with classical nucleation theory. The induction time increases with decreasing solubility under a constant thermodynamic driving force. The position of a nucleation point may be determined by comparing the nucleation energy barrier and supersaturation generated in solute-rich and solute-lean phases. The estimated interfacial energy is in the range of 0.422−1.315 m·J/m2, which is in agreement with nucleation theory. A homogeneous nucleation process was observed under high supersaturation, and heterogeneous nucleation took place at low supersaturation. The growth mechanism was identified with the interfacial tension. The continuous growth dominates the whole growth process. resultant crystals.32 The low purity caused by solvent inclusion and the weak mechanical strength of the spherical crystals, however, indicated improvements to be made to the oiling-out crystallization process. Nucleation, wherein a new solid phase is formed from the mother liquor, represents the initial and most important step of the crystallization process. It plays a decisive role in determining the main properties of the crystal population, including the polymorph and size distribution.33−35 Therefore, the success of optimizing crystallization conditions relies on the ability to achieve and control nucleation. With the appearance of a second liquid phase, knowledge of the location of the nucleation point is essential for nucleation control. In situ process analytical techniques36−38 have been used to characterize the oiling-out phenomenon.39 Duffy,2 Deneau,27 and coworkers investigated the nucleation process using particle vision monitor and optical microscopy and indicated that the crystal nucleates from the solute-rich phase. By contrast, Maeda et al.40 reported that nucleation takes place from the solute-lean phase. Ensuring the location of the nucleation point is difficult as nucleation occurs fairly rapidly in solution. Accurate determination of crystal nucleation rates may yield molecular-level information on the nucleation process. The nucleation energy barrier and supersaturation are two factors dominating the nucleation process. Both factors are affected by the composition of the solution, and the latter has also been related to mixing effects in the solution. The nucleation point can be estimated by analyzing the nucleation energy barrier and supersaturation generated at each phase.

1. INTRODUCTION Antisolvent crystallization has been extensively studied for the past 50 years, but many problems associated with process control remain.1 Supersaturation, purity, mixing intensity, and particle size are the most important factors that must be controlled.2 The difficulty in controlling these factors would be exacerbated when a second liquid phase is formed. The phenomenon wherein oil droplets appear during crystallization is called liquid−liquid phase separation, or oiling out,3−8 and generally occurs during crystallization of an insoluble solute9 by using a mixed solvent of water and water miscible organic solvents. The effects of pH,10,11 protein−protein interactions,12 and ionic strength13 on the oiling-out phenomenon have been investigated recently. Traditional crystallization methods can no longer be employed because the solution “oils out” before crystallization. It can result in low purity and unsatisfactory crystal size. Thus, the crystallization process must be fully understood to avoid the oiling-out phenomenon. The oiling-out phenomenon was first reported during protein crystallization,14−22 which is similar to phase behavior in binary polycyclic aromatic hydrocarbons system.23 Few reports are available on oiling-out crystallization in small molecules,24−27 especially water insoluble pharmaceuticals. As impurities are well-dissolved in the oil phase, the purity of the product will decrease. Furthermore, previous results indicate that the nucleation rate in oiling-out crystallization is generally slow even with a high supersaturation level.2,5,28 In many cases, no crystal was obtained after the crystallization process.29 According to the Ostwald rule,30 the oil droplets formed hinder primary and secondary nucleation processes. Hence, the oilingout phenomenon is undesirable and should be avoided if possible during industrial processes. Veesler et al.31 were able to utilize oiling out to acquire spherical crystals, thereby proving the advantage of the oilingout phenomenon in controlling the physical properties of the © 2016 American Chemical Society

Received: Revised: Accepted: Published: 766

November 2, 2015 December 13, 2015 January 4, 2016 January 4, 2016 DOI: 10.1021/acs.iecr.5b04155 Ind. Eng. Chem. Res. 2016, 55, 766−776

