Effects of Different Organic Acids on Solubility and Metastable Zone

Article pubs.acs.org/jced

Effects of Different Organic Acids on Solubility and Metastable Zone Width of Zinc Lactate Xiangyang Zhang, Gang Qian, and Xinggui Zhou* State Key Laboratory of Chemical Engineering, East China University of Science and Technology, 200237, Shanghai, China ABSTRACT: Effects of three different organic acids including racemic malic acid, succinic acid, and citric acid, which act as an impurity on the solubility and metastable zone width of zinc lactate (ZnL2), have been studied. The results show that the presence of all examined impurities increases the solution solubility and the values of solubility increase with increasing impurity concentration. The introduction of impurity also leads to a reduction on the metastable zone width, and the reductions are pronounced when the impurity concentration increased. Further, experimental data of metastable zone width were analyzed using the expression of the Nývlt’s approach and self-consistent Nývlt-like approach, which can be expressed in the form: ln(ΔTmax/ T0) = Φ + β ln b, with intercept Φ = {(1 − m)/m}ln(ΔHd/RTlim) + (1/m)ln( f/KT0) and slope β = 1/m. Here T0 and Tlim are the saturation and nucleation temperature, respectively. m is the apparent nucleation order, and K is a new nucleation constant related to the factor f defined as the number of stable nuclei per unit volume, ΔHd, the heat of dissolution and R the gas constant. Comparing to the former one, the latter approach provides a more satisfactory estimation for the metastable zone width at varying saturation temperature T0. The constant β for specific system reveals independence of the temperature, while the constant Φ increases with increasing saturation temperature. In addition, both constants are proportional to the impurity concentration. Crystal habits of final products are also influenced in the presence of impurities, but the crystal structures are barely changed.

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INTRODUCTION As an important purification and separation process, crystallization is widely used in biological, chemical, pharmaceutical, and environmental industries. Accurate solubility and metastable zone width data are required for the process design to obtain products with high purity and proper physical properties such as crystal morphology, size, and size distribution.1 The solubility of materials is one of the most fundamental physiochemical properties, which depends on their chemical composition and with temperature. Most solutes exhibit increasing solubility with increasing temperature, although the rate of the increase varies widely from compound to compound. Solubility is also affected by the pH, by the presence of additional species in the solution, and by the use of different solvents. Especially, small amounts of impurities involved in the solution usually result in significant change in solubility.2 Broul et al. indicated that the variation of solubility in the presence of impurities can be attributed to the electrostatic interactions between ions in the solution.3 Toward the crystallization process involving minerals, the organic acid has been found to bind to metal ions to form metal−organic complexes.4 Giordano and Kharaka suggested that the formation of such complexes enhance the solubility of mineral in aqueous solution.5 The determination of the metastable zone width is essential for the optimization of reasonable crystallization process and further design of the crystallizer. The product with desired quality can only be realized by controlling the supersaturation within the metastable region throughout the crystallization process.6−10 Many factors, such as initial solution concentration, impurities, cooling rate, selected solvent, working volume, and stirring rate, were shown to alter the values of metastable zone width.11−15 © 2012 American Chemical Society

Among them, the effects of impurity on the metastable zone width can be attributed to the change on nucleation and growth mechanism of the compound of interest and is therefore difficult to foresee.16−20 Various effects of impurities can be observed: the impurities where shown to enhance the metastable zone width of compounds while other impurities turned out to reduce the width of metastable zone of the same compounds. Effects of impurity concentration on the metastable zone width can also be observed: the metastable zone width either increases or decreases when adding more impurities in the crystallization system.21,22 The width of metastable zone is usually determined experimentally by varying the temperature of a saturated solution (T0) to a temperature Tlim in which the occurrence of nuclei is detected visually.16−18,23 As the presence of impurity can affect the values of T0, to determine the metastable zone width (ΔTmax = T0 − Tlim), the effect of impurity and its concentration on T0 need to be considered. However, there are only few papers relating metastable zone width with changes on T0 by the addition of various concentrations of impurities.17 ZnL2 is an important chemical used in food and pharmaceutical industries.24,25 The effect of racemic malic acid on the crystallization process of zinc lactate at a concentration of 0.0307 mol·kg−1 H2O has been investigated in our earlier work.20,26 This paper is part of an ongoing effort to investigate the influence of impurities including racemic malic acid, succinic acid, and citric acid, which are usually contained in the mother Received: April 19, 2012 Accepted: September 6, 2012 Published: September 27, 2012 2963

