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Solubility and metastable zone width of aqueous sodium dichromate dihydrate solutions in the presence of sodium chromate additive
Journal of Crystal Growth 454 (2016) 105–110
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Solubility and metastable zone width of aqueous sodium dichromate dihydrate solutions in the presence of sodium chromate additive Liping Wang a,b,c, Haitao Feng a,c, Yaping Dong a,c,n, Jiaoyu Peng a,b,c, Wu Li a a
Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, 810008 Xining, China University of Chinese Academy of Sciences, 100049 Beijing, China c Key Lab of Comprehensive and Highly Efficient Utilization of Salt Lake Resource, Chinese Academy of Science, 810008 Xining, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 29 March 2016 Received in revised form 29 August 2016 Accepted 5 September 2016 Communicated by Dr. T.F. Kuech Available online 5 September 2016
Solubility and metastable zone width (MSZW) of aqueous sodium dichromate solutions in different concentration of sodium chromate were studied experimentally by the polythermal method using a turbidity monitoring technique. The effects of cooling rate R, saturation temperature T0 of sodium dichromate and concentration ci of sodium chromate on the MSZW were studied. The results show that the MSZW widens with increasing cooling rate R but it narrows with increasing saturation temperature T0 of sodium dichromate and concentration ci of sodium chromate. The experimental data were analyzed by using an equation, based on the classical three-dimensional nucleation theory, relating MSZW with cooling rate R. & 2016 Published by Elsevier B.V.
Keywords: A1. Metastable zone width A1. Solubility A1. Nucleation kinetics A2. Crystallization A3. Sodium dichromate dihydrate
1. Introduction Crystallization as an important technique in chemical industry serves the dual purposes of separation and purification of the chemical products [1,2]. The primary goal of crystallization is obtain crystals with high purity, optimum particle size distribution and ideal morphology [3,4]. To achieve this goal, the operating conditions should be optimized and controlled within the metastable zone throughout the crystallization process [5,6]. Metastable zone, which represents the interval between solubility and supersolubility curves, is considered as the critical nucleation parameter in industrial crystallization [3,7]. As required for the design, control and optimization of the process of crystallization, various factors affecting the values of metastable zone width (MSZW) of numerous compounds have been investigated during the last four decades [8]. Moreover, the MSZW data and the relations between MSZW and parameters such as cooling rate R are used to understand the processes associated with nucleation mechanisms [6,9]. Recently, Sangwal's group has proposed the novel equation of three-dimensional nucleation theory to explain the nucleation mechanism and physical basis of MSZW of solute– solvent systems [10–12]. n Corresponding author at: Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, 810008 Xining, China. E-mail address: [email protected] (Y. Dong).
http://dx.doi.org/10.1016/j.jcrysgro.2016.09.011 0022-0248/& 2016 Published by Elsevier B.V.
During the last years, Wang and his coworkers have investigated the MSZW of sodium dichromate dihydrate from aqueous solutions and discussed the experimental data of the relationship of maximum supercooling ΔTmax on cooling rate R and saturation temperature T0 using the recently advanced approaches [13]. However, until now no study of impurities on the MSZW of sodium dichromate dihydrate has been carried out by the traditional polythermal method. In this paper, the MSZW of sodium dichromate dihydrate in different composition of sodium chromate solution has been determined by turbidity technology. The effects of cooling rate, saturation temperature, mass fraction of sodium chromate on the solubility and MSZW of sodium dichromate dihydrate have been investigated. The novel equation of three-dimensional nucleation theory was suggested to study the nucleation kinetics.
2. Experimental 2.1. Materials and apparatus Sodium dichromate dihydrate (Tianjin Paisen Technology Corporation) has been recrystallized twice from aqueous solution before using in experiments. Deionized water (Resistivity: more than 18.25 MΩ cm) was obtained from a water purification system (UPT – Ⅱ – 20T, Chengdu Ultrapure Technology Co., Ltd). The solubility and MSZW of sodium dichromate dihydrate were
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measured by a CrystalSCAN PolyBlock with four parallel reactors (E1061, United Kingdom He., Ltd). As each reactor has independent control systems, turbidity and temperature sensors, it can carry out the experiment independently and offers the measurement of MSZW for same or different samples simultaneously. The accuracy of the temperature sensor was 0.1 K. Precise temperature control was introduced along with refrigerated/heating circulators (FP50HL, Julabo Technology Co., Ltd). The products containing hydrates crystallized from sodium chromate solution were identified by X-ray diffractometer (X'Pert PRO, 2006 PANalytical). 2.2. Solubility and metastable zone width measurements The solubility and MSZW of sodium dichromate dihydrate were measured by polythermal method using turbidity monitoring technology. Certain mass of sodium chromate and sodium dichromate were weighed to the crystallizer. Then deionized water was weighed and transferred to the crystallizer to guarantee the total amount of mixture was 80 g. In the process of measurement, the stirring rate was fixed with 450 rpm. At first, the temperature was raised for about 10 K above the dissolution temperature and held constant for 15 min to ensure that all of the nuclei were fully dissolved. Then the solution was cooled with a settled cooling rate until crystallites appeared. Finally, the mixture was kept 10 K below the nucleation temperature for 15 min and then was heated at the same constant rate until all the crystallites appeared. Five different cooling/heating rates of 55, 45, 35, 25, 15 K h 1 were performed for all the measurements. The temperatures of disappearance and appearance of crystallites were recorded as Tdis and Tnuc, respectively. The saturation temperature T0, which is defined as the temperature of dissolution at an infinitely slow rate [5,14], can be obtained by extrapolating of the curve of dissolution temperature (Tdis) against the heating rate [15]. For each measurement, a set of at least two experiments was performed in parallel reactors to verify the reproducibility of the process and each data point represents a mean value of these measurements. The values of metastable zone width ΔTmax were calculated from the difference between the saturation temperature T0 and the nucleation temperature Tnuc, i.e. ΔTmax ¼T0 Tnuc.