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Industrial & Engineering Chemistry Research

relative standard uncertainty of the solubility measurement was estimated to be 0.05. 2.5. Induction Time Measurements. The spontaneous nucleation of EES was performed in a 100 mL, round-bottomed jacketed, glass batch crystallizer. The induction time was generally defined as the time period elapsed between the moments a constant supersaturation formed in solution and the instant of detectable crystal particles. The induction time of EES was measured by FBRM with nine different compositions under a temperature of 35 °C. Over 200 induction time measurements were made across all nine compositions. The experimental apparatus and procedure mainly consisted of four parts: a FBRM monitoring observation system, a feeding system, a mixing system, and a crystallizer with temperature control. The FBRM monitoring system included a fiber optic, a beam splitter, a sapphire window, and a detector. The experimental procedure is briefly described as follows: A desired quantity of a solution of EES in THF was added into the crystallizer and agitated with a mechanical stirrer under a steady desired temperature. The temperature was controlled by a thermostat bath (Julabo CF41, Germany) with uncertainty of ±0.01 K. The stirring rate was set at 400 rpm, and the FBRM probe was introduced to the crystallizer. Then a certain amount of water at the same temperature was added quickly into the crystallizer by pipet, and the FBRM monitoring was started simultaneously. The time for water addition should be less than 5 s. The nucleation point was monitored by the FBRM probe with a precision of 1 μm, which provides a measurement of the particle chord lengths, depending on the optical properties of the liquid medium and crystals. The counts with the chord length ranging from 10 to 50 μm were utilized to indicate the nucleation point. This value was chosen because it detected the onset point of nucleation process and avoided the noise caused by agitation and antisolvent addition. When detectable particles appeared, the counts of 10−50 μm decreased greatly because the death rate of the droplet is much higher than the birth rate of the crystal nucleus in this study. Thus, the time elapsed between the addition of water and the quick variation of the chord mounts was termed the induction time. Induction time measurements were carried out in different amounts of water addition under the same temperature. Three reproducible experiments were performed at each composition, and the relative average deviations (RADs) calculated by eq 1 were applied to evaluate the accuracy of the data. The relative standard uncertainty of the induction time measurement was estimated to be 0.05.

The study aims to determine the position of nucleation points for the erythromycin ethylsuccinate (EES) system. The solubility line was first determined and also correlated for supersaturation calculation. The induction time of nucleation in the oiling-out system was then determined by focused beam reflectance measurements (FBRM) under different supersaturation levels and the same temperature. Afterward, the nucleation energy barrier was calculated using nucleation theory. The nucleation point was confirmed by comparing the nucleation energy barrier and supersaturation obtained in different phases. Finally, the growth mechanism and effect of supersaturation on the crystal morphology of EES were investigated.

2. EXPERIMENTAL SECTION 2.1. Materials. EES was supplied by Xi’an Lijun Co. Ltd. with the mass fraction purity of more than 0.98. Tetrahydrofuran of analytical reagent grade (mass fraction purity > 0.995) was obtained from Tianjin Kewei Chemical Reagent Co. Ltd. of China and used as a solvent without further purification. Distilled−deionized water (conductivities < 0.5 μs cm−1) was prepared in our laboratory and used throughout. 2.2. Thermal Analysis. Differential scanning calorimetry (DSC) analyses of the samples were performed on a DSC 1/ 500 instruement (Mettler−Toledo). The melting temperature, Tm, and the enthalpy of fusion, ΔfusH1, of EES were measured under the protection of nitrogen atmosphere. Accurately weighed samples (5 × 10−6 kg to 10 × 10−6 kg) were placed into pierced aluminum pans and scanned from 298.15 to 523.15 K under a nitrogen purge with a flow rate of 1.667 × 10−6 m3·s−1. The heating rate was preset to be 0.025 K·s−1. The relative standard uncertainty of Δfus H1 was estimated to be 0.02, and the standard uncertainty of Tm was estimated to be 0.5 K 2.3. Identification of EES Polymorphs. The PXRD patterns of the solid before and after solubility measurement were collected on a D/MAX-2500 X-ray diffractometer (Rigaku, Japan) with Cu Kα radiation (1.5405 Å). The samples were scanned over the 2θ range from 2° to 50° with a stepsize of 0.02°. 2.4. Solubility Measurements. The solubility of EES in tetrahydrofuran (THF)−water mixtures was measured by an analytical method at 308.15 K. Excess solid EES was added to different solvents (Vwater/Vtotal = 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95) and kept at 308.15 K controlled by an Eppendorf Thermomixer (Eppendorf, Germany) with uncertainty of ±0.05 K. The suspensions were shaken for 12 h, which had been tested to be enough to reach the solid−liquid equilibrium. Then the upper solution of 0.5 mL was sampled and filtered by 0.22 μm poly(vinylidene fluoride) (PVDF) filters. All the PVDF filters were placed in the solution’s temperature before they were used. The sampled solutions were diluted by acetonitrile to avoid crystallization during the measurement. The concentration of EES in sample solutions was monitored by Waters Acquity UPLC-SDQ2Mass instrument (Waters). The chromatographic analysis was performed on a Waters BEH C18 column (2.1 × 50 mm, 1.7 μm) with a mobile phase of 0.1% formic acid in water and 0.1% formic acid in acetonitrile at a flow rate of 0.8 mL·min−1. The sampled solid was analyzed by X-ray powder diffraction to verify that the form did not change during the solubility measurement. All measurements were repeated three times, and then an average value was given. The