dx.doi.org/10.1021/je3006453 | J. Chem. Eng. Data 2012, 57, 2963−2970

Journal of Chemical & Engineering Data

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Self-Consistent Nývlt-like Approach. Recently, Sangwal proposed a self-consistent Nývlt-like approach based on the regular solution theory and Nývlt’s approach.13 Using the regular solution theory, one may write the relationship between the ratio of solution concentration clim and cmax corresponding to temperatures Tlim and T0, respectively, and maximum supercooling ΔTmax in the form

liquid, on the solubility and width of metastable zone of ZnL2. Two theoretical approaches, the Nývlt’s equation and selfconsistent Nývlt-like equation, were used to analyze the metastable zone width data obtained experimentally. A HEL PolyBLOCK system equipped with turbidity meter was used to measure the width of metastable zone of ZnL2 in aqueous solution.

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THEORETICAL BACKGROUND Nývlt’s approach and the self-consistent Nývlt-like approach were employed to analyze the experimental metastable zone width data presented in this work. Nývlt’s Approach. Nývlt’s equation relating the maximum temperature difference ΔTmax (ΔTmax = T0 − Tlim, T0 and Tlim denote saturation and nucleation temperatures, respectively) with the cooling rate b is frequently used for the study of nucleation kinetics by the polythermal method. Following Nývlt27 upon nucleation, the maximum achievable supercooling, ΔTmax, and the corresponding cooling rate, b = ΔT/Δt (here ΔT is the linear decrease in temperature after time Δt), is given as ln ΔTmax =

1 − m ⎛ dc ⎞ 1 1 ln⎜ ⎟ − ln K + ln b ⎝ dT ⎠T m m m

⎛ c ⎞ ⎛ ΔHd ΔTmax ⎞ ln Smax = ln⎜ max ⎟ = ⎜ ⎟ ⎝ c lim ⎠ ⎝ RTlim T0 ⎠

(2)

where Smax is the supersaturation ratio when spontaneous nucleation sets in, ΔHd the heat of dissolution, and R the gas constant. With λ=

u=

ΔHd RT0

(3)

ΔTmax T0

(4)

Equation 2 may be rewritten in the form

(1)

where c is the mole fraction solubility and b is the cooling rate. Equation 1 predicts a linear dependence of ln ΔTmax on ln b, which enables us to calculate the nucleation order m and nucleation constant K because (dc/dT)|T can be determined from the solubility data. Nývlt’s equation is particularly useful for the product and process design in industrial crystallization. Unfortunately, the two parameters have complicated units, and their physical significance still remains obscure.

ln Smax =

λu 1−u

(5)

Assumes that the nucleation rate J is given by a power-law relation J = K (ln Smax )m

(6)

where m is the apparent nucleation order, and K is the new nucleation constant related to the number of stable nuclei forming per unit volume per unit time. On substituting the value of ln S from eq 5 in eq 6 ⎛ λu ⎞ m ⎟ J = K⎜ ⎝1 − u ⎠

(7)

Since the nucleation rate J is proportional to the rate of change of solution supersaturation Δc/cmax with time t, eq 7 can be rewritten as J=f Figure 1. Schematic diagram of experimental apparatus for measurements of solubility: (1) thermostat; (2) magnetic stirrer; (3) doublejacketed vessel; (4) thermometer; (5) pH meter.

