Effect of Impurities on the Solubility, Metastable Zone Width, and

Article pubs.acs.org/IECR

Effect of Impurities on the Solubility, Metastable Zone Width, and Nucleation Kinetics of Borax Decahydrate Jiaoyu Peng,† Yaping Dong,*,† Liping Wang,†,‡ LiLi Li,†,‡ Wu Li,† and Haitao Feng† †

Engineering and Technology Research Center of Comprehensive Utilization of Salt Lake Resources, Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, 810008, Xining, China ‡ University of Chinese Academy of Sciences, 100039, Beijing, China ABSTRACT: The solubility and nucleation of borax decahydrate in the presence of Cl− and SO42− ions have been studied by two different methods: polythermal crystallization and isothermal crystallization. The results revealed that both anions had a saltin effect on the solubility. A noticeable widening of the metastable zone was observed after the addition of the two anion impurities. For the isothermal crystallization, two different nucleation mechanisms were obtained. When the supersaturation ratio S > 1.3, the nucleation appears to be homogeneous, whereas at the supersaturation ratio S < 1.25, heterogeneous nucleation predominates. From the prolonged induction period in the presence of the two anions, we conclude that the nucleation of borax decahydrate was suppressed after the addition of impurities. The values of the interfacial energy γ calculated by isothermal method are lower than those obtained by polythermal method due to the underestimated values of ln S.

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of borax decahydrate have been studied in our previous papers.7,8 In our studies, the MZW of borax decahydrate increases with the increase of the lithium impurity concentrations. However, the effect of potassium impurities varied with the potassium chloride concentrations ranging from 1.84 to 11.19%. The MZW at low potassium chloride concentrations decreased rapidly, whereas at high impurity concentrations, it increased until reaching its maximum and then began to fall with further increasing impurity concentrations. These investigations about borax, however, have been limited primarily to those cations. Therefore, it was considered worthwhile to investigate the effect of anions on the MZW of borax decahydrate. In the present work, based on the above brine constitutions, we explore the influences of chloride and sulfate ions on the solubility, MZW, and nucleation kinetics of borax decahydrate using laser-intensity technology.

INTRODUCTION On Qinghai-Tibet Plateau, China, most of the salt lakes contain abundant boron and lithium mineral resources.1 A typical example of a boron-containing lake is the Da Qaidam salt lake, which is located in the Qaidam Basin. The brine of this salt lake mainly contains chlorides, sulfates, and borates of magnesium, potassium, and lithium and belongs to borate salt lake of MgSO4 subtype according to Valiashko’s classification of salt lakes.2 Gao and Li3 investigated the chemical behavior of the borate during brine evaporation. The results indicated that the Mg borate in this brine, in general, does not crystallize out but accumulates in the highly concentrated brine, in the form of comprehensive statistics as tetraborate. Meanwhile, Gao et al.4 also studied the kinetics of the dissolution and crystallization process of magnesium borate in concentrated brine and found that borate has a high metastability because of the complexity of its polyborate ions in the solution. Therefore, this high boronbearing concentrated brine can be used for the production of boric acid and borax. Borax is one of the most important commercial boron compounds and has several industrial applications. It can be used as an agent that modifies the structure of glass, as a detergent and purifying agent, as a herbicide or as boron fertilizers to promote plant growth, and as an important ingredient in the manufacture of enamel and ceramics.5 During the manufacture of borax, the mineral resources coexisting in salt lakes, such as lithium, potassium, calcium, magnesium, sulfate, and chloride, can change the equilibrium saturation concentration, and nucleation and growth mechanisms of the main compound. They work as impurities and affect the metastable zone region of borax. The influence of magnesium and calcium impurities on the metastable zone width (MZW) of borax decahydrate has been studied by Gürbüz and Ozdemir.6 Their results showed that both cations retard the nucleation and broaden the MZW, especially for magnesium when its concentration is up to 200 ppm. The effects of potassium and lithium impurites on the crystallization © 2014 American Chemical Society