RAD =

1 N

N

∑ i=1

t ind,i − t ind,i ̅ t ind,i ̅

(1)

where N is the number of experimental measurements under a same condition; tind refers to the experimental induction time, and ti̅ nd represents the average value of reproducible experiments. All the RADs were less than 5%, indicating a good reproducibility for the induction time data determined at each solvent composition. The error is mainly due to the time lag of the measuring technique. An average induction time was then used in the analysis of the final results.

3. RESULTS AND DISCUSSION 3.1. EES Solubility in Binary Solvents of Tetrahydrofuran and Water. Supersaturation is of great importance when considering the crystallization process,41 and the 767

DOI: 10.1021/acs.iecr.5b04155 Ind. Eng. Chem. Res. 2016, 55, 766−776

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= 429.75 K; zinc, ΔfusH = 7028.35 J·mol−1, Tm = 692.65 K). Given the appearance of liquid−liquid equilibrium, the solubility line is divided into two parts separately belonging to the solid−liquid and solid−liquid−liquid equilibrium area. Addition of antisolvent changed the composition of the solution for nucleation based on the ternary phase diagram, thus implying that different solubility lines should be used for the supersaturation calculation. The isothermal solubility of EES in binary solvents significantly decreased with increasing mole fraction of water. This phenomenon could be well explained by the “like dissolves like” rule, which generally relates to the dielectric constant as a good polarity index. Another obvious phenomenon is that the decreasing rate of solubility slowed down as the solution changed from the solid− liquid−liquid phase to the solid−liquid phase. The solubility line corresponding to the solid−liquid−liquid phase does not really exist. The solution is an unstable thermodynamic system when the solution state is analyzed from the view of Gibbs energy. Further phase separation would take place immediately as the Gibbs energy of the solution on the line between two equilibrium liquid points exceeds the sum of Gibbs energies at these two equilibrium liquid points. Thus, the equilibrium solubility for the solid−liquid−liquid phase should be calculated using the linear fitting method (eq 2):

solubility affects supersaturation degree generated in solution. The mole fraction solubility data of EES in binary solvents of tetrahydrofuran−water were measured under a given temperature. The PXRD (Figure 1) and DSC (Figure 2) results of

Figure 1. X-ray powder diffraction pattern of EES.

0 x1 = Px 1 2 + P2

(2)

P1 and P2 were empirical parameters which are calculated through the composition of two equilibrium liquid phases, indicating the boundary between two-liquid equilibrium and solid−liquid−liquid equilibrium. x02 was the water composition in binary solvents on the solute-free basis. The compositions of these two points were calculated using the non-random twoliquid model with the liquid−liquid equilibrium data in our previous study. The solubility at the solid−liquid phase was determined by fitting the solubility data using eq 3:43 ln x1 = B0 + B1x 20 + B2 x 202 + B3x 203 + B4 x 204

(3)

The experimental (x1) and calculated solubility (xcal 1 ) values are listed in Table 1, and the corresponding parameters B0, B1, B2, B3, and B4 are summarized in Table 2. As shown in Figure 3a, the solubility data was well-correlated with eq 3. The following model44 can be used for further understanding of the solubility behavior of EES during antisolvent crystallization. This model can quantitatively describe the relationship between dielectric constants and the solubility of hydropholic pharmaceuticals (eq 4).

