Homogeneous and Heterogeneous Nucleation of Potash Alum in

Article Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Homogeneous and Heterogeneous Nucleation of Potash Alum in Drop-Based Microfluidic Device Huanhuan Shi,†,‡ Yan Xiao,†,‡ Xin Huang,†,‡ Ying Bao,†,‡ Chuang Xie,†,‡ and Hongxun Hao*,†,‡ †

National Engineering Research Center of Industrial Crystallization Technology, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, P. R. China ‡ Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300072, P. R. China

Ind. Eng. Chem. Res. Downloaded from pubs.acs.org by WESTERN UNIV on 09/15/18. For personal use only.

S Supporting Information *

ABSTRACT: In this work, homogeneous and heterogeneous nucleation of potash alum were investigated using a drop-based microfluidic device made of a T-junction and transparent Teflon tubes. Monodisperse droplets were formed through the T-junction geometries, and their sizes could be adjusted by changing the velocities and viscosity of solutions and silicone oil. Ideal droplets which acted as independent crystallizers were successfully obtained. By monitoring each droplet using microscope equipped with a high-speed camera, probabilities of droplets without crystals at different time were determined. By applying or not applying filtration to the experimental solutions, both homogeneous and heterogeneous nucleation were observed. Different models were used to correlate the probability data to derive nucleation rates of potash alum under different conditions. The obtained nucleation rates from homogeneous and heterogeneous nucleation were compared and discussed. The nucleation parameters such as interfacial tension under different conditions were also determined and discussed. their nucleation and growth behavior.18−21 Furthermore, because of the finite-volume and monodisperse characteristics, crystals obtained in drop-based microfluidic devices usually have narrow crystal size distributions.22 More importantly, in the drop-based microfluidic system, a considerable number of monodisperse droplets can be generated and act as independent crystallizers for a statistical analysis to estimate nucleation kinetics.23,24 Because of the small droplet volume and spatial confinement, it is convenient to directly observe and monitor nucleation in the droplets. Also, in microfluidic devices, nucleation can be studied under no impurities conditions, and homogeneous or heterogeneous nucleation can be determined with minimal error.14,25,26 With all these advantages, various microfluidic systems and approaches have been applied to investigate nucleation of organic compounds based on the probability of crystal appearance in droplets versus time evolution.20,27−29 However, few applications of microfluidic technology for investigating nucleation rates of inorganics have been reported.23,30,31 In this work, microfluidic technology was used to investigate the nucleation behaviors of inorganic compounds by using potash alum as a model compound.

1. INTRODUCTION In crystallization processes, to obtain crystal products with desired quality, such as polymorph,1 crystal habit,2 and crystal size distribution,3 it is essential to understand the nucleation mechanism and control the nucleation kinetics. Because of the above reasons, crystal nucleation has been enormously studied.4−8 However, due to the stochastic characteristics of primary nucleation and the difficulty of ruling out secondary nucleation process, it remains a tricky problem to determine primary nucleation rates by conventional methods based on a large volume system.9−11 Therefore, it is necessary to find a better way to investigate crystal nucleation more conveniently and accurately. Recently, microfluidics has attracted more and more attention from researchers in the field of crystallization since microfluidic technology shows great potential in studying nucleation mechanisms, especially for crystallization of protein and active pharmaceutical ingredient (API).12−14 Microfluidic devices can offer a platform for investigating crystal nucleation under more precise conditions. By using microfluidic devices, crystallization experiments can be conveniently implemented under conditions of free interface diffusion and in nanoscale. Therefore, it has been used to prepare high quality nanocrystals.15−17 Microfluidic technology is also a high-throughput technology. It only requires a few micrograms or less amount of materials to conduct a series of crystallization experiments under various conditions. This characteristic has been applied to grow high-quality protein crystals and to investigate © XXXX American Chemical Society

Received: Revised: Accepted: Published: A

July 17, 2018 August 30, 2018 September 3, 2018 September 3, 2018 DOI: 10.1021/acs.iecr.8b03286 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

Figure 1. Schematic of microfluidic setup for potash alum crystallization.