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THEORETICAL APPROACHES OF THE MZW The MZW for a substance depends on a variety of factors such as the saturation temperature, impurities, seeds, solution stirring, and cooling rate. The theoretical interpretation of the dependence of MZW on various factors using the traditional Nývlt’s equation9 has been reviewed by Nývlt et al.10 Nývlt’s equation involves two parameters (the “apparent nucleation order”, m, and the “mass nucleation rate constant”, k), which have no physical significance. However, Nývlt’s equation has been extensively used in the past for the analysis of experimental data in nucleation kinetics.6,11−14 Recently, Sangwal advanced two approaches for explaining the dependence of the MZW on various factors.15,16 The first one refers to the novel equation based on the classical three-dimensional nucleation theory,15 and the second approach is called the self-consistent Nývlt-like equation based on the Received: Revised: Accepted: Published: 12170

November 29, 2013 June 9, 2014 July 3, 2014 July 3, 2014 dx.doi.org/10.1021/ie404048m | Ind. Eng. Chem. Res. 2014, 53, 12170−12178

Industrial & Engineering Chemistry Research

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power-law relationship between the nucleation rate J and the maximum supersaturation, Smax.16 Classical Three-Dimensional Nucleation Theory Approach (3D CNT).15 Based on the classical 3D nucleation theory, Sangwal proposed another approach for the calculation of MZW. The rate of formation of the stable 3D spherical nuclei at supersaturation ln Smax may be given by17,18 ⎡ ⎤ B ⎥ J = A exp⎢ − ⎣ (ln Smax )2 ⎦

Equation 8 predicts a linear dependence of ln(ΔTmax/T0) on ln R. The term ΔHs/RGTlim and the constant f can be calculated from the solubility of the investigated compound; the values of nucleation order m and the nucleation constant K can be obtained from the slope β and the intercept Φ, respectively.

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EXPERIMENTAL SECTION Materials and Apparatuses. Borax decahydrate (purity of >99.5%), supplied from Tianjin Yongda Chemical Reagent Co., Ltd. China, was recrystallized from aqueous solution. Anhydrous lithium chloride (purity of >99%) and lithium sulfate (purity of >99%), provided from J&K Scientific Co., Ltd., were used without further purification. Water (resistivity 18.25 MΩ·cm) was deionized from a water purification system (UPT-II-20T, Chengdu Ultrapure Technology Co., Ltd.) before the experiments. The experimental setup used in this study has been described in our previous report.7 Polythermal Solubility and MZW Determination. The experiments were performed in a 100 mL triple-jacketed glass crystallizer containing approximately 80 g mixtures of Na2B4O7− LiCl/Li2SO4−H2O. The mixtures were heated above the saturation temperature, then they were filtered using a membrane filter (Millipore 0.22 μm pore size), and the filtrate was placed into the glass vessel. The cooling and heating cycles of aqueous borax decahydrate were performed repeatedly at known rates of 15, 25, 35, 45, and 55 K·h−1 while observing the dissolution temperature Tdis and nucleation temperature Tlim. The constant stirring rate was 200 rpm. The temperature in the reactor is controlled by manipulating a programmable thermostatic bath with an accuracy of ±0.1 K. At the beginning of each crystallization cycle, the temperature was raised to 10 K above the dissolution temperature and held constant for 15 min to ensure that all of the nuclei were fully dissolved. The saturation temperature T0, which is defined as the temperature of dissolution at an infinitely slow rate, can be obtained by the yintercept of the plot Tdis against the heating rate.19 For each cooling/heating cycle, a set of at least two experiments was performed to verify the reproducibility of the process. The difference between the saturation temperature and the temperature at the point of nucleation is considered as the MZW(ΔTmax), which can be given as ΔTmax = T0 − Tlim. Isothermal Nucleation and Induction Period Measurements. For induction period measurements, a saturated solution of borax decahydrate with an amount of lithium chloride or lithium sulfate was prepared at 303.15 K. The solution was heated to a temperature 10 K higher than the saturated temperature and then held for 15 min. Then, the solution was cooled to the desired temperature Tc with a cooling rate of 45 K· h−1, and held constant at that temperature until the point of nucleation. The corresponding time from the point at which the desired temperature Tc was reached to the onset of nucleation observed by the laser technology was recorded as the induction period τ. The supersaturation ratios S used were 1.15, 1.20, 1.25, 1.30, 1.40, and 1.50. Additionally, at least two experiments were performed to ensure the reproducibility of the induction period τ. The units of the solute concentration applied to calculate the supersaturation ratio S is grams per 100 grams of water. It is usually assumed20,21 that the induction period τ for the formation of 3D nuclei is inversely proportional to the nucleation rate J, i.e.