Fig. 1. XRD patterns of crystallized product in the presence of sodium chromate additive of different concentrations: (a) no additive, (b) 2.66%, (c) 5.06%, (d) 7.91%, and (e) 10.05%.
3. Results and discussion 3.1. XRD analysis Powder X-ray diffraction (XRD) has been used to identify the crystal composition obtained by crystallization from the solution during the process of MSZW measurement. The pure sodium dichromate dihydrate pattern obtained from the PDF card (Reference code: 00–022–1366) has been showed in Fig. 1a. Fig. 1b–e shows XRD patterns of the solid phase crystallized from aqueous solutions containing 2.66, 5.06, 7.91 and 10.05 wt% of sodium chromate, respectively. From the positions of peaks of XRD patterns in Fig. 1, all solids crystallized from sodium chromate solutions in our experiment were identified as sodium dichromate dihydrate. 3.2. Solubility of sodium dichromate The dependence of solubility s (or c*) of sodium dichromate on temperature T0 in water containing different concentrations of sodium chromate is shown in Fig. 2. These results show that the solubility of sodium dichromate decreases significantly with the increasing sodium chromate concentration w and decreasing saturation temperature T0. Compared with the data in pure aqueous solution [13], sodium chromate has a great salt-out effect on the solubility of sodium dichromate.
Fig. 2. Solubility s (mass fraction) of sodium dichromate as a function of temperature T0 in the presence of different concentration of sodium chromate in water.
The above experimented solubility data of sodium dichromate in solutions containing different concentration of sodium chromate were analyzed using Van't Hoff equation:
ln c *=−
ΔHd ΔSd + R GT0 RG
(1)
where c* solubility, expressed in mole fraction, of sodium dichromate, ΔHd is the dissolution enthalpy, ΔSd is the dissolution entropy, RG is the gas constant, and T0 is the saturation temperature. The dependence of lnc* on T0 1 for sodium dichromate at different concentration of sodium chromate is shown in Fig. 3. The best-fit plots of the data are drawn with the values of ΔHd and ΔSd listed in Table 1. It may be seen from Table 1 that for all additive concentrations ΔHd 40, which proves the dissolution of sodium dichromate in water containing sodium chromate additive is an endothermic process. 3.3. MSZW of sodium dichromate dihydrate The metastable zone widths of sodium dichromate dihydrate at
L. Wang et al. / Journal of Crystal Growth 454 (2016) 105–110
107
Fig. 3. Van't Hoff plot of logarithm of solubility c* (mole fraction) of sodium dichromate against inverse of temperature T 0 in the presence of different concentration of sodium chromate in water. Table 1 The dissolution enthalpy and entropy values of sodium dichromate dihydrate in different concentration of sodium chromate solution. w (Na2CrO4) (%)
ΔHd (kJ mol 1)
ΔSd (J mol 1 K 1)
RC
2.66 5.06 7.91 10.05
7.54 7.04 7.84 9.06
8.45 5.96 7.92 11.30
0.9789 0.9810 0.9918 0.9652
five different cooling rates with various saturation temperatures in different additive concentration of sodium dichromate have been measured by polythermal method. The variations of ΔTmax with cooling rates R are presented in Fig. 4. From Fig. 4a–c, we may find that the MSZW of sodium dichromate increases with increasing cooling rate R for a given additive concentration of sodium dichromate whereas its value decreases with increasing saturation temperature T0 and additive concentration of sodium dichromate for a given cooling rate R.
3.4. Effect of saturation temperature and additive concentration on MSZW To explain the effects of different experimental parameters on nucleation, the classical 3D nucleation theory is often used. When the classical 3D nucleation theory holds, the relationship between nucleation rate J and the maximum supersaturation ratio Smax of the solution is given by [7,16] 2⎤ ⎡ J = A exp⎣ −B/( lnSmax ) ⎦
(2)
with the parameter 3 16π ⎛ γ Ω2/3 ⎞ ⎜⎜ ⎟⎟ B= 3 ⎝ kB Tnuc ⎠
Fig. 4. Examples of plots of ΔTmax as a function of cooling rate R for aqueous sodium dichromate solutions containing different concentrations of sodium chromate: (a) no additive, (b) 2.66%, and (c) 7.91%.