Figure 2. DSC curve of EES with a melting temperature of 383.15 K and a fusion enthalpy of 30.98 kJ·mol−1.

EES remained unchanged in each experiment, indicating no polymorph transformation under the conditions employed for solubility measurements. The determined melting point, Tm (383.15 K), was in good agreement with the values obtained from the literature.42 The fusion enthalpy of EES was derived to be 30.98 × 103 J·mol−1; this study is the first to report such a value. The instrument was calibrated by using the phasetransition temperature and phase-transition enthalpy of reference materials (and the onset temperature was chosen as the melting temperature: indium, ΔfusH = 3266.57 J·mol−1, Tm

⎛ M ⎞ x1 = k 0 exp⎜ − ⎟ ⎝ Rεm(T ) ⎠

(4)

Table 1. Experimental and Correlated Mole Fraction Solubility, x1, of Erythromycin Ethylsuccinate in Binary Solvents of Different Compositions (p = 0.1 MPa)a Xc

0.8862

0.9034

0.9232

0.9413

0.9578

0.9730

0.9871

x1b c xcal 1

4.388 × 10−4 4.257 × 10−4

2.728 × 10−4 2.789 × 10−4

1.937 × 10−4 2.003 × 10−4

1.613 × 10−4 1.542 × 10−4

1.203 × 10−4 1.188 × 10−4

8.714 × 10−5 9.066 × 10−5

7.021 × 10−5 6.915 × 10−5

a Standard uncertainty, u, is u(T) = 0.01 K and u(P) = 10 kPa; relative standard uncertainty, u, is ur(x) = 0.05 (0.95 level of confidence). bx1 is experimental molar fraction solubility of EES in binary solvents of different compositions at temperature T. cxcal 1 is calculated molar fraction solubility of EES in binary solvents of different compositions at temperature T.

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Industrial & Engineering Chemistry Research Table 2. Fitting Parameters for Erythromycin Ethylsuccinate Solubility in Binary Solventsa

a

B0

B1

B2

B3

B4

1.350 × 104

−5.646 × 104

8.848 × 104

−6.160 × 104

1.607 × 104

Relative standard uncertainty in the parameters B0, B1, B2, B3, and B4 is less than 0.02.

and x3 refer to the mole fractions of water and tetrahydrofuran in binary solvents, respectively. The correlation of solubility data with the dielectric constant model is shown in Figure 3b. The results indicate that this model can predict EES solubility in the investigated solvents and that the polarity of the solvent mixture restrains EES solubility. The EES solubility decreased with increasing water content in the binary solvents, and this result agreed with the “like dissolves like” rule. The value of M is estimated from the slope of ln x1 versus −1/εm, which represents the dissolution capacity of EES in binary solvents. The solubility was applied as the fundamental data to calculate the supersaturation level of the nucleation process of EES, especially in the study of EES with liquid−liquid equilibrium under a certain temperature and concentration. 3.2. Nucleation Analysis of EES in Binary Solvents. With the appearance of the liquid−liquid equilibrium phase in the ternary phase diagram under a given temperature, the nucleation point is essential for crystallization control. A proper agitation rate was chosen because the time needed for generating the initial supersaturation must be shorter than the induction time to exclude any possible mixing effects. Thus, the antisolvent can be well-distributed to the whole solution rapidly. The final agitation rate used to measure the induction time was 400 rpm. As diffusion effects of the antisolvent were negligible in this study, the location of the nucleation points can be identified by comparing the nucleation rates in each phase. According to classical nucleation theory, the homogeneous nucleation rate is obtained by (eq 7): ⎛ −16πγ 3V 2 ⎞ J = J0 exp⎜ 3 3 2 1 ⎟ ⎝ 3k T ln S ⎠