(1)

with 3 16π ⎛ γ Ω2/3 ⎞ ⎟ ⎜ B= 3 ⎝ kBTlim ⎠

(2)

where A is a kinetic constant (number of nuclei·m−3 s−1), γ is the interface energy, Ω is the molecular volume (m3), and kB is the Boltzmann constant (J·K−1). T0 is the saturation temperature, and Tlim is the temperature at which the first crystals are detected in the solution at a constant cooling rate. Using the same set of equations as above, Sangwal derived a new linear relationship between (T0/ΔTmax)2 and ln R: (T0/ΔTmax )2 = F + F1 ln R

(3)

where F = F1(X + ln T0)

F1 =

1 ⎛ ΔHs ⎞ ⎟ ⎜ B ⎝ R GTlim ⎠

⎛ AR T ⎞ X = ln⎜ G lim ⎟ ⎝ f ΔHs ⎠

(4)

(5)

(6)

ΔHs is the heat of dissolution, RG is the ideal gas constant, and f is a constant expressed in number of nuclei·m−3. Equation 3 predicts the values of γ and A from the slope F1 and the intercept F, respectively. Self-Consistent Nývlt-Like Equation.16 Sangwal simplified the complicated units of the nucleation constant k in Nývlt’s equation, by expressing the nucleation rate J using the following power-law relationship: J = K (ln Smax )m

(7)

where m is the apparent nucleation order and K is a new nucleation constant (number of nuclei·m−3 s−1). Using the theory of regular solutions to express ln Smax, and assuming that the nucleation rate J is dependent on the solution supersaturation and cooling rate, Sangwal obtained a linear relationship between the dimensionless maximum supercooling ratio ΔTmax/T0 and the cooling rate R: ln(ΔTmax /T0) = Φ + β ln R

(8)

where Φ = Φ′ − β ln T0

(9)