(3)
where A is a constant associated with the kinetics of formation of nuclei, kB is the Boltzmann constant (kB ¼RG/NA, NA is Avogadro's number), γ is the interfacial energy, which was strongly influenced by solute-solvent interactions, Ω is the molecular volume, and the factor 16π/3 refers to the formation of 3D spherical nuclei. Based on the classical 3D nucleation theory, Sangwal [10] gives a linear relationship between (T0/ΔTmax)2 and lnR in the form
2
( T0/ΔTmax)
)
= F − F1 ln R = F ( 1−Z ln R
(4)
where 2
F=
1 ⎛ ΔHd ⎞ ⎜ ⎟ ZB ⎝ R GTnuc ⎠
(5)
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F1 =
2 1 ⎛ ΔHd ⎞ ⎜ ⎟ B ⎝ R GTnuc ⎠
(6)
Z=
⎛ f ΔH ⎞ F1 d =ln⎜ ⎟ F ⎝ AT0 R GTnuc ⎠
(7)
In the above equations, f is the number of nuclei per unit volume and can be estimated from solute concentration in saturated solution, whereas all other symbols have been defined above. The values of enthalpy ΔHd of dissolution are obtained from the solubility data using Eq. (1). According to Eq. (3), plots of (T0/ΔTmax)2 on ln R for sodium dichromate dihydrate in different concentrations of sodium chromate solution were represented in Fig. 5. The plots of (T0/ΔTmax)2 against ln R show a linear dependence for the entire data of the analyzed systems. The best-fit values of F1 (intercept), F (slope) and the corresponding regression coefficients (RC) are given in Table 2. The value of Z was calculated by Eq. (7) and also shown in Table 2. It is found from Table 2 that the values of F, F1 and Z increase with the increasing saturation temperature T0 and additive concentrations of sodium chromate. It is noted from Eq. (5) that the value of F depends on Tnuc and Z. the value of Z given by Eq. (7) also contains Tnuc. As the MSZW was calculated by ΔTmax ¼T0 Tnuc, the effects of additive concentrations of sodium chromate on MSZW may be explained by the tendency of F and Z with additives. From Table 2 one also observes that the parameter Z increases with additive concentration. This is related to the effect of additive on solubility. There are several equations describing the
relationship between solubility of compounds and their interfacial energy γ. The higher the solubility of different compounds in given solvent, the lower are the values of Z [17,18]. Therefore, the dependence of Z on additive concentration of sodium chromate may be explained in terms of the effect of additive on solubility of sodium dichromate. As found earlier, the data of F as a function of saturation temperature T0 may be related by Arrhenius-type equation [10,12,19]:
F1/2 = F0e−Esat/ R GT0
(8)
rewritten in the form
ln(F1/2)=ln(F1/2)0 − Esat/R GT0
(9)
where Esat is the activation energy associated with the diffusion of solute in the solution. The values of Esat and ln(F1/2)0 can be obtained from the slope and the intercept of the straight line according to Eq. (9), respectively. Fig. 6 shows the dependence of ln (F1/2) against 1/T0 for sodium dichromate dihydrate in different concentrations of sodium chromate solution. It is noted that the linear dependence of ln (F1/2) on 1/T0 in different additive sodium chromate solutions were nearly parallel. Values of Esat, ln (F1/2)0 and the corresponding regression coefficients (RC) are given in Table 3. The values of Esat and ln (F1/ 2 )0 can be calculated by the slope and intercept of the straight line according to Eq. (9), respectively. It may be observed from Table 3 that the values of Esat and ln (F1/2)0 increase with the increasing additive concentrations of sodium chromate. As Eq. (9) is a consequence of diffusion of solute ions/molecules in solution, it is
Fig. 5. Plots of (T0/ΔTmax)2 against lnR at various saturation temperature T0 of sodium dichromate containing at different concentrations of sodium chromate additive: (a) 2.66%, (b) 5.06%, (c) 7.91%, and (d) 10.05%.
L. Wang et al. / Journal of Crystal Growth 454 (2016) 105–110
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Table 2 Values of F, F1 and Z for sodium dichromate dihydrate in sodium chromate solutions. w (Salt concentrations) (%) Na2CrO4
s (Solubility) (%) Na2Cr2O7 2H2O
2.66
71.31 73.62 74.22 75.12 76.92 69.55 70.57 71.77 72.77 74.18 68.36 69.03 70.37 71.15 73.06 66.55 67.82 69.58 70.96 72.38
5.06
7.91
10.05
T0/K
297.51 308.38 313.14 315.31 323.54 299.37 304.15 311.10 316.19 321.00 302.76 305.78 312.24 315.56 323.07 302.09 309.80 314.57 320.07 324.04
F
F1
Z
RC
3048.35 4357.13 5164.98 5686.16 6676.12 4373.17 5339.84 6006.27 8184.30 8967.42 5304.51 6154.93 7605.77 9223.59 10,545.02 7152.25 10,213.77 13,262.58 16,470.26 19,627.81
521.90 761.31 919.31 1002.65 1196.00 798.43 995.54 1095.59 1517.08 1658.90 962.40 1136.60 1403.19 1693.76 1954.63 1314.22 1957.66 2535.64 2995.95 3746.33
0.1712 0.1747 0.1780 0.1763 0.1791 0.1826 0.1864 0.1824 0.1854 0.1850 0.1814 0.1847 0.1845 0.1836 0.1854 0.1837 0.1917 0.1912 0.1819 0.1909
0.9949 0.9949 0.9731 0.9861 0.9872 0.9637 0.9444 0.9966 0.9939 0.9766 0.9960 0.9656 0.9820 0.9955 0.9913 0.9757 0.9448 0.9968 0.9944 0.9601
Table 3 Values of ln (F1/2)0 and Esat for sodium dichromate dihydrate in sodium chromate solutions. w (Na2CrO4) (%)
ln (F1/2)0
Esat (kJ mol 1)
RC
2.66 5.06 7.91 10.05
9.02 9.56 9.88 11.92
12.40 13.36 14.04 18.80
0.9862 0.9561 0.9665 0.9981
sodium dichromate on the additive concentration may be explained in terms of the effect of additive sodium chromate on solubility of sodium dichromate.