⎛ λ ⎞⎛ b ⎞ Δc Δc ΔT ⎟⎜ =f = f⎜ ⎟ ⎝ 1 − u ⎠⎝ Tlim ⎠ cmax Δt cmax ΔT Δt

(8)

where the proportionality constant f has units as a number of entities per unit volume. From eqs 7 and 8, one gets

Figure 2. Experiment equipment (HEL PolyBLOCK): 1, oil bath; 2, charge pump; 3, thermostatic bath; 4, poly block; 5, PC. 2964


Journal of Chemical & Engineering Data ⎛ f ⎞1/ m⎛ λ ⎞(1 − m)/ m 1/ m ⎟ u=⎜ b ⎟ ⎜ ⎝ KT0 ⎠ ⎝ 1 − u ⎠

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Metastable Zone Width Measurement. The determination of metastable zone width was performed in a HEL PolyBLOCK reactor shown in Figure 2, which offers independent control and logging of all parameters such as turbidity, stirring rate, and temperature, and so forth. To measure the width of metastable zone, a certain mass of pure and impure ZnL2 solution was heated to a temperature higher than that of solubility to ensure complete dissolution of the solid and then cooled at a fixed constant rate from (5 to 20) °C·h−1, until the occurrence of nucleation. The nucleation point can be determined easily by the variation of turbidity signal; the corresponding nucleation

(9)

which, upon taking logarithm on both sides and rearrangement, gives ln u = ϕ + β ln b

(10)

where ϕ=

β=

1 − m ⎛⎜ λ ⎞⎟ 1 ⎛ f ⎞ ln + ln⎜ ⎟ ⎝1 − u ⎠ m m ⎝ KT0 ⎠

(11)

1 m

(12)

Equation 10 can be used to predict linear dependence of ln u on ln b. This linear dependence enables to calculate the values of nucleation order m from the slope and the term ln( f/KT0) from the intercept because ΔHd/RTlim can be calculated from solubility data of the investigated compound. The factor f may be calculated independently from the equilibrium solute concentration at temperature T0, while the value of K depends on the supersaturation range where eq 6 holds.

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EXPERIMENTAL SECTION Materials. Racemic zinc lactate was obtained from the recrystallization of the commercial product. The purity is above 99.5 %. Other chemicals used for the experiments were supplied by Shanghai Lingfeng Chemical Reagent Co. and Sinopharm Chemical Reagent Co, respectively, with purity higher than 99 %. Double-distilled water was used in all experiments. Solubility Measurements. The measurement of solubility was performed in a double-jacketed vessel through which a temperature controlled liquid was circulated, and the process temperature was measured by a probe with an accuracy of ± 0.05 K. Mixing was provided by a magnetic stirrer rotating at 300 rpm. The apparatus is shown in Figure 1. To measure the solubility, excess ZnL2 and fixed amounts of impurity were suspended in aqueous solution at a certain temperature under stirring for 4 h. Then, the solution was maintained for 2 h to allow the fine crystals to deposit completely. To determine the solubility, three samples of 10 mL each were carefully extracted from the upper solution and complexometrically titrated with ethylenediaminetetraacetic acid (EDTA) disodium to measure the concentration of zinc in solution.28

Figure 4. Effects of impurities on the solubility of ZnL2 at various concentrations. (a) Malic acid, (b) succinic acid, (c) citric acid.

Figure 3. Graphical example of time versus turbidity and temperature. 2965



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Table 1. Solubility of ZnL2 in the Presence of Different Impuritiesa,b cimp

T

solubility

cimp

T

solubility

cimp

T

solubility

malic acid

0.0153

citric acid

0.0119

31.6 35 40.8 51 63.6 33 42.5 52.2 59.4 66.7 32 40.5 50 58 65

0.091 0.094 0.1 0.127 0.174 0.0817 0.101 0.124 0.149 0.183 0.091 0.103 0.125 0.154 0.184

0.0307

0.0112

0.083 0.088 0.095 0.116 0.163 0.078 0.096 0.12 0.14 0.17 0.082 0.095 0.115 0.145 0.172