where J represents the nucleation rate, k the Boltzmann constant, T the absolute temperature, J0 the pre-exponential factor, S the supersaturation level, γ the crystal−solution interfacial tension, and V1 the EES molecular volume. Different functions have been proposed to determine the pre-exponential factor with different kinetic association models. The induction time is generally used as an important macroscopic measurement of the nucleation event.46 Induction time is also a global measurement of the time needed for the occurrence of different physical events, including the time needed to achieve a quasi-steady-state distribution of the clusters, the time needed for the formation of stable nuclei, and the time for the growth of nuclei into detectable size. The measured induction times at different water compositions are shown in Figure 4 a−c. Nucleation time lag was not considered in this study because of its insignificance according to Söhnel and Mullin.46 Thus, induction time is inversely proportional to the nucleation rate and depends on both the interfacial tension and the temperature. For many crystallization systems of industrial interest, recording the nucleation event is the most useful method for determining the interfacial tension. Because the nucleation rate is inversely related to the induction time,47 the relationship between supersaturation and induction time can be expressed as eq 8:

Figure 3. (a) Experimental and correlated solubility of EES in binary solvents of different compositions. The solid lines are calculated values based on the polynomial fitting model. (b) Correlation of EES solubility in binary solvents of different compositions and the dielectric constant.

where x1 is the mole solubility of EES; εm(T) refers to the dielectric constants of binary solvents under a determined temperature; k0 represents the pre-exponential factor; and M is a kind of characteristic constant, R the gas constant, and T the absolute temperature. The dielectric constants of pure solvents at each temperature can be calculated using eq 5:45 ln[εi(T )] = a + bT + cT 2

(5)

where a, b, and c are empirical constants. The sum law of cube roots was used to calculate the dielectric constants of a binary system (eq 6): εm1/3 = x 2ε21/3 + x3ε31/3

(7)

(6)

where εm, ε2, and ε3 are the dielectric constants of binary solvent mixtures, water, and tetrahydrofuran, respectively; x2 769


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Figure 4. Induction time of EES over a range of supersaturation levels with different water contents: (a) (82.48−82.91) mixture, (b) (54.68− 77.97) mixture, and (c) (85.66−86.21) mixture (mol % water composition in binary solvents on a solute-free basis).

ln t ind = K +

Figure 5. Plot of ln tind versus 1/ln2 S in binary solvents of different water contents: (a) (82.48−82.91) mixture, (b) (54.68−77.97) mixture, and (c) (85.66−86.21) mixture (mol % water composition in binary solvents on a solute-free basis).

16πγ 3V12 3k3T 3 ln 2 S

(8)

heterogeneous48 to homogeneous49 as supersaturation increases. At certain temperatures and supersaturation levels, the induction time increases as the composition of water increases. The supersaturation level for homogeneous nucleation is low in the solute-rich phase and tends to become higher as the water composition increases. The highest supersaturation level can be observed in the solute-lean phase. This phenomenon implies that the primary nucleation becomes more and more difficult as crystallization proceeds. In other

where K is a kind of empirical constant, k the Boltzmann constant, T the absolute temperature, S the supersaturation level, γ the crystal−solution interfacial tension, and Vm the EES molecular volume. The measured induction time in different solvent compositions can be plotted against supersaturation in Figure 5, and two linear regions with different slopes can be drawn. The occurrence of two distinct regions has been attributed to the change in nucleation mechanism from 770


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Figure 6. (a) Critical radius of a cluster; (b) number of molecules in a cluster; (c) nucleation barrier of a cluster versus solvent composition for a given driving force (Δμ/kT = 0.2); (d) critical radius of a cluster; (e) number of molecules in a cluster; and (f) nucleation barrier of a cluster versus solubility for a given driving force (Δμ/kT = 0.2).

words, the metastable state of the EES solution can be maintained for a longer period of time with increasing water composition. The activation energy for nucleation is determined using thermodynamic analysis, which considers the change in the Gibbs free energy, ΔG, as the formation of spherical nuclei occurs in a supersaturated solution (eq 9):