4. Conclusion Fig. 6. Plots of ln(F1/2) against 1/T0 for sodium dichromate dihydrate at various saturation temperature T0 of sodium dichromate containing at different concentrations of sodium chromate additive.
natural to expect the relationship between the Esat and the nature of diffusing ions/molecules. According to the hole theory of liquids, the value of the activation energy ED for self-diffusion in pure liquid electrolytes is a constant and can be related by Eq. [12]:
ED/R G=3. 7Tm
(10)
where Tm denotes the melting point of electrolyte. As the melting point of water was 373 K, a result of ED ¼8.4 kJ mol 1 can be obtained by Eq. (10). Generally, when the value of activation energy Esat was equal to that of ED, it shows an ideal behavior for the diffusing ions/molecules in solutions. As seen from Table 3, all the values of Esat are much higher than ED, implying that the diffusing ions/molecules of sodium dichromate dihydrate in sodium chromate solutions do not show ideal behavior. The high value of Esat of sodium dichromate dihydrate in sodium chromate solutions indeed suggests strong solute-solvent interactions, leading to the formation of large clusters. Table 3 also shows an obvious increase of Esat with the increasing additive concentrations of sodium chromate. As reported [17], the high solubility of solute suggests stronger solute-solvent interactions. The dependence of Esat of
The solubility and MSZW sodium dichromate dihydrate in different concentration of sodium chromate solution were determined by the polythermal method. It was found that the sodium chromate had a salt-out effect on the solubility of sodium dichromate. The MSZW of sodium dichromate dihydrate becomes wider with the increasing cooling rate, while the saturation temperature has an opposite effect. In order to analyze the nucleation kinetics of sodium dichromate dihydrate in various mass fraction of sodium chromate, the experimental data was analyzed by the novel equation of three-dimensional nucleation theory. The values of F, F1 and Z were obtained from Eqs. (3) and (7). The increased value of Z with additive concentration is intimately connected with the lower solubility of sodium dichromate in higher sodium chromate solutions. The values of Esat and ln (F1/2)0 were calculated by Eq. (9) from the dependence of ln (F1/2) against 1/T0 for sodium dichromate dihydrate in different concentrations of sodium chromate solution. The observation of Esat 4ED shows an unideal behavior for the diffusing ions/molecules and strong solute-solvent interactions in solutions. The increase value of Esat with the increasing additive concentrations of sodium chromate is a consequence of stronger solute-solvent interactions in a higher additive sodium chromate.
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Acknowledgments This work is financially supported in part by Science and Technology Plan Project of Qinghai Province, China (2014-ZJ-707), National Natural Science Foundation of China (Nos. 41273032 and 21501187).
References [1] X. Jiang, X. Ruan, W. Xiao, D. Lu, G. He, A novel membrane distillation response technology for nucleation detection, metastable zone width measurement and analysis, Chem. Eng. Sci. 134 (2015) 671–680. [2] J. Garside, Industry crystallization from solution, Chem. Eng. Sci. 40 (1985) 3–26. [3] A. Mersmann, Crystallization Technology Handbook, Marcel Dekker, New York, 2001. [4] S.S. Kadam, J.A.W. Vissers, M. Forgione, R.M. Geertman, P.J. Daudey, A. I. Stankiewicz, H.J.M. Kramer, Rapid crystallization process development strategy from lab to industrial scale with PAT tools in skid configuration, Org. Process Res. Dev. 16 (2012) 769–780. [5] J.W. Mullin, Crystallization, 4th ed., Butterworth-Heinemann, Oxford, 2001. [6] S.A. Kulkarni, S.S. Kadam, H. Meekes, A.I. Stankiewicz, J.H. ter Horst, Crystal nucleation kinetics from induction times and metastable zone widths, Cryst. Growth Des. 13 (2013) 2435–2440. [7] J. Nývlt, O. Soehnel, M. Matuchova, The Kinetics of Industrial Crystallization, Academia, Prague, 1985. [8] X. Zhang, Z. Yang, J. Chai, J. Xu, L. Zhang, G. Qian, X. Zhou, Nucleation kinetics of lovastatin in different solvents from metastable zone widths, Chem. Eng.