Potash alum can easily grow into large crystals that can be detected and observed clearly under the microscope. Its basic physicochemical data are also available for building the nucleation kinetic model. In this work, a droplet-based microfluidic device was designed to investigate nucleation kinetics of potash alum under stagnant conditions. The monodisperse droplets were generated by a T-junction and stored in Teflon tubes. In each measurement, up to 200 monodisperse droplets that contained potash alum aqueous solutions were prepared and dispersed by silicone oil to avoid coalescence between adjacent droplets. The percentage of droplets without crystals was measured through image analysis at different times. Both homogeneous nucleation and heterogeneous nucleation were investigated by changing the experimental conditions. By using classical nucleation theory, nucleation rates and kinetic parameters of potash alum in water were determined and discussed in detail. The results were compared with results reported by J. Mullin.32

Figure 2. (a) Drop formation frequency as a function of the rate ratio q (Qd /Qc). (b) Drop flow velocity under different flow rates of oil phase and aqueous phase.

2. THEORY In droplet-based microfluidic systems, nucleation in each droplet is an independent event, and the random crystal nucleation process can be assumed to follow Poisson Distribution.33,34 The probability of droplets that contain crystals after a certain period is related to the nucleation rate. Therefore, by measuring the fraction of droplets that contain no crystals as a function of time, the primary nucleation rate can be determined. Under the assumption that nucleation rate is constant and only primary homogeneous nucleation occurs in the identical droplets, the number of empty droplets can be expressed as eq 1 after time t. N0(t ) = Ntotal exp( −JVt )

where J is the nucleation rate, V is the volume of droplet, Ntotal is the total number of droplets, N0(t) is the number of uncrystallized droplets after time t. Since temperature and supersaturation will affect the nucleation rate, eq 1 is only applicable to conditions where both temperature and supersaturaiton are constant. Under the same assumption, the logarithm of probabilities of empty drops, ln P0(t), that contain no nuclei at time t can be obtained from eq 1: ln P0(t ) = ln

(1)

N0(t ) = −JVt Ntotal

(2)

Table 1. Flow Rates of the Potash Alum Solution and Silicone Oil potash alum solution flow rate Qd (μL/min)

silicone oil flow rate Qc (μL/min)

rate ratio q

droplet formation frequency (drop/min)

droplet volume V(nL)

droplet equivalent diameter (mm)

2.5 4.5 7.5 3 5 10 5 10 15 5 10 15

15 15 15 20 20 20 30 30 30 40 40 40

0.17 0.30 0.50 0.15 0.25 0.50 0.17 0.33 0.50 0.13 0.25 0.38

4 6 9 6 8 14 10 14 20 10 17 24

625 750 833 500 625 714 500 714 750 500 588 625

1.06 1.13 1.17 0.98 1.06 1.11 0.98 1.11 1.13 0.98 1.04 1.06

B

DOI: 10.1021/acs.iecr.8b03286 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research where P0 is the probability of droplets that contain no crystals. Hence, the primary nucleation rate J can be determined from eq 2. According to classical nucleation theory, the homogeneous nucleation rate can be expressed as the function of supersaturation and temperature as follows:26 ij 16πγ 3v 2 yz J = K 0 expjjj− 3 3 m2 zzz j 3K T ln S z k {

(3)

where γ is the crystal−solution interfacial tension, vm is the molecular volume, K is Boltzmann constant, S is the supersaturation ratio (defined as eq 5), and K0 is the kinetic preexponential factor. According to eqs 2 and 3, the logarithm of probability of empty drops, ln P0(t), can be expressed as a function of S and T: 3 2 ln P0(t ) ji 16πγ v zy = −K 0 expjjj− 3 3 m2 zzz j 3K T ln S z Vt k {

S=

C C*

(4)

(5)

where C is the actual solution concentration, and C* is the equilibrium solubility. According to the previous work of Pound and Lamer,35 in the case of ln P0 vs t does not follow a linear relationship, which may result from both homogeneous and heterogeneous nucleation process, the probability P0 can be expressed as follows: P0 = e−m(e−k 0t − 1) + e−mexp(me−kt )