ΔG = ΔG V + ΔGS =

4 3 πr Δg V + 4πr 2γ 3

(9)

Here, ΔGV represents the free energy difference between the solute in solution and the solid crystalline structure; ΔGs is a positive term as the free energy of the solid bulk is lower than that of the solid surface, and ΔgV is the free-energy difference per unit volume. ΔgV is a negative quantity because the free 771


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Industrial & Engineering Chemistry Research energy of the solute in solution is higher than that of the solid bulk. r is the radius of the particle. Considering the size dependence of the free-energy difference, the total Gibbs freeenergy change has a maximum value and growth is thermodynamically favorable beyond the corresponding size. The activation energy for nucleation refers to the maximal freeenergy change. The critical size of a stable nucleus was calculated by eq 10:

dΔG =0 dr

ln t ind =

16πγ 3V12 α α= 2 ln s 3k3T 3

(13)

The crystal−solution interfacial tension at a given temperature and solvent composition can be calculated from eq 14: ⎛ 3α k3T 3 ⎞1/3 ⎟ γ=⎜ 2 ⎝ 16πV1 ⎠

(14)

Figure 7a shows the experimentally obtained interfacial tension versus solubility at different solvent compositions under

(10)

Assuming that spherical nuclei are formed, the equations become eqs 11 and 12: ΔGcrit =

rcrit =

16πγ 3V12 3k2T 2 ln 2 S

2γV1 Δμ

(11)

(12)

where V1 represents the molecular volume of EES; ΔGcrit and rcrit can be calculated using these equations. Figure 6a−f shows the effect of solvent composition and solubility on the nucleation barrier, critical radius, and the number of molecules in the critical nuclei under a given driving force (dimensionless Δμ supersaturation kT = 0.2 ). The number of molecules forming the critical nucleus was determined by dividing the volume of the critical nucleus with the molecular volume of EES. The number of molecules and the critical radius needed for nucleation increased with decreasing solubility of EES in the binary solvents and increasing water content. The radius of the critical nucleus was in the range of 13−41 Å depending on the solvent composition, and the number of molecules forming the nuclei ranged from a few molecules to a few hundred molecules. The smaller critical size observed is related to the lower interfacial tension, which, in turn, relates to the small free-energy difference between the crystal surface and the crystalline structure of the crystal. The unsatisfied bonds of the crystal structure at the interface are well-compensated by interactions with the surrounding solution. The low interfacial tension also leads to a smaller nucleation barrier. The real solution for nucleation is the physical mixing of two equilibrium liquid phases during the whole nucleation process. As the water composition increases, the nucleation barrier increases under the same temperature and supersaturation because of the increasing volume fraction in the solute-lean phase. The antisolvent can be well-distributed to the whole solution because the mixing time of the solution can be neglected. Thus, the solvent composition of the solute-rich phase changes greater than that of the solute-lean phase in this study. The greater change in equilibrium solubility then leads to higher supersaturation in the solute-rich phase. Therefore, the nucleation rate of the solute-rich phase is higher than that of the solute-lean phase during the nucleation process. Thus, the nucleation point of EES in liquid−liquid equilibrium area appears to be located in the solute-rich phase. 3.3. Interfacial Tension Determination. As the net effect of the changing solvent is expected, decreasing solubility increases the induction time at constant temperature and supersaturation because of the increasing interfacial tension. The interfacial energy can be estimated from the slope eq 13:50

Figure 7. (a) Influence of solvent composition on interfacial tension and (b) interfacial tension versus solubility.

a given temperature. It also reveals that the interfacial tensions obtained from the solute-rich phase to the solute-lean phase are in the range of 0.422−1.315 mJ·m−2, similar to the values reported for other poorly water soluble organic molecules, e.g., 0.3−0.9 mJ·m−2 for tetracosane, 1.4−2.8 mJ·m−2 for paracetamol, and 1.4−1.8 mJ·m−2 for ketoprofen. The interfacial tension is obviously dependent on water composition (Figure 7b). The equilibrium solubility decreased with increasing water composition, thereby increasing the interfacial tension in agreement with nucleation theory. Increasing levels of supersaturation can also enhance the formation rate of nuclei and shorten the induction time. 772