Sci. 133 (2015) 62–69. [9] D.M.C. Corzo, A. Borissova, R.B. Hammond, D. Kashchiev, K.J. Roberts, K. Lewtas, I. More, Nucleation mechanism and kinetics from the analysis of polythermal crystallisation data: methyl stearate from kerosene solutions, CrystEngComm 16 (2014) 974–991. [10] K. Sangwal, Novel approach to analyze metastable zone width determined by the polythermal method: physical interpretation of various parameters, Cryst. Growth Des. 9 (2009) 942–950. [11] K. Sangwal, K. Wojcik, Investigation of metastable zone width of ammonium oxalate aqueous solutions, Cryst. Res. Technol. 44 (2009) 363–372. [12] K. Sangwal, Some features of metastable zone width of various systems determined by polythermal method, CrystEngComm 13 (2011) 489–501. [13] L. Wang, H. Feng, J. Peng, N. Dong, W. Li, Y. Dong, Solubility, metastable zone width, and nucleation kinetics of sodium dichromate dihydrate, J. Chem. Eng. Data 60 (2015) 185–191. [14] J.Y. Peng, Y.P. Dong, Z. Nie, F.Z. Kong, Q.F. Meng, W. Li, Solubility and metastable zone width measurement of borax decahydrate in potassium chloride solution, J. Chem. Eng. Data 57 (2012) 890–895. [15] J. Peng, Y. Dong, L. Wang, L. Li, W. Li, H. Feng, Effect of impurities on the solubility, metastable zone width, and nucleation kinetics of borax decahydrate, Ind. Eng. Chem. Res. 53 (2014) 12170–12178. [16] D. Kashchiev, Nucleation: Basic Theory with Applications, Butterworth-Heinemann, Oxford, 2000. [17] K. Sangwal, K.W. Smith, On the metastable zone width of 1,3-dipalmitoyl-2oleoylglycerol, tripalmitoylglycerol, and their mixtures in acetone solution, Cryst. Growth Des. (2010). [18] K. Sangwal, Effect of impurities on the metastable zone width of solute–solvent systems, J. Cryst. Growth 311 (2009) 4050–4061. [19] K. Sangwal, A novel self-consistent Nyvlt-like equation for metastable zone width determined by the polythermal method, Cryst. Res. Technol. 44 (2009) 231–247.
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Solubility and metastable zone width of aqueous sodium dichromate dihydrate solutions in the presence of sodium chromate additive Liping Wang a,b,c, Haitao Feng a,c, Yaping Dong a,c,n, Jiaoyu Peng a,b,c, Wu Li a a
Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, 810008 Xining, China University of Chinese Academy of Sciences, 100049 Beijing, China c Key Lab of Comprehensive and Highly Efficient Utilization of Salt Lake Resource, Chinese Academy of Science, 810008 Xining, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 29 March 2016 Received in revised form 29 August 2016 Accepted 5 September 2016 Communicated by Dr. T.F. Kuech Available online 5 September 2016
Solubility and metastable zone width (MSZW) of aqueous sodium dichromate solutions in different concentration of sodium chromate were studied experimentally by the polythermal method using a turbidity monitoring technique. The effects of cooling rate R, saturation temperature T0 of sodium dichromate and concentration ci of sodium chromate on the MSZW were studied. The results show that the MSZW widens with increasing cooling rate R but it narrows with increasing saturation temperature T0 of sodium dichromate and concentration ci of sodium chromate. The experimental data were analyzed by using an equation, based on the classical three-dimensional nucleation theory, relating MSZW with cooling rate R. & 2016 Published by Elsevier B.V.
Keywords: A1. Metastable zone width A1. Solubility A1. Nucleation kinetics A2. Crystallization A3. Sodium dichromate dihydrate
1. Introduction Crystallization as an important technique in chemical industry serves the dual purposes of separation and purification of the chemical products [1,2]. The primary goal of crystallization is obtain crystals with high purity, optimum particle size distribution and ideal morphology [3,4]. To achieve this goal, the operating conditions should be optimized and controlled within the metastable zone throughout the crystallization process [5,6]. Metastable zone, which represents the interval between solubility and supersolubility curves, is considered as the critical nucleation parameter in industrial crystallization [3,7]. As required for the design, control and optimization of the process of crystallization, various factors affecting the values of metastable zone width (MSZW) of numerous compounds have been investigated during the last four decades [8]. Moreover, the MSZW data and the relations between MSZW and parameters such as cooling rate R are used to understand the processes associated with nucleation mechanisms [6,9]. Recently, Sangwal's group has proposed the novel equation of three-dimensional nucleation theory to explain the nucleation mechanism and physical basis of MSZW of solute– solvent systems [10–12]. n Corresponding author at: Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, 810008 Xining, China. E-mail address: [email protected] (Y. Dong).
http://dx.doi.org/10.1016/j.jcrysgro.2016.09.011 0022-0248/& 2016 Published by Elsevier B.V.
During the last years, Wang and his coworkers have investigated the MSZW of sodium dichromate dihydrate from aqueous solutions and discussed the experimental data of the relationship of maximum supercooling ΔTmax on cooling rate R and saturation temperature T0 using the recently advanced approaches [13]. However, until now no study of impurities on the MSZW of sodium dichromate dihydrate has been carried out by the traditional polythermal method. In this paper, the MSZW of sodium dichromate dihydrate in different composition of sodium chromate solution has been determined by turbidity technology. The effects of cooling rate, saturation temperature, mass fraction of sodium chromate on the solubility and MSZW of sodium dichromate dihydrate have been investigated. The novel equation of three-dimensional nucleation theory was suggested to study the nucleation kinetics.