with β = 1/m, and Φ′ =

1 − m ⎛ ΔHs ⎞ 1 ⎛f⎞ ln⎜ ln⎜ ⎟ ⎟+ m m ⎝K⎠ ⎝ R GTlim ⎠

J = K ′/τ

(10) 12171

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kg−1, and that of SO42− ions was 0.141 mol·kg−1. As seen from Figure 1, the peaks of the solids overlapped those of pure borax decahydrate. The crystallographic parameters of borax decahydrate in the presence of Cl− ion are C2/c, Z = 4, a = 11.875 Å, b = 10.578 Å, c = 12.282 Å, β = 106.365°, α = 90°, and γ = 90°, and in the presence of SO42− ions are C2/c, Z = 4, a = 11.850 Å, b = 10.601 Å, c = 12.283 Å, β = 106.493°, α = 90°, and γ = 90°, which are in close agreement with the reported values.22,23 Additionally, we have also obtained the same conclusions as above about borax decahydrate XRD patterns with the other concentrations of Cl− and SO42− ions used in our text. Solubility and Polythermal Crystallization. One of the important effects of impurities is through the changes they introduce in the solubility of the parent salt and how they affect the metastable zone. Thus, it is of paramount importance to know the correct solubility of borax decahydrate in the presence of impurities. The obtained experimental solubility data are demonstrated graphically in Figure 2. The estimated solubility uncertainty (in Figure 2) is approximately ±(0.05−0.24) g/100 g of water. It is found that both ions have salt-in effects on the solubility of borax decahydrate. The solubility increases with increasing concentrations of impurities. Comparing the two anions’ influence on the solubility at any concentration (see Figure 3), the behavior of the SO42− anion is more obvious than that of the Cl− anion. Note also that the solubility in the presence of the SO42− anion with concentrations of 0.035 and 0.071 mol· kg−1 is similar to that of the Cl− anion with concentrations of 0.141 and 0.278 mol·kg−1, respectively, which reveals that, for the same solubility data of borax decahydrate, the concentration of Cl− ions is at least 4 times higher than that of the SO42− anions. The phenomenon above can be mainly explained by the differing ionic strength between the lithium chloride solution and the lithium sulfate solution. The negative charge of the sulfate is twice that of the chloride. When the two anions have the same molality, according to the formula of the solution ionic strength (I = (1/2)∑B mBzB2), mB is the concentration of a particular type of ion in moles and zB is the valency of the ion. The ionic strength of the lithium sulfate solution is 3 times that of the lithium chloride solution.18,24 Additionally, the presence of impurities can alter the solution structure;18 in the anionic coordination polygon of the sulfate group (SO42−), the S−O terminals regarded as proton acceptors can form strong hydrogen bonds with the proton donors of O−H terminals of polyborate anions compared to the bond strength for the Cl− anion. This intermolecular interaction strongly affects the solubility of the solute. Last, the SO42− anion with a larger ionic volume would also inhibit the diffusion of the solute from solution to the solid state, in which the strong solute−solute interactions lead to molecular self-assembly. This may also generate a higher solute concentration in the solution and thus increase the solubility of borax decahydrate. The dependence of the borax decahydrate solubility (mole fraction) on the temperature from 283.15 to 333.15 K is displayed in Figure 4. The value of ΔHs/RG calculated from the slope of the plot of ln c versus 1/T and the corresponding regression coefficients (RC) are given in Table 1. From the values of ΔHs/RG and RC in Table 1, the experimental data are more well fitted to the published data25 than to another report’s data,26 except for several measurement errors. Because the temperature range studied in our experiment is from 293 to 307 K, we choose the value of ΔHs/RG = 4252 K as a constant when calculating the nucleation kinetics below.

Therefore, combining eqs 1 and 11, the relationship between τ and S can be given as

ln τ = q + B(ln S)−2

(12)

with

⎛ K′ ⎞ q = ln⎜ ⎟ ⎝A⎠

(13)

where K′ is a proportionality constant, As seen from eq 12, there is a linear relationship between ln τ and 1/(ln S)2 at a fixed saturation temperature. The slope B (see eq 2) of this straight line gives values of the interfacial energy γ calculated by

γ=

3

3R G 3T 3B 16π Ω2NA 3

(14) −1

where NA is Avogadro’s number (mol ). Eq 11 can also be expressed by J J′ = = τ −1 (15) K′ According to eq 15, the nucleation rate J′ can be obtained from the induction period τ. Solid-State Characterization. The product crystals that crystallized out of the solution were characterized using X-ray powder diffraction (XRD) with a tube voltage and current of 40 kV and 30 mA, respectively. The scanning range 2θ was from 5.0014 to 69.9754°. The crystal morphologies were observed by low vacuum scanning electron microscopy (SEM).

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RESULTS AND DISCUSSION XRD Analysis. Powder X-ray diffraction (XRD) was used to confirm the identity of the solid material. Figure 1 a shows the

Figure 1. Powder XRD pattern of borax decahydrate crystallized from various systems: (a) pure system;18 (b) impure system with 0.278 mol· kg−1 Cl− ions; (c) impure system with 0.140 mol·kg−1 SO42− ions.

pure borax decahydrate pattern obtained from the Powder Diffraction File (PDF) card (reference code 01-075-1078) by Levy and Lisensky22 using neutron diffraction data. Figure 1b and Figure 1c show the crystal patterns growing from aqueous borax decahydrate solutions in the presence of Cl− and SO42−ions, respectively. The concentration of Cl− ions used was 0.278 mol· 12172

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Figure 2. Solubility of borax decahydrate as a function of the temperature and impurities. (a) Cl− ion: (□) 0.0, (★) 0.029, (◆) 0.070, (▼) 0.141, and (■) 0.278 mol·kg−1. (b) SO42− ion: (□) 0.0, (★) 0.015, (◆) 0.035, (▲) 0.071, and (●) 0.140 mol·kg−1.