0.0229

succinic acid

32 37 41.6 50.6 63.2 32.4 41.8 52 59.2 64.5 32.2 40.6 49 58.5 64.8

35 42 50.8 61.2 64.2 33 41.5 52 59.4 65.4 32.4 41.8 49.1 58.6 67

0.1 0.109 0.132 0.174 0.185 0.088 0.108 0.135 0.159 0.191 0.097 0.113 0.133 0.165 0.203

impurity

a

0.0174

0.0214

0.0348

0.0277

Solubility and cimp in mol·kg−1 H2O; T in °C. bThe uncertainty is estimated to be ± 0.002 mol·kg−1 H2O.

temperature was then recorded. To ensure the measurement accuracy, three cycles for each system were carried out. The solution volume and stirring rate for experiments mentioned above are 100 mL and 300 rpm, respectively. A graphical example of time versus turbidity and temperature measured using HEL PolyBLOCK reactor is shown in Figure 3.

Table 2. Changes of the Metastable Zone Width of Pure ZnL2 with Initial Concentration at Different Cooling Ratesa,b ΔTmax

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RESULTS AND DISCUSSION Solubility of ZnL2 in the Presence of Impurities. Solubility data of pure and impure ZnL2 in aqueous solution are summarized in Figure 4 and Table 1. It can be noticed that the presence of all examined impurities increases the solubility of ZnL2, and the values of solubility data increase with increasing impurity concentration. Besides, all of the solubility curves determined experimentally are approximately parallel to each other. Similar results can also be found in many published papers.20,21,29 The variation of solubility can be attributed to changes on molecular interactions caused by the introduction of impurities. To the zinc lactate system, the presence of organic acid alters the pH of the solution; however, the variation of solubility caused by the pH is far lower than the measured solubility. For example, considering the effect of pH, the calculated solubility of zinc lactate in the presence of 0.0307 mol·kg−1 H2O at 35 °C was 0.081 mol·kg−1 H2O, while the measured solubility was 0.1 mol·kg−1 H2O. Given this situation, Giordano and Shock and Korestsky suggested that the formation constant of Znorganic complex is the key factor to determine the solubility variation.30,31 This can be proven by the fact that the measured solubility of zinc lactate in the presence of three different organic acid increases as: citric acid > malic acid > succinic acid. It is consistent with the order of different Zn-organic complex formation constants.32 Metastable Zone Width in ZnL2 Solution. The width of metastable zone of pure zinc lactate has been measured at different cooling rates b and saturation temperatures T0 to determine the nucleation kinetics for a crystallizer design. From Table 2, it can be noticed that the width of metastable zone of pure ZnL2 varies from (8 to 19.9) °C and exhibits a tendency of increasing with and increase on initial concentration and cooling rate. Moreover, it needs to be mentioned that, under the same cooling rate, the maximum difference on metastable zone width at varying initial solution concentrations was higher than 3 °C.

c

b=5

b = 7.5

b = 10

b = 12.5

b = 15

b = 20

0.196 0.134 0.104 0.0833

9.8 9.2 8.6 8

12.4 11.4 10.4 9.4

14.3 13.3 12.3 11.3

16 15 14 12.9

17.2 16.2 15.2 14.2

19.9 18.9 17.9 16.5

a c in mol·kg−1 H2O; T0 in °C; ΔTmax in °C; b in °C·h−1. bThe uncertainty is estimated to be ± 0.2 °C.

Effects of impurities on the metastable zone width of ZnL2 have also been investigated at an initial ZnL2 concentration of 0.196 mol·kg−1 H2O; the results are listed in Table 3. As Table 3. Changes of the Metastable Zone Width of ZnL2 with Impurity Concentration at an Initial ZnL2 Concentration of 0.196 mol·kg−1 H2Oa,b ΔTmax impurity malic acid

succinic acid

citric acid

cimp

T0

0.0153 0.0229 0.0307 0.0112 0.0174 0.0348 0.0119 0.0214 0.0277

70.3 69.5 67.8 70 69.4 67.8 69.3 66.7 65.4

b = 7.5

10.7

10.7

b = 10

b = 12.5

b = 15

13.8 13.2 12.2 12.8 12.4 11.9 13.1 11 11.5

15.6 15 14 14.4 14 13.5 14.7 12.8 13.1

17 16.4 15.5 16.3 15.9 15.4 16.6 14.6 15.1

a cimp in mol·kg−1 H2O; T0 in °C; ΔTmax in °C; b in °C·h−1. bThe uncertainty is estimated to be ± 0.2 °C.