2. Experimental 2.1. Materials and apparatus Sodium dichromate dihydrate (Tianjin Paisen Technology Corporation) has been recrystallized twice from aqueous solution before using in experiments. Deionized water (Resistivity: more than 18.25 MΩ cm) was obtained from a water purification system (UPT – Ⅱ – 20T, Chengdu Ultrapure Technology Co., Ltd). The solubility and MSZW of sodium dichromate dihydrate were
106
L. Wang et al. / Journal of Crystal Growth 454 (2016) 105–110
measured by a CrystalSCAN PolyBlock with four parallel reactors (E1061, United Kingdom He., Ltd). As each reactor has independent control systems, turbidity and temperature sensors, it can carry out the experiment independently and offers the measurement of MSZW for same or different samples simultaneously. The accuracy of the temperature sensor was 0.1 K. Precise temperature control was introduced along with refrigerated/heating circulators (FP50HL, Julabo Technology Co., Ltd). The products containing hydrates crystallized from sodium chromate solution were identified by X-ray diffractometer (X'Pert PRO, 2006 PANalytical). 2.2. Solubility and metastable zone width measurements The solubility and MSZW of sodium dichromate dihydrate were measured by polythermal method using turbidity monitoring technology. Certain mass of sodium chromate and sodium dichromate were weighed to the crystallizer. Then deionized water was weighed and transferred to the crystallizer to guarantee the total amount of mixture was 80 g. In the process of measurement, the stirring rate was fixed with 450 rpm. At first, the temperature was raised for about 10 K above the dissolution temperature and held constant for 15 min to ensure that all of the nuclei were fully dissolved. Then the solution was cooled with a settled cooling rate until crystallites appeared. Finally, the mixture was kept 10 K below the nucleation temperature for 15 min and then was heated at the same constant rate until all the crystallites appeared. Five different cooling/heating rates of 55, 45, 35, 25, 15 K h 1 were performed for all the measurements. The temperatures of disappearance and appearance of crystallites were recorded as Tdis and Tnuc, respectively. The saturation temperature T0, which is defined as the temperature of dissolution at an infinitely slow rate [5,14], can be obtained by extrapolating of the curve of dissolution temperature (Tdis) against the heating rate [15]. For each measurement, a set of at least two experiments was performed in parallel reactors to verify the reproducibility of the process and each data point represents a mean value of these measurements. The values of metastable zone width ΔTmax were calculated from the difference between the saturation temperature T0 and the nucleation temperature Tnuc, i.e. ΔTmax ¼T0 Tnuc.
Fig. 1. XRD patterns of crystallized product in the presence of sodium chromate additive of different concentrations: (a) no additive, (b) 2.66%, (c) 5.06%, (d) 7.91%, and (e) 10.05%.
3. Results and discussion 3.1. XRD analysis Powder X-ray diffraction (XRD) has been used to identify the crystal composition obtained by crystallization from the solution during the process of MSZW measurement. The pure sodium dichromate dihydrate pattern obtained from the PDF card (Reference code: 00–022–1366) has been showed in Fig. 1a. Fig. 1b–e shows XRD patterns of the solid phase crystallized from aqueous solutions containing 2.66, 5.06, 7.91 and 10.05 wt% of sodium chromate, respectively. From the positions of peaks of XRD patterns in Fig. 1, all solids crystallized from sodium chromate solutions in our experiment were identified as sodium dichromate dihydrate. 3.2. Solubility of sodium dichromate The dependence of solubility s (or c*) of sodium dichromate on temperature T0 in water containing different concentrations of sodium chromate is shown in Fig. 2. These results show that the solubility of sodium dichromate decreases significantly with the increasing sodium chromate concentration w and decreasing saturation temperature T0. Compared with the data in pure aqueous solution [13], sodium chromate has a great salt-out effect on the solubility of sodium dichromate.
Fig. 2. Solubility s (mass fraction) of sodium dichromate as a function of temperature T0 in the presence of different concentration of sodium chromate in water.
The above experimented solubility data of sodium dichromate in solutions containing different concentration of sodium chromate were analyzed using Van't Hoff equation:
ln c *=−
ΔHd ΔSd + R GT0 RG
(1)
where c* solubility, expressed in mole fraction, of sodium dichromate, ΔHd is the dissolution enthalpy, ΔSd is the dissolution entropy, RG is the gas constant, and T0 is the saturation temperature. The dependence of lnc* on T0 1 for sodium dichromate at different concentration of sodium chromate is shown in Fig. 3. The best-fit plots of the data are drawn with the values of ΔHd and ΔSd listed in Table 1. It may be seen from Table 1 that for all additive concentrations ΔHd 40, which proves the dissolution of sodium dichromate in water containing sodium chromate additive is an endothermic process. 3.3. MSZW of sodium dichromate dihydrate The metastable zone widths of sodium dichromate dihydrate at
L. Wang et al. / Journal of Crystal Growth 454 (2016) 105–110
107
Fig. 3. Van't Hoff plot of logarithm of solubility c* (mole fraction) of sodium dichromate against inverse of temperature T 0 in the presence of different concentration of sodium chromate in water. Table 1 The dissolution enthalpy and entropy values of sodium dichromate dihydrate in different concentration of sodium chromate solution. w (Na2CrO4) (%)
ΔHd (kJ mol 1)
ΔSd (J mol 1 K 1)
RC
2.66 5.06 7.91 10.05
7.54 7.04 7.84 9.06
8.45 5.96 7.92 11.30
0.9789 0.9810 0.9918 0.9652
five different cooling rates with various saturation temperatures in different additive concentration of sodium dichromate have been measured by polythermal method. The variations of ΔTmax with cooling rates R are presented in Fig. 4. From Fig. 4a–c, we may find that the MSZW of sodium dichromate increases with increasing cooling rate R for a given additive concentration of sodium dichromate whereas its value decreases with increasing saturation temperature T0 and additive concentration of sodium dichromate for a given cooling rate R.