Figure 4. Solubility dependence of borax decahydrate on temperature. (△) Experimental data, (□) literature data,20 and (■) literature data.21

Figure 3. Solubility comparison of borax decahydrate in the presence of chloride and sulfate anions. Cl− ion: (×) 0.0, (▲) 0.070, (◆) 0.141, and (●) 0.278 mol·kg−1. SO42− ion: (△) 0.035, (◇) 0.071, and (○) 0.140 mol·kg−1.

Table 1. Best-Fit Values of the Constants Obtained from the Plots of ln c versus 1/T

Examination of the polythermal nucleation data of borax decahydrate in the presence of Cl− and SO42− ions is given in Tables 2 and 3, respectively. The estimated MZW uncertainty in our experiment is approximately ±(0.11−0.48) °C. This reveals that the MZW strongly depends on the saturation temperatures as well as the cooling rates. The MZW increases with the rise of the cooling rates, whereas it decreases as the saturation temperature increases. This shows that nucleation is easier to achieve at a higher saturation temperature due to the higher solution concentration supplying more fresh material for nucleation. The dependence of MZW on the cooling rates also suggests that crystallization is closely related to the nucleation kinetics. From Tables 2 and 3, one can observe that both ions have increased the MZW values of borax decahydrate and that the MZW increases with the rise in the impurity concentration. The widening of MZW in the presence of additives is associated with the nucleation kinetics in the solutions. However, the saturation temperature and cooling rate have more pronounced effects than the additives.

data

ΔHs/RG (K)

RC

lit.25 data lit.26 data exptl data

4488 4639 4252

0.9936 0.9879 0.9973

Figures 5a, 6a, and 7a present the data of Tables 2 and 3 as plots of ln(ΔTmax/T0) versus ln R according to eq 8, and Figures 5b, 6b, and 7b show the same data as plots of (T0/ΔTmax)2 versus ln R according to eq 3. It can be seen that the plots of Figures 5−7 for individual values of T0 follow linear dependences with best-fit regression coefficients (RCs) ranging from 0.97 to 0.99. Values of the parameters (m, K, A, γ) calculated from Figures 5−7 are given in Tables 4 and 5, respectively. From Tables 4 and 5 the following features may be noted: 1. The nucleation order m of borax decahydrate in an aqueous solution is approximately 3.3 despite several measurement errors, which is in good agreement with the literature values of 3.386 and 3.30 ± 0.3.17 The addition of both anions has no noticeable influence on the nucleation order. 12173



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2. In the investigated range of temperature, the value of the interfacial energy γ for borax decahydrate lies between 2.0 and 2.5 and decreases with an increased saturation temperature T0, while it increases with increasing concentration of impurities. 3. The value of K increases with an increase in the saturation temperature T0, but the value of A remains fairly constant. The reason follows that, according to eq 7, the nucleation rate J at various temperatures is associated with three factors: the constant K, the nucleation order m, and the maximum supersaturation Smax. When Smax and m remain constant, the nucleation rate J is proportional to the constant K and it increases with increasing saturation temperature T0. Therefore, the constant K is proportional to the saturation temperature T0. Isothermal Crystallization: Nucleation Mechanism. Figure 8a shows the dependency of the induction period τ on the saturation temperature T0 and the supersaturation ratio S. It was found that the induction period τ for borax decahydrate decreases with increased supersaturation ratio S and saturation temperature T0. The reason is that the higher solution supersaturation causes an increase in the undercooling ΔT (defined as ΔT = T0 − Tc) during isothermal crystallization. The nucleation rate J, which is inversely proportional to the induction period τ (see eq 11), can increase and then shorten the induction period τ. In Figure 8b, it is obvious that the additives have increased the induction period τ. The influence of SO42− ions on the induction period τ is greater than that of Cl− ions, further supporting the conclusion made in the polythermal experiment. The relationships between the induction period τ and the supersaturation S in the presence of two impurities are shown in Figure 9. Obviously, the relationships for each system are made of two straight lines with different slopes, which suggests that nucleation mechanisms were produced in the crystallization