(6) Figure 3. Characterization of the droplet generated under different conditions. (a) Droplet volume versus the flow rate ratio q. (b) Volume equivalent diameter of droplets as a function of q.

where k0 and k are homogeneous and heterogeneous nucleation rate, respectively, m represents the arithmetic average number of foreign nuclei or centers per droplet. Equation 6 allows us to get the amount of impurities m and nucleation rate from experimental data.

in Figure 1. The microfluidic system consists of T-junction and optically transparent Teflon tubes with inner diameter of 1.2 mm and outer diameter of 1.4 mm. The microfludic device was mounted on the inverted microscope (Nikon ECLIPSE TS100) equipped with a CCD camera (FASTCAM Mini UX50). One end of the tubes was connected with syringe pumps which were used to adjust the flow rates of oil phase or aqueous solutions. The other end of tubes was connected to the T-junction. Potash alum solutions were preheated to above the saturation temperature to avoid crystallization before being divided into small drops by silicone oil. Droplets could be separated from the inner surface of tubes due to the surface characteristics and the existence of silicone oil, which further ensured the smooth flow of the droplets to avoid clogging. By altering the relative velocities of two immiscible phases, the size of droplets could be controlled and adjusted. The experiments could reach steady stage in 15 min after the first droplet formation. The setup used in this work is flexible and convenient to use. For instance, the channel length could be changed according to different experimental requirements, such as different number of droplets or different residence time of droplets in the channel. To ensure that the system will remain stable in the subsequent study, the ends of the tubes were sealed after the setup has reached balance with the ambient pressure, which could avoid droplet movement due to changes in external conditions during crystal nucleation. Then, the tubes were stored in a glass jacket connected to a constant temperature water

3. EXPERIMENTAL SECTION 3.1. Potash Alum Solution Preparation. Potash alum (purity >99.5%) was purchased from Tianjin Kemiou Chemical Reagent Co., Ltd. (Tianjin, China) and was used without any further purification. The resistivity of distilled water was about 18 MΩ cm. Solutions of potash alum were prepared by dissolving suitable amount of potash alum in distilled water at temperature higher than 40 °C. Solubility of potassium alum in water has been determined by Yang et al. and was correlated by the following equation:36 C* = 1.2780 × 10−5exp(3.07324 × 10−2T )

(7)

where, C* is the saturation concentration in kg solute/kg solution, and T is the temperature in Kelvin, K. 3.2. Droplets Generation. Silicone oil (purity >99.5%, 500 cSt), supplied by Tianjin Yuxiang Technology Co., Ltd. (Tianjin, China), was chosen as continuous fluid and was used without further purification. In the experiments, silicone oil acted as carrier phase to transport droplets and prevent droplets from coalescing and contacting the inner wall. In the T-junctions, due to the different viscosities and velocities of potash alum solutions and oil phases, the shear stress between silicone oil and aqueous solutions will accelerate the droplet detachment. Then, the monodisperse liquid drops can be obtained. 3.3. Microfluidic Setup and Experimental Procedure. Schematic diagram of the device used in this work was shown C


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Figure 4. Photographs of droplets formed in the microfluidic under different conditions: (a−c) Qc = 15 μL/min, q = 0.17, 0.30, 0.50 (left to right); (d−f) Qc = 20 μL/min, q = 0.15, 0.25, 0.50 from left to right, respectively. (g−i) Qc = 30 μL/min, q = 0.17, 0.33, 0.50 from left to right, respectively. (j−l) Qc = 40 μL/min, q = 0.13, 0.25, 0.38 from left to right, respectively. Scale bar: 500 μm.