3.4. Effect of saturation temperature and additive concentration on MSZW To explain the effects of different experimental parameters on nucleation, the classical 3D nucleation theory is often used. When the classical 3D nucleation theory holds, the relationship between nucleation rate J and the maximum supersaturation ratio Smax of the solution is given by [7,16] 2⎤ ⎡ J = A exp⎣ −B/( lnSmax ) ⎦
(2)
with the parameter 3 16π ⎛ γ Ω2/3 ⎞ ⎜⎜ ⎟⎟ B= 3 ⎝ kB Tnuc ⎠
Fig. 4. Examples of plots of ΔTmax as a function of cooling rate R for aqueous sodium dichromate solutions containing different concentrations of sodium chromate: (a) no additive, (b) 2.66%, and (c) 7.91%.
(3)
where A is a constant associated with the kinetics of formation of nuclei, kB is the Boltzmann constant (kB ¼RG/NA, NA is Avogadro's number), γ is the interfacial energy, which was strongly influenced by solute-solvent interactions, Ω is the molecular volume, and the factor 16π/3 refers to the formation of 3D spherical nuclei. Based on the classical 3D nucleation theory, Sangwal [10] gives a linear relationship between (T0/ΔTmax)2 and lnR in the form
2
( T0/ΔTmax)
)
= F − F1 ln R = F ( 1−Z ln R
(4)
where 2
F=
1 ⎛ ΔHd ⎞ ⎜ ⎟ ZB ⎝ R GTnuc ⎠
(5)
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L. Wang et al. / Journal of Crystal Growth 454 (2016) 105–110
F1 =
2 1 ⎛ ΔHd ⎞ ⎜ ⎟ B ⎝ R GTnuc ⎠
(6)
Z=
⎛ f ΔH ⎞ F1 d =ln⎜ ⎟ F ⎝ AT0 R GTnuc ⎠
(7)
In the above equations, f is the number of nuclei per unit volume and can be estimated from solute concentration in saturated solution, whereas all other symbols have been defined above. The values of enthalpy ΔHd of dissolution are obtained from the solubility data using Eq. (1). According to Eq. (3), plots of (T0/ΔTmax)2 on ln R for sodium dichromate dihydrate in different concentrations of sodium chromate solution were represented in Fig. 5. The plots of (T0/ΔTmax)2 against ln R show a linear dependence for the entire data of the analyzed systems. The best-fit values of F1 (intercept), F (slope) and the corresponding regression coefficients (RC) are given in Table 2. The value of Z was calculated by Eq. (7) and also shown in Table 2. It is found from Table 2 that the values of F, F1 and Z increase with the increasing saturation temperature T0 and additive concentrations of sodium chromate. It is noted from Eq. (5) that the value of F depends on Tnuc and Z. the value of Z given by Eq. (7) also contains Tnuc. As the MSZW was calculated by ΔTmax ¼T0 Tnuc, the effects of additive concentrations of sodium chromate on MSZW may be explained by the tendency of F and Z with additives. From Table 2 one also observes that the parameter Z increases with additive concentration. This is related to the effect of additive on solubility. There are several equations describing the
relationship between solubility of compounds and their interfacial energy γ. The higher the solubility of different compounds in given solvent, the lower are the values of Z [17,18]. Therefore, the dependence of Z on additive concentration of sodium chromate may be explained in terms of the effect of additive on solubility of sodium dichromate. As found earlier, the data of F as a function of saturation temperature T0 may be related by Arrhenius-type equation [10,12,19]:
F1/2 = F0e−Esat/ R GT0
(8)
rewritten in the form
ln(F1/2)=ln(F1/2)0 − Esat/R GT0
(9)
where Esat is the activation energy associated with the diffusion of solute in the solution. The values of Esat and ln(F1/2)0 can be obtained from the slope and the intercept of the straight line according to Eq. (9), respectively. Fig. 6 shows the dependence of ln (F1/2) against 1/T0 for sodium dichromate dihydrate in different concentrations of sodium chromate solution. It is noted that the linear dependence of ln (F1/2) on 1/T0 in different additive sodium chromate solutions were nearly parallel. Values of Esat, ln (F1/2)0 and the corresponding regression coefficients (RC) are given in Table 3. The values of Esat and ln (F1/ 2 )0 can be calculated by the slope and intercept of the straight line according to Eq. (9), respectively. It may be observed from Table 3 that the values of Esat and ln (F1/2)0 increase with the increasing additive concentrations of sodium chromate. As Eq. (9) is a consequence of diffusion of solute ions/molecules in solution, it is
Fig. 5. Plots of (T0/ΔTmax)2 against lnR at various saturation temperature T0 of sodium dichromate containing at different concentrations of sodium chromate additive: (a) 2.66%, (b) 5.06%, (c) 7.91%, and (d) 10.05%.