Table 2. Effect of Chloride Ions on the Metastable Zone Width of Borax Decahydrate ΔTmax (K) c(Cl−) (mol·kg−1)

R (K·h−1)

293.89 K

298.78 K

303.78 K

307.78 K

pure

15 25 35 45 55 15 25 35 45 55 15 25 35 45 55 15 25 35 45 55 15 25 35 45 55

9.34 10.59 11.54 12.54 13.14 9.16 10.41 11.41 12.26 12.96 9.14 10.34 11.44 12.54 13.24 9.38 10.58 11.53 12.43 13.33 9.45 11.05 12.15 12.95 13.55

8.18 9.43 11.33 10.53 12.03 8.29 9.69 10.59 11.24 11.94 8.44 9.64 10.59 11.44 12.14 8.50 9.85 10.75 11.45 12.25 8.91 10.16 10.96 11.76 12.46

7.28 8.38 9.28 10.03 10.63 7.31 8.36 9.26 10.16 10.66 7.49 8.54 9.44 10.44 10.84 7.58 8.73 9.63 10.43 10.93 7.74 9.04 9.94 10.64 11.14

6.68 7.83 8.33 9.03 9.48 6.76 4.66 8.21 8.76 9.31 6.83 7.73 8.33 8.78 9.33 6.95 7.75 8.35 8.85 9.45 7.07 8.07 8.62 9.12 9.57

0.029

0.070

0.141

0.278

Table 3. Effect of Sulfate Ions on the Metastable Zone Width of Borax Decahydrate ΔTmax (K) c(SO42−) (mol·kg−1)

R (K·h−1)

295.35 K

298.78 K

301.44 K

304.11 K

307.78 K

pure

15 25 35 45 55 15 25 35 45 55 15 25 35 45 55 15 25 35 45 55 15 25 35 45 55

8.60 10.00 11.00 12.00 12.50 8.60 9.90 11.00 11.90 12.40 8.99 10.44 11.44 12.04 12.74 9.04 10.49 11.44 12.19 12.84 9.24 10.54 11.49 12.54 13.14

8.18 9.43 10.53 11.33 12.03 8.25 9.45 10.40 11.45 12.05 8.37 9.62 10.62 11.62 12.12 8.49 9.94 10.79 11.64 12.24 8.67 10.12 11.12 11.72 12.47

7.74 9.04 9.84 10.59 11.29 7.69 8.99 9.89 10.59 11.24 7.93 9.39 10.18 11.09 11.48 8.09 9.39 10.29 11.09 11.79 8.25 9.60 10.40 11.30 11.90

7.11 8.36 9.06 9.86 10.36 7.04 8.29 9.04 9.64 10.34 7.41 8.61 9.46 10.16 10.66 7.69 8.84 9.79 10.54 11.04 8.02 9.17 10.07 10.87 11.47

6.68 7.93 8.33 9.03 9.48 6.80 7.65 8.45 8.95 9.45 6.84 7.64 8.44 9.04 9.54 7.03 7.93 8.63 9.33 9.78 7.41 8.31 8.96 9.66 10.26

0.015

0.035

0.071

0.140

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Figure 5. Plots of (a, left) ln(ΔTmax/T0) versus ln R and (b, right) (T0/ΔTmax)2 versus ln R at various saturation temperatures according to eqs 8 and 3: (□) 293.89, (■) 295.35, (○) 298.78, (●) 301.44, (★) 303.78, and (☆) 304.11 K.

Figure 6. Plots of (a, left) ln(ΔTmax/T0) versus ln R and (b, right) (T0/ΔTmax)2 versus ln R at various saturation temperatures in the presence of Cl− ion impurities. For 0.278 mol·kg−1 Cl− ion: (■) 293.89, (●) 298.78, (▲) 303.78, and (▼) 307.78 K. For 0.140 mol·kg−1 Cl− ion: (□) 293.89, (○) 298.78, (△) 303.78, and (▽) 307.78 K.