size and formation frequency of droplets should be optimized first. Table 1 lists the properties of droplets obtained in this work. In this table, droplet size is characterized by volume equivalent diameter. It can be seen that droplets with different volumes and different formation frequency were generated by changing the flow rates of potash alum solution and silicone oil. Stable and uniform droplets were successfully obtained in absence of surfactants by optimizing the relative flow rates and T-junction. Figure 2 shows the drop formation frequency and drop flow velocity as a function of the flow rate ratio between the aqueous phase and the oil phase q = Qd/Qc, at different silicone oil flow rate. Figure 3 shows the drop volume and equivalent diameter as a function of the flow rate ratio q at different oil phase flow rate. As shown in Figure 2, both the drop formation frequency and flow velocity increase with the flow rate ratio and oil phase flow rate. When the flow rate of silicone oil decreased, the distance between two adjacent droplets increased while the total number of droplets generated decreased and might not be able to meet the experimental requirements in the device. However, as depicted by Figure 3, the drop volume and size increased with the flow rate of potash alum solution, while decreased with the flow rate of silicone oil. When the flow rate of silicone oil was too high, the droplet size became too small, which would result in undesired movement inside the channel. In addition, the distance between the droplets was too short, causing coalescence between adjacent droplets. The shapes of typical droplets formed in the channel under different conditions are shown in Figure 4. Considering

bath whose temperature was controlled at desired point to create appropriate supersaturation for inducing crystallization. At regular time intervals, crystals formed in the droplets were directly observed and detected by inverted microscope (equipped with a CCD camera) to investigate the nucleation kinetics.

4. RESULTS AND DISCUSSION 4.1. Optimization of Microfluidic Droplets. Stable droplets of potash alum solution were generated by T-junction system and delivered by the continuous silicone oil phase. Generally, in microfluidic environments, the size of droplets might affect the likelihood that nucleation will occur in the droplet as well as the size of the obtained crystals.37 For homogeneous nucleation, the nucleation rate was proportional to droplet volume. While for heterogeneous nucleation, the nucleation rate was proportional to the surface area of the droplet.38−40 In larger droplets, larger crystals might be formed, resulting in an increased probability of blockage of the channels. Since potash alum is easy to grow into large crystals, the size of droplets along the direction of the channel should be properly reduced to avoid clogging of the channels. Alternatively, if the size is too small, then droplets are prone to move randomly or could even be deformed when moving along the tube. In addition, the frequency of droplets formation is also a crucial parameter to ensure the success of experiments. High frequency will cause coalescence between adjacent droplets while low frequency could result in insufficient quantities of droplets in the system. Hence, both the D


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Industrial & Engineering Chemistry Research the effect of all factors, to ensure a sufficient number of droplets (∼200 drops) while avoiding movement or coalescence of droplets, the flow rate of aqueous phase was optimized to be 10 μL/min and the flow rate of oil phase was optimized to be 30 μL/min in this study (Figure 4h). Under these conditions, not only could a sufficient number of droplets be obtained, but also clogging problem caused by longer droplets could be avoided. In addition, the probability of nucleation was investigated. On the basis of the above flow rate conditions, the probability of droplets that contain crystals was plotted as a function of flow rate ratio in Figure 5. From Figure 5, it could be seen that

Figure 6. Photographs of droplets containing potash alum crystals. (a) Droplet containing one crystal and (b) droplet containing more than one crystals. The inner diameter of the tube used in this work is 1.2 mm.

Figure 5. Probability of droplets that contain crystals vs flow rate ratio q.

nucleation probability increases with the increasing of droplet volume. The error bars were negligible when flow rates of continuous phase were lower than 30 μL/min. However, the error bar became bigger when the continuous phase flow rate increased to 40 μL/min. Higher nucleation probability will be helpful for the determination of nucleation rate. In this work, 30 μL/min flow rate of continuous phase was selected since the higher nucleation probability and lower error. Under the optimized conditions, droplets with ideal size and appropriate concentration of model compound were generated. After the entire channel was filled with stable droplets and the device was in equilibrium with ambient pressure, the tube was sealed and placed under the designed temperatures. Under supersaturated conditions, the crystals nucleated in the droplets gradually. Inverted microscope equipped with a fast camera was used to observe the crystals formed inside the droplets. Several representative images are shown in Figure 6. 4.2. Determination of Nucleation Rates. By using the droplet-based microfluidic device, the nucleation rates of potash alum from aqueous solution were determined from the probability distribution of empty droplets as a function of time at constant temperature. The total number of droplets under each condition was about 200. To evaluate both the homogeneous and heterogeneous nucleation, two series of experiments were carried out and compared. In the first series of experiments, all prepared solutions were filtered by membrane filter (0.22 μm) before conducting nucleation experiments. One typical nucleation results are shown in Figure S1 of the Supporting Information (SI) which gives the variation of the percentage of droplets containing no potash alum crystals with time at S = 1.84, T = 299.15 K. It can be seen from this figure that the number of empty droplets