mentioned above, all examined impurities lead to an increase in the solubility of zinc lactate. Therefore, the authors took into account the change in the solubility of zinc lactate in the calculation of MSZW in the presence of these impurities. Compared to the MSZW of pure zinc lactate shown in Table 3, the presence of all examined impurities reduces the width of metastable zone of ZnL2, and the reduction of MSZW varies from (0.2 to 2.8) °C. These effects also exhibit a tendency of 2966



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nucleation kinetics of pure ZnL2. The dependence of ln(ΔTmax) versus ln b for Nývlt’s theory according to eq 1 is shown in Figure 5a, and Figure 5b presents the plot of ln(ΔTmax/T0) against lnb based on eq 10. The estimated nucleation parameters shown in both approaches are presented in Table 4 and Figure 6.

increasing with an increase on impurity concentration, and the maximum difference caused by the variation of impurity concentration was 1.6 °C. Moreover, it can be noticed that, with respect to zinc lactate system, citric acid has the largest effect on the MSZW which is consistent with the effects on solubility. It is well-known that, to a specific compound, the solubility increases with a decrease in the solid−liquid interfacial energy γ.14,33 The decrease in γ consequently results in the easier occurrence of nucleation; namely, the MSZW becomes narrower. A possible mechanism can be explained by the adsorption of impurities on the nuclei that promotes the formation of nuclei and consequently narrows the metastable zone width. Kubota et al. suggested that these effects depend on the coverage fraction of impurity on the surface of solute nuclei, which is associated with the impurity concentration.34 The reduction on metastable zone width consequently causes the control of crystallization process to be difficult. As discussed above, the uncontrolled crystallization process in turn affects the downstream processing and handling, e.g. Given this situation, determination of accurate metastable zone width data is crucial for the crystallization operation. Estimated Nucleation Kinetics of Pure ZnL2. Two approaches mentioned above have been employed to estimate

Table 4. Values of Best-Fit Nucleation Parameters for Pure ZnL2 Using Different Theoretical Approaches Nývlt

self-consistent

T0/°C

m

K

β

(-)Φ

71.2 59 49.1 39.5

1.98 2.07 2.11 2.01

8.89 15.7 23.9 38.1

0.51 0.51 0.52 0.53

2.78 2.69 2.61 2.48

Figure 6. Plots of K and Φ on 1/T0.

One can find that the values of m and β for a specific system, within the experimental errors, are independent of the saturation temperature, which is consistent with the fact that the plots of ln(ΔTmax) against ln b for different systems are parallel to each other.13,14 The value of β(1/m) is about 0.5, which gives m = 2. The relatively low value of m = 2 suggests that nuclei in the bulk are formed by an instantaneous nucleation mechanism.33 This value of m also suggests the occurrence of three-dimensional heterogeneous nucleation and/or secondary

Figure 5. (a) Dependence of ln(ΔTmax) versus ln b for various saturation temperatures using Nývlt’s theory according to eq 7. (b) The plot of ln(ΔTmax/T0) against ln b for various saturation temperatures using a self-consistent Nývlt-like approach based on eq 10.

Figure 7. Metastable zone width for pure ZnL2 aqueous solution at a cooling rate of 10 °C·h−1. 2967



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nucleation in the solution volume. These results are coincident with the abrupt change of solution turbidity during the cooling process as shown in Figure 3. The values of K and Φ depend linearly on 1/T0. As the physical significance of constant K is complex, no simple explanation can be obtained. To the value of Φ, Sangwal suggested a linear dependence on 1/T0 following an Arrheniustype equation.31

Further, the calculated nucleation parameters were used to predict the width of metastable zone for pure ZnL2 solution at a constant cooling rate of 10 °C·h−1, and the results are shown in Figure 7. Compared to the experimental data, it can be clearly

Figure 9. Plots of β and Φ against cimp for different impurities contained in ZnL2 aqueous solution.