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Industrial & Engineering Chemistry Research Table 3. Experimental Surface Entropy Factors, f, at Different Water Contents (mole %) mole

0.5468

0.7540

07797

0.8248

0.8289

0.8291

0.8566

0.8600

0.8621

f

0.4773

0.8853

0.9474

1.051

1.101

1.111

1.396

1.432

1.485

An entirely different experimental method to measure γ is achieved by determining the contact angle (θ) between the solvent and the solute, which relates γ to the solid−vapor (γsl) and the liquid−vapor (γlv) surface tension. Because this method is based on a balance of interfacial tensions, the rule is reasonable for van der Waals interactions but unreliable when polar interactions are present. The model is generally not applicable to a mixture of solvents, and estimation of the interfacial tension by contact angle can be used as only an approximate value. Different correlations relating the interfacial tension to its equilibrium solubility have been proposed. Two equations commonly used to estimate interfacial tension are as follows51,52 (eqs 15 and 16): γ ≅ kTV1−2/30.25(0.7 − ln xeq)

γ = 0.414kT (csNA )2/3 ln

cs ceq

mechanism can be determined by calculating f. As shown in Table 3, the calculated values of f in binary solvents of different water compositions range from 0.47 to 1.49. Thus, the growth mechanism of EES in the binary solvents investigated is continuous growth because the value of f is less than 3. 3.5. Effect of Supersaturation on the Crystal Properties of EES. EES morphology was determined through optical microscopy to evaluate the effect of supersaturation on crystal shape. The crystals were prepared in different homogeneous solutions with the concentrations corresponding to solute-rich phase and solute-lean phase separately. As shown in Figure 8,

(15)

(16)

where k is the Boltzmann constant and T the absolute temperature; V1 refers to the molecular volume of EES, and xeq is the mole fraction of EES in a saturated solution. The interfacial tension estimated using the induction time was compared with values obtained through theoretical calculation using eqs 15 and 16 and plotted in Figure 7; the estimated interfacial tension values were much lower than those predicted from eqs 15 and 16. However, the trends of the influence of solvent composition on interfacial tension estimated from the experimental results were similar to those calculated from eq 15. 3.4. Growth Mechanism Determination. The crystallization process can normally be divided into nucleation and growth. The former refers to the birth of crystals from the mother liquid, whereas the latter represents the growth of crystals to larger sizes. Further understanding of the mechanism of growth is of great importance for achieving better control of the polymorph and morphology of the resultant crystals. The crystal−solution interfacial tension is also a crucial parameter involved in the growth mechanism of a crystal. Three important growth models, namely, the continuous growth model, birth and spread model, and spiral growth model, are often used to describe crystal growth. The surface entropy factor, f, is an important index of the degree of roughness of a crystal face. The crystal surface becomes smoother as f increases; hence, crystal growth becomes more difficult. Davey47 suggested calculating the surface entropy factor from interfacial tension data by using the following equation:

f=

4V12/3γ kT

Figure 8. Optical microscopy images of EES crystallized from a THF− water binary solvent system at different supersaturation (T = 308.15 K). The aspect ratio is defined as the ratio of length to width: (a) S = 1.29 (solute-rich phase), aspect ratio ranges from 2 to 6; (b) S = 1.78 (solute-lean phase), aspect ratio ranges from 10 to 15.

rodlike crystals were formed at the solute-lean phase, whereas flakelike particles were formed at the solute-rich phase. Therefore, differences in supersaturation between solute-lean and solute-rich phases are the key factors affecting the morphology of EES crystals. The aspect ratios of EES ranged from 10−15 (solute-lean phase) to 2−6 (solute-rich phase). The variable trend of the aspect ratio can be explained by differences in crystal growth rate between the solute-rich and solute-lean phases in relation to different supersaturation levels.