decreased with time. Using Poisson Distribution to evaluate the nucleation rates, data in Figure S1 was transformed into Figure S2 using ln P0 as Y axis. As shown in Figure S2, the plot of ln P0 vs t follows a linear relationship, which indicates that the nucleation is homogeneous and follow Poisson Distribution (eq 2). Then, the primary homogeneous nucleation rate was obtained from the slope and the mean droplet volume. The linear line here is ln P0 = −0.02649t (R2 = 0.9924), which gives the primary homogeneous nucleation rate of 1.03 × 104 m−3 s−1. Similarly, the homogeneous nucleation rates under different conditions could be obtained in the same way (Figure 7). The results are summarized in Table 2. To obtain the nucleation parameters by using eq 3, the relationship between the logarithm of homogeneous nucleation rate and T−3(ln S)−2 is shown in Figure 8. It can be seen that it is a linear relationship. The nucleation parameters, including γ, K0, were obtained by using the data in Figure 8, with the molecular volume of potash alum vm = 4.45 × 10−28 m3. The results are given in Table 3. It was worth mentioning that the interfacial tension γ = 1.70 mJ m−2 for homogeneous nucleation obtained in this work was close to the value (∼2.00 mJ m−2) near 15 °C reported by J. Mullin et al.32 Besides, the impact of different initial supersaturations on potash alum nucleation kinetics under same flow rates was also investigated. The results are shown in Figure S3, which is expressed by the probability of empty droplets at 15 °C after 24 h. The fitted line was based on eq 4, under assumption that K0 was a constant which did not change with temperature. The results indicated that the probability of empty droplets decreased with the increase of initial supersaturation slowly E


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Figure 8. Linear relationship between homogeneous nucleation rates and 1/(T3(ln S)2).

Table 3. Classical Nucleation Theory Parameters γ and K0 Determined with Eq 3

Table 2. Homogeneous Nucleation Rates of Potash Alum Aqueous Solution final temperature T (K)

supersaturation, S

nucleation rate 10−3 J (m−3·s−1)

1 2 3 4

288.15 299.15 289.15 288.15

2.57 1.84 1.80 2.15

13.8 10.3 8.96 13.0

K0 (m−3 s−1)

γ (mJ m−2)

R2

9.86

1.91 × 104

1.70

0.94

is shown in Figure S4 which gives the fraction of droplets containing no crystals over time at T = 291.15 K and S = 2.35. It can be clearly seen that ln P0 vs t showed nonlinear relationship, as expected. It indicates that both homogeneous and heterogeneous nucleation happened in this situation. In this case, model that considers both homogeneous and heterogeneous nucleation process should be used. In this work, the model proposed by Pound and Lamer (eq 6) was applied to correlate the experimental data. The results are given in Figure S4. It was found that eq 6 worked very well, which confirmed the happening of heterogeneous nucleation. More experimental results under similar conditions (no filtration of solution) are shown in Figure 9. It can be seen that all the plots of ln P0 vs t were nonlinear. These data in Figures S4 and 9 were used to calculate the homogeneous rate k0, heterogeneous nucleation rate k and the arithmetic average number of foreign nuclei or centers per droplet m. The results are given in Table 4. From data listed in Table 4, it can be found that the heterogeneous nucleation rate was several orders of magnitude higher than the homogeneous nucleation rate, indicating that the impurities, acting as active centers, promoted the nucleation rate greatly. Figure 10 illustrates the relationship of homogeneous nucleation rate k0 and heterogeneous nucleation rate k based on eq 6. Using data in Figure 10, the interfacial tension γ was determined to be 1.07 mJ m−2 through linear fitting, which was slightly lower than the interfacial tension for homogeneous nucleation (1.70 mJ m−2) and confirmed the existence of impurities. As for the discrepancy between the fitted data and the data reported by Mullin,32 one possible explanation is the existence of impurities. But not all impurities in the solution have equal effective as nucleation agents at a given temperature or supersaturation.35