Figure 8. Plot of ln(ΔTmax/T0) against ln b for ZnL2 aqueous solution (0.1956 mol·kg−1 H2O) containing different concentrations of impurities. (a) Malic acid; (b) succinic acid; (c) citric acid.

Figure 10. Comparison of XRD spectra in the presence of different impurities. 2968



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Figure 11. SEM images of zinc lactate crystals in presence of different impurities: (a) pure zinc lactate; (b) in the presence of citric acid; (c) in the presence of malic acid; (d) in the presence of succinic acid.

Figure 11 shows the habit of the zinc lactate crystals crystallized in and without the presence of impurities. It can be found that the zinc lactate crystals in the presence of impurities exhibit differently comparing with the crystal habit of pure zinc lactate. This can be explained by the selectively adsorption of impurities on the specific crystal face and then depresses the growth of corresponding crystal face under the combined effects of thermodynamic and kinetic aspects.

observed that the Nývlt-like approach provides a more reliable estimation of metastable zone width. Sangwal attributed this reason to be the replacement of the term ln(dc/dT) by ln(ΔHd/ RTlim) in the Nývlt-like approach that excludes the effect of T0 on dc/dT.13 The Nývlt-like approach was then utilized to estimate the metastable zone width of impure ZnL2. Estimated Nucleation Kinetics of Impure ZnL2. Figure 8 plots ln(ΔTmax/T0) on ln b for impure ZnL2 solution. In all cases, the ln(ΔTmax/T0) depends linearly on ln b. The calculated values of constants Φ and β for different impurities are presented in Figure 9. It can be noticed that the constant β depends linearly on the impurity concentration cimp, while Φ exhibits an opposite trend. In addition, the variation rates of constants Φ and β for different impurities increase as: citric acid > malic acid > succinic acid, which is consistent with the order of effects of different organic acids on the solubility of ZnL2. With respect to these results, Sangwal suggests, among others, that the solubility of a solute plays a key role in determining the values of nucleation order m (1/β); the lower the solubility of a solute in a given solvent, the higher is the value of m. As to values of Φ, it is associated with the ability of the adsorption of impurity on the critically sized stable nuclei.35 Effects of Impurities on the Crystal Habit. The final products obtained by cooling crystallization mentioned above are analyzed by X-ray diffraction (XRD) and scanning electron microscopy (SEM) to investigate the influence of impurities on the crystal habit. The results of XRD spectra are compared in Figure 10. It can be noticed that, for the four samples, the positions of the main peaks, which reflect the symmetry and size of unit cell, are almost the same, indicating the negligible influence of impurities on the cell parameters. However, the peak relative intensities are substantially different, which is an indication of the difference in the orientation of alignment of the unit cell.

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CONCLUSION In this study, the solubility and metastable zone width of pure and impure ZnL2 have been determined. The results show that the presence of all examined impurities increases the solubility of ZnL2 and the values of solubility are increased when more impurities were added in the solution. The introduction of impurities also leads to the reduction on metastable zone width, and the reductions are pronounced when the impurity concentration increased. To analyze the experimental data of pure ZnL2, Nývlt’s approach and the self-consistent Nývlt-like equation were employed. The latter one was found to provide a more satisfactory estimation for the dependence of ΔTmax/T0 on the saturation temperature T0, and the constant β for a specific system reveals independence of the temperature, while the constant Φ depends linearly on the saturation temperature. Further, the latter approach was extended to investigate the influence of impurity on the width of metastable zone of ZnL2. The results show that the values of constants β are proportional to the concentration cimp of different impurities, while Φ exhibits an opposite trend. Concerning the crystal habit, crystals grown in impure media appear to be different, while the change of crystal structure by different impurities mentioned in our work is negligible. 2969



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AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-21-64253509. Fax: +86-21-64253528. E-mail address: [email protected]. Funding

We thank the NSFC (20476026), 111 Project (B08021), and Open Project of Skloche (08C08) for financial support. Notes

The authors declare no competing financial interest.

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REFERENCES

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Effects of Different Organic Acids on Solubility and Metastable Zone

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