Measurements and Correlations of the SolidâLiquid Equilibrium of

Article pubs.acs.org/jced

Measurements and Correlations of the Solid−Liquid Equilibrium of RbCl/CsCl + [Cnmim]Cl (n = 2, 4, 6, 8) + H2O Ternary Systems at T = (288.15, 298.15, and 308.15) K Jing Tang, Shu’ni Li,* Quanguo Zhai, Yucheng Jiang, and Mancheng Hu* Key Laboratory of Macromolecular Science of Shaanxi Province, School of Chemistry & Chemical Engineering, Shaanxi Normal University, Xi’an, Shaanxi 710062, P.R. China S Supporting Information *

ABSTRACT: The solubility, density and refractive index of RbCl/CsCl + [Cnmim]Cl (n = 2, 4, 6, 8) + H2O saturated systems have been studied at T = (288.15, 298.15 and 308.15) K. The solubility data were correlated by the nonrandom twoliquid (NRTL) model and an empirical equation. Both models can qualitatively represent the equilibrium behavior. In addition, the results denote that all the ionic liquids trigger salting-out effects with the order: [C2mim]Cl > [C4mim]Cl > [C6mim]Cl > [C8mim]Cl. The density and refractive index of the saturated solutions were determined for describing the relationship between the physical property and composition of the solution.

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INTRODUCTION Ionic liquids (ILs) are liquid salts near room temperature composed of ions. They are considered green and ideal substitutes for traditional volatile solvents because of their low melting point, negligible vapor pressures, and nonflammability. To explore the applications of ILs more effectively, the chemical and physical properties of ionic liquids-containing systems have received considerable attention recently. Brennecke et al.1−3 have done much work investigating the interactions between ILs and water or organic molecules in solutions of ionic liquid-based binary systems by experimental, modeling, and calculated methods. ILs containing aqueous biphasic systems (ABS) have been the subject of much focus after Rogers’s pioneering research on the systems of ionic liquids + inorganic salts + H2O.4−7 Among the numerous emerging ILs, imidazolium-based ionic liquids are one of the commonly studied ILs because of their stability to air and moisture, easy availability, and lower price. Coutinho and co-workers8−11 have researched the salting-out effects of imidazolium ionic liquids + sodium salt/potassium salts + H2O ternary systems, and show that the ILs possessing long alkyl side chains tend to form liquid−liquid solution. Peng et al.12 investigated the solubility of KCl or NaCl in 1-butyl-3methylimidazolium chloride ([C4mim]Cl) + water mixture in a temperature range of (298.15 to 343.15) K. There is a saltingout effect produced when adding [C4mim]Cl to the aqueous solution of NaCl/KCl. Hu et al.13 studied the solubility of ILs in aqueous solutions containing inorganic salt (NaCl, NaNO3, Na2CO3 Na2SO4, Na2PO4 and so on). They found that the inorganic anion with higher valence has a better salting-out effect than the one with lower valence. It should be pointed out that the ionic liquids and inorganic salts compete with each other for water molecules in the ionic liquid + salt + water mixed solution. Thus, the addition of ILs to the aqueous solution of inorganic salts may cause the salting-out © 2014 American Chemical Society

effect and can be employed in crystallization for producing supersaturation in a solution. In the past decade, our group has focused on the phase behavior of the ternary or quaternary systems consisting of the heavy alkaline metal (Rb, Cs) salts and organic solvent−water mixtures14,15 to evaluate the application of the salting-out effect in increasing the yield of expensive Rb and Cs salts. As a continuation of our series work, we reported herein the solubility, density, and refractive index of RbCl/CsCl + ILs + H2O ternary solutions. The ionic liquids involved were 1-ethyl-3methylimidazolium chloride ([C2mim]Cl), 1-butyl-3-methylimidazolium chloride ([C4mim]Cl), 1-hexyl-3-methylimidazolium chloride ([C6mim]Cl), and 1-octyl-3- methylimidazolium chloride ([C8mim]Cl). Furthermore, the experimental data have also been correlated by NRTL and empirical equations. To the best of our knowledge, the NRTL model is rarely introduced into the ion liquid solvent systems. Furthermore, the solid−liquid equilibrium data reported herein show that the addition of 1-alkyl-3methylimidazolium ion liquids can effectively improve the yield of CsCl or RbCl.