Figure 7. Plots of (a, left) ln(ΔTmax/T0) versus ln R and (b, right) (T0/ΔTmax)2 versus ln R at various saturation temperatures in the presence of SO42− ion impurities. For 0.140 mol·kg−1 SO42− ion: (□) 295.35, (△) 298.78, (○) 301.44, (▽) 304.11, and (☆) 307.78 K. For 0.071 mol·kg−1 SO42− ion: (■) 295.35, (▲) 298.78, (●) 301.44, (▼) 304.11, and (★) 307.78 K.

process. 21,27 At lower supersaturation (S < 1.25), the heterogeneous/second nucleation may be the predominant mechanism, whereas at higher supersaturation (S > 1.3)

homogeneous nucleation is the most important phenomenon regardless of the impurities added. In the homogeneous nucleation region, the dependency of the interfacial energy γ, 12175



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Table 4. Calculated m and K for Borax Decahydrate in Both Pure and Impure Systems K (×1028 m−3·h−1)

m − a

c(Cl )

a

T0 (K)

pure

0.140

0.278

293.89 295.35 298.78 301.44 303.78 304.11 307.78

3.62 3.35 3.23 3.38 3.31 3.36 3.67

3.60

3.44

3.49

3.77

3.39

3.43

4.18

c(Cl−)

c(SO42−)

4.24

0.071

0.140

3.59 3.44 3.35

3.50 3.50 3.43

3.44 3.79

3.49 3.91

c(SO42−)

pure

0.140

0.278

3.05 3.29 3.81 5.41 6.58 7.37 13.7

3.28

2.68

4.53

4.96

6.75

6.40

25.5

23.8

0.071

0.140

3.46 4.09 4.74

3.14 3.96 4.77

6.39 14.3

5.94 13.6

c in mol·kg−1.

Table 5. Calculated A and γ for Borax Decahydrate in Both Pure and Impure Systems A (×1028 m−3·h−1)

γ (mJ·m−2)

− a

c(Cl )

a

c(SO4 )

T0 (K)

pure

0.140

0.278

293.89 295.35 298.78 301.44 303.78 304.11 307.78

2.62 1.82 2.05 2.14 2.05 2.06 2.33

2.52

2.22

2.22

2.59

2.04

2.04

3.01

−

2−

2.99

0.071

c(SO42−)

c(Cl ) 0.140

2.43 2.20 2.09

2.39 2.26 2.17

2.13 2.51

2.21 2.69

pure

0.140

0.278

2.54 2.33 2.25 2.19 2.08 2.06 2.00

2.47

2.46

2.28

2.39

2.09

2.12

2.05

2.09

0.071

0.140

2.45 2.31 2.22

2.46 2.36 2.26

2.15 2.06

2.22 2.14

c in mol·kg−1.

Figure 8. Induction period versus supersaturation ratio with various temperatures and impurity concentrations. (a) Temperature: (▲) 25, (■) 30, and (●) 35 °C. (b) Chloride ion: (+) 0.0, (◇) 0.124, and (○) 0.245 mol·kg−1. Sulfate ion: (◆) 0.066 and (●) 0.128 mol·kg−1.

calculated from the slope B of the straight lines, on the impurity concentration is shown in Table 6. The results show that the interfacial energy γ increases with rising impurity concentrations and that the influence of SO42− ion is more noticeable than that of the Cl− anion. Moreover, the values of γ in Table 6 are lower than those obtained by Sangwal’s 3D CNT approach at the saturation temperature of approximately 303.15 K (see Table 5) by the polythermal method. This feature can be associated with the underestimated values of ln S, which were calculated using the values of the solute concentration c rather than the activity a. The chemical potential difference Δμ for crystallization is given by18,28

Δμ = R GTc ln(a0 /ac) = R GTc ln S = R GTc[ln(c 0 /cc) + ln(f0 /fc )]

(16)

where a0 and ac are the activities of the solution at T0 and Tc, respectively. f 0 and fc are the corresponding activity coefficients, and Δμ = (ΔHs/T0)ΔT

(17)

In our calculations of ln S for Figure 9, we used values of the concentrations c0 and cc alone, which are lower than the real values obtained from the activities a of the solution. This is because, in reality, the ratio f 0/fc > 1 for aqueous solutions of fairly soluble electrolytes. Therefore, it is more realistic to 12176



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Figure 9. Logarithms of induction period versus 1/(ln S)2 at 30 °C for various impurity concentrations. (a) Chloride ion: (■) 0.0, (★) 0.124, and (▼) 0.245 mol·kg−1. (b) Sulfate ion: (■) 0.0, (▲) 0.066, and (●) 0.128 mol·kg−1.