(17)

The parameters are defined the same as in eq 8. The calculated surface entropy factor, f, is used to identify the crystal growth mechanism further. An f of less than 3 means the interface is rough and continuous growth should be expected. When f is greater than 5, the growth mechanism changes to spiral growth or screw dislocation. Crystal growth slows as the crystal surface smoothens, and nucleation and spread growth occur when f ranges from 3 to 5. Therefore, the growth 773


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R = gas constant, 8.314 J·(mol·K)−1 T = absolute temperature (K) a = empirical constants b = empirical constants c = empirical constants J = nucleation rate (no.·s−1· mL−1) J0 = pre-exponential factor S = supersaturation ratio V1 = EES molecular volume (mL) K = empirical constant r = radius of the particle (m) rcrit = critical radius of the particle (m) f = surface entropy factor xeq = mole fraction of EES in a saturated solution cs = concentration of solute in the solid phase (mol·mL−1) ceq = solubility of solution (mol·mL−1) NA = Avogadros number, 6.023 × 1023 mol−1

4. CONCLUSIONS The relationships among the induction time for primary nucleation of EES in THF−water mixtures, the solvent composition, and the interfacial energy are investigated. The induction time increases with decreasing solubility under a constant thermodynamic driving force. In other words, induction time increases with increasing water content. The nucleation point of EES is located in the oil phase based on a comparison of the nucleation energy barrier and supersaturation at each phase studied. The interfacial energy estimated through induction time increases with decreasing EES solubility in the binary solvents, which is in agreement with nucleation theory. The estimated interfacial energy is in the range of 0.422−1.315 m J·m−2, which is significantly lower than the values predicted by theoretical calculations. These low interfacial energies lead to smaller sizes of the critical nucleus, which in turn leads to hundreds of molecules in the critical nucleus under low supersaturation and only a few under high supersaturation. According to estimations of the surface entropy factor with interfacial tension, continuous growth dominates the whole growth process. The different supersaturation levels generated in each phase lead to different aspect ratios of the final product.

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Greek Letters

α = slope of linear correlation for induction time θ = contact angle between the solvent and the solute (deg) γlv = interfacial tension between the liquid and the vapor (J· m−2) γsv = interfacial tension between the solid and the vapor (J· m−2) γ = crystal−solution interfacial tension (J·m−2) εi(T) = dielectric constants under a certain temperature εm(T) = dielectric constants of binary solvents under a determined temperature ΔGV = free-energy difference between the solid crystalline structure and the solute in solution (J) ΔGS = free-energy difference between the solid surface and the solid bulk (J) ΔgV = corresponding free-energy difference per unit volume (J·m−3) Δμ = chemical-potential difference between the solid crystalline structure and the solute in solution (J)

AUTHOR INFORMATION

Corresponding Author

*Tel.: 86-22-27405754. Fax: 86-22-27374971. E-mail: zhao_ [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The support from National Natural Science Foundation of China (21206109) and China Ministry of Science and Technology for the key technology of preparation of edible pigment and industrialization project (2011BAD23B02) are greatly appreciated.

Superscripts

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cal = calculated data

NOTATION Tm = melting temperature (K) ΔfusH1 = enthalpy of fusion (J·mol−1) Vwater = volume of water in solution (mL) Vtotal = volume of whole solution (mL) RAD = relative average deviation N = number of experimental measurements tind = experimental induction time (s) ti̅ nd = average value of experimental induction time (s) x1 = experimental mole fraction solubility of EES x2 = mole fractions of water in binary solvents x3 = mole fractions of tetrahydrofuran in binary solvents xcal 1 = calculated mole fraction solubility of EES x01 = mole ratio of water to THF P1 = model parameter in eq 2 P2 = model parameter in eq 2 B0 = model parameter in eq 3 B1 = model parameter in eq 3 B2 = model parameter in eq 3 B3 = model parameter in eq 3 B4 = model parameter in eq 3 k = Boltzmann constant, 1.38 × 10−23 J·K−1 k0 = pre-exponential factor M = characteristic constant

Subscripts

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1 = EES 2 = water 3 = tetrahydrofuran

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