Figure 7. (a) P0 versus time t, P0 is the probability of droplets that containing no crystals. (b) ln P0 as a function of time t for the same data set, the linear fitted of the data according to eq 2.

no.

ln K0 (m−3 s−1)

at first, which was consistent with previous literature.41 Along with further increase of supersaturation, the fraction of droplets containing no crystals reduced more sharply, which might result from the exponential increase of nucleation rate with higher supersaturation. However, more work needs to be done to completely verify and understand this phenomenon. In the second series of experiments, the solutions were not filtered through membrane filter before conducting experiments. In this case, the content of impurities inside the droplet would be relatively higher. Generally, impurities have certain impact on the nucleation process, such as resulting in occurrence of heterogeneous nucleation and hence accelerating the nucleation rate (Pound and Lamer, ref 36.). If heterogeneous nucleation does happen, then the plot of ln P0 vs t will not show linear relationship. In this work, one typical nucleation experimental result without filtration of the solution

5. CONCLUSIONS In this work, nucleation mechanism of potash alum was studied in droplet-based microfluidic device. Optimized flow F


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rates of the potash alum aqueous solution and silicone oil were determined to obtain appropriate droplets for conducting nucleation experiments. The homogeneous and heterogeneous nucleation rates of potash alum were derived from the probability of noncrystallized droplets vs time profile in fast cooling crystallization. The thermodynamic and kinetic nucleation parameters were also determined by using the classical nucleation theory. And the results were in good agreement with those reported previously.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.8b03286. Detailed information on screening conditions for droplets, droplet characteristics, and fitting results of nucleation rates (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*Phone: 86-22-27405754; fax: +86-22-27374971; e-mail: [email protected] (H.H.). ORCID

Ying Bao: 0000-0002-4461-8035 Hongxun Hao: 0000-0001-6445-7737 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was financially supported by National Natural Science Foundation of China (No. 21376165) and National Key Research and Development Program of China (No. 2016YFB0600504.)

Figure 9. (a) P0 versus time t, P0 is the probability of droplets that containing no crystals. (b) ln P0 as a function of time t for the same data set, the lines are fitted data according to eq 6.

■

NOMENCLATURE C = the actual solution concentration C* = the equilibrium solubility J = the nucleation rate k0 = homogeneous nucleation rate k = heterogeneous nucleation rate K = Boltzmann constant K0 = the kinetic pre-exponential factor m = the arithmetic average number of foreign nuclei or centers per droplet N0(t) = the number of uncrystallized droplets after time t Ntotal = the total number of droplets P0 = the probability of droplets that contain no crystals Qc = silicone oil flow rate Qd = potash alum solution flow rate q = flow rate ratio, Qd/Qc R = gas constant S = supersaturation ratio, C/C* T = absolute temperature vm = the molecular volume V = average volume of droplets t = time elapsed after the tube sealed γ = the crystal−solution interfacial tension

Table 4. k0, k, and m Fitted by Eq 6 under Different Conditions no. I II III IV

T (K) 290.15 288.15 291.15 291.15

S 1.60 1.70 1.55 2.35

k0 (s−1) 5.19 6.81 4.42 5.83

× × × ×

k (s−1) −7

10 10−7 10−7 10−7

1.81 1.87 2.31 1.47

× × × ×

10−4 10−4 10−4 10−4

m 0.145 0.019 0.042 0.095

■

Figure 10. Change curve of homogeneous nucleation rates (k0) and heterogeneous nucleation rates (k) with 1/(T3(ln S)2).

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