Table 6. Interfacial Energy γ Estimated by Experiment for Various Impurity Concentrations system pure Cl− SO42−

concn (mol·kg−1)

B

γ (mJ·m−2)

0.141 0.278 0.071 0.140

0.149 0.162 0.166 0.166 0.180

1.69 1.74 1.76 1.76 1.81

increases with an increase in the surpersaturation ratio S and a decrease in the impurity concentration. The results indicate that the nucleation of borax decahydrate from aqueous solutions in the presence of Cl− and SO42− ions is suppressed.This was consistent with the conclusion above obtained from the polythermal experiment, stating that both ions increase the MZW of the borax−water system. Effect of Impurities on the Crystal Morphologies. Figure 11 shows SEM images of the product obtained from both pure and impure solutions at a saturation temperature of 30 °C. As seen in Figure 10, there is a broad size distribution and some aggregation at each experiment. This is because the fast cooling rates (45 K·h−1) used in the experiments lead to rapid nucleation and growth and then generate the agglomerated particles. The surface crack may be due to the dehydration of the crystals during the drying process. Note that the SO42− ion causes serious aggregation during borax decahydrate crystallization.

describe the chemical potential difference Δμ in terms of the undercooling ΔT than the supersaturation ln S. Note that the ln S and ΔT in the isothermal method are the ln Smax and ΔTmax in the polythermal method. Therefore, the interfacial tension γ values calculated using ln S in the isothermal method are lower than the values obtained from ΔTmax (MZW) by the polythermal method. The strong dependence of the nucleation rate J′, defined as J/ K′, on the supersaturation ratio S, especially for S > 1.3, is shown in Figure 10. It is clearly shown that the nucleation rate J′

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CONCLUSIONS The solubility and MZW of borax decahydrate solutions in the presence of the two anions Cl− and SO42− have been determined by polythermal crystallization, and the induction period was measured by isothermal crystallization. For the former method, two approaches (Nývlt-like equation and 3D CNT) were used to calculate the nucleation kinetics (m, K, A, γ). The nucleation order m of the borax−water system is approximately 3.3, which is consistent with the value in a previous study. Both anions had no apparent effect on the nucleation order m. The interfacial energy γ increases with an increase in the impurity concentration. The value of K increases with the increase in the saturation temperature T0, but A remains constant over the temperature range considered. For the latter method, a longer induction period was obtained after the addition of the two anions. The induction period decreases with the increase of the supersaturation ratio S. For S < 1.25, it is possible that heterogeneous nucleation predominates. For S > 1.3, homogeneous nucleation appears to occur. The values of the interfacial energy γ calculated by the isothermal method are lower than the values obtained from the polythermal method due to the underestimated values of ln S calculated from the solute concentration c instead of the activity a.

Figure 10. Nucleation rate J′ (proportional to the reciprocal of the induction period) plotted versus the supersaturation ratio S. (■) 0.0; (□) 0.124 mol·kg−1 Cl−; (▽) 0.245 mol·kg−1 Cl−; (●) 0.066 mol·kg−1 SO42−; (◆) 0.128 mol·kg−1 SO42−. 12177



Article

Figure 11. SEM images of borax decahydrate crystallized from an aqueous solution. (a) Pure system, (b) containing 0.278 mol·kg−1 Cl− ion, and (c) containing 0.141 mol·kg−1 SO42− ion (N = 300 rpm, Tsat = 30 °C, 48 °C·h−1).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 86-971-6302023. Fax: 86-971-6310402. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is financially supported in part by the National Natural Science Foundation of China (No. 41273032) and the Geological Survey Projects (No. 1212010011809).

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Effect of Impurities on the Solubility, Metastable Zone Width, and

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