L. Wang et al. / Journal of Crystal Growth 454 (2016) 105–110
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Table 2 Values of F, F1 and Z for sodium dichromate dihydrate in sodium chromate solutions. w (Salt concentrations) (%) Na2CrO4
s (Solubility) (%) Na2Cr2O7 2H2O
2.66
71.31 73.62 74.22 75.12 76.92 69.55 70.57 71.77 72.77 74.18 68.36 69.03 70.37 71.15 73.06 66.55 67.82 69.58 70.96 72.38
5.06
7.91
10.05
T0/K
297.51 308.38 313.14 315.31 323.54 299.37 304.15 311.10 316.19 321.00 302.76 305.78 312.24 315.56 323.07 302.09 309.80 314.57 320.07 324.04
F
F1
Z
RC
3048.35 4357.13 5164.98 5686.16 6676.12 4373.17 5339.84 6006.27 8184.30 8967.42 5304.51 6154.93 7605.77 9223.59 10,545.02 7152.25 10,213.77 13,262.58 16,470.26 19,627.81
521.90 761.31 919.31 1002.65 1196.00 798.43 995.54 1095.59 1517.08 1658.90 962.40 1136.60 1403.19 1693.76 1954.63 1314.22 1957.66 2535.64 2995.95 3746.33
0.1712 0.1747 0.1780 0.1763 0.1791 0.1826 0.1864 0.1824 0.1854 0.1850 0.1814 0.1847 0.1845 0.1836 0.1854 0.1837 0.1917 0.1912 0.1819 0.1909
0.9949 0.9949 0.9731 0.9861 0.9872 0.9637 0.9444 0.9966 0.9939 0.9766 0.9960 0.9656 0.9820 0.9955 0.9913 0.9757 0.9448 0.9968 0.9944 0.9601
Table 3 Values of ln (F1/2)0 and Esat for sodium dichromate dihydrate in sodium chromate solutions. w (Na2CrO4) (%)
ln (F1/2)0
Esat (kJ mol 1)
RC
2.66 5.06 7.91 10.05
9.02 9.56 9.88 11.92
12.40 13.36 14.04 18.80
0.9862 0.9561 0.9665 0.9981
sodium dichromate on the additive concentration may be explained in terms of the effect of additive sodium chromate on solubility of sodium dichromate.
4. Conclusion Fig. 6. Plots of ln(F1/2) against 1/T0 for sodium dichromate dihydrate at various saturation temperature T0 of sodium dichromate containing at different concentrations of sodium chromate additive.
natural to expect the relationship between the Esat and the nature of diffusing ions/molecules. According to the hole theory of liquids, the value of the activation energy ED for self-diffusion in pure liquid electrolytes is a constant and can be related by Eq. [12]:
ED/R G=3. 7Tm
(10)
where Tm denotes the melting point of electrolyte. As the melting point of water was 373 K, a result of ED ¼8.4 kJ mol 1 can be obtained by Eq. (10). Generally, when the value of activation energy Esat was equal to that of ED, it shows an ideal behavior for the diffusing ions/molecules in solutions. As seen from Table 3, all the values of Esat are much higher than ED, implying that the diffusing ions/molecules of sodium dichromate dihydrate in sodium chromate solutions do not show ideal behavior. The high value of Esat of sodium dichromate dihydrate in sodium chromate solutions indeed suggests strong solute-solvent interactions, leading to the formation of large clusters. Table 3 also shows an obvious increase of Esat with the increasing additive concentrations of sodium chromate. As reported [17], the high solubility of solute suggests stronger solute-solvent interactions. The dependence of Esat of
The solubility and MSZW sodium dichromate dihydrate in different concentration of sodium chromate solution were determined by the polythermal method. It was found that the sodium chromate had a salt-out effect on the solubility of sodium dichromate. The MSZW of sodium dichromate dihydrate becomes wider with the increasing cooling rate, while the saturation temperature has an opposite effect. In order to analyze the nucleation kinetics of sodium dichromate dihydrate in various mass fraction of sodium chromate, the experimental data was analyzed by the novel equation of three-dimensional nucleation theory. The values of F, F1 and Z were obtained from Eqs. (3) and (7). The increased value of Z with additive concentration is intimately connected with the lower solubility of sodium dichromate in higher sodium chromate solutions. The values of Esat and ln (F1/2)0 were calculated by Eq. (9) from the dependence of ln (F1/2) against 1/T0 for sodium dichromate dihydrate in different concentrations of sodium chromate solution. The observation of Esat 4ED shows an unideal behavior for the diffusing ions/molecules and strong solute-solvent interactions in solutions. The increase value of Esat with the increasing additive concentrations of sodium chromate is a consequence of stronger solute-solvent interactions in a higher additive sodium chromate.
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Acknowledgments This work is financially supported in part by Science and Technology Plan Project of Qinghai Province, China (2014-ZJ-707), National Natural Science Foundation of China (Nos. 41273032 and 21501187).
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