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EXPERIMENTAL SECTION

Chemicals. RbCl and CsCl (mass fraction 99.5 %, Shanghai China Lithium Industrial Co., Ltd.) were dried in vacuum at 400 K for 24 h before use. The analytical grade ionic liquids ([C2mim]Cl, [C4mim]Cl, [C6mim]Cl, and [C8mim]Cl) with the mass fraction purity more than 99 % were all purchased from Shanghai Chengjie Chemical Co., Ltd. The ILs were dried in vacuum at 333.15 K overnight and stored in a desiccator. All Received: September 4, 2013 Accepted: February 19, 2014 Published: March 4, 2014 726

dx.doi.org/10.1021/je4007986 | J. Chem. Eng. Data 2014, 59, 726−735

Journal of Chemical & Engineering Data

Article

Table 1. Values of Parameters of eqs 1 and 2 at 298.15 K a0

system

a1

a2

[C2mim]Cl [C4mim]Cl [C6mim]Cl [C8mim]Cl

1.33257 1.33247 1.33246 1.33250

0.09033 0.09283 0.09183 0.09433

[C2mim]Cl [C4mim]Cl [C6mim]Cl [C8mim]Cl

1.33253 1.33247 1.33256 1.33250

0.07967 0.07700 0.08183 0.08217

RbCl + [Cnmim]Cl + H2O 0.17290 0.17344 0.17430 0.17222 CsCl + [Cnmim]Cl + H2O 0.17042 0.17494 0.17491 0.1704

b0

b1

b2

0.99708 0.99681 0.99693 0.99714

0.75233 0.75450 0.74400 0.74630

0.12446 0.08700 0.05695 0.02221

0.99683 0.99690 0.99693 0.99714

0.78692 0.78233 0.78900 0.78667

0.12189 0.08050 0.05618 0.02665

Table 2. Solubilities, Density, and Refractive Index of RbCl/CsCl in Pure Water at T = (288.15, 298.15, 308.15) K both from the Literature and from This Study T/K

ws

288.15

0.4681 0.4647 0.4686 0.4659 0.4858 0.4827 0.4854 0.4854 0.4842

298.15

308.15

0.5035 0.4995 0.5047 0.5049 0.5009

ρ/(g/cm3)

nD

RbCl 1.48046

1.38745 1.38739

1.49652

1.38846

1.50084 1.50084

1.38851 1.38851

1.51755

1.38941

20 15 21 20 15 22 21

20 15 22 21

1.38937 1.38949

ρ/(g/cm3)

0.6481 0.6491 0.6430 0.6422 0.6551 0.6547 0.6547 0.6574 0.6564 0.6647 0.6679 0.6699 0.6678 0.6692 0.6707

1.89401 1.89340

1.41806 1.41806

1.92079 1.92428 1.92428

1.41973 1.41963 1.41963

1.94639 1.94635 1.94899

1.42053 1.42044 1.42093

nD

ref

15 21 23 15 22 23 21 24 15 22 21 23

liquid in dilute solution, respectively. First three groups of salt concentration (w = 0.0000, 0.0300, and 0.0600) must be prepared by directly weighing the materials. Afterward, the ionic liquid was arranged in a sequence to form an unsaturated standard solution; the density and refractive index of the unsaturated standard solution were measured at T = 298.15 K. The data for the calibration curves for the RbCl/CsCl + [Cnmim]Cl + H2O system at 298.15 K are given in Table S1 and S2 of the Supporting Information. Calibration plots of the refractive index and density versus the content of ILs of the ternary systems RbCl/CsCl + [Cnmim]Cl + H2O were prepared for different concentrations of the salts. For example, the calibration plots of RbCl + [C2mim]Cl + H2O system were given in the Supporting Information, Figure S1. The symbols a0, a1, a2, b0, b1, and b2 are parameters which can be obtained from the calibration curves and the values are listed in Table 1. The mass fractions of ionic liquid and salt in the saturated solutions can be determined and calculated using eqs 1 and 2 with the parameters listed in Table 1. It should be pointed out that eqs 1 and 2 were only applicable for solutions with ws ≤ 0.06 and wIL ≤ 0.12. Hence, the saturated solutions must be diluted to this mass fraction ranges before measuring the density and refractive index. All the measurements were performed in triplicate and the average values were considered for further study.

the chemicals were used without further purification, and double-distilled water was used in this work. Apparatus and Procedure. The apparatus used in this experiment have been described in detail previously.16 The samples were prepared by mixing a known mass ionic liquid and water with excess alkali metal salt, using an analytical balance (Mettler AL 204) with an accuracy of ± 0.1 mg. The prepared samples were stirred for 48 h and allowed to settle for 24 h at T = (288.15, 298.15 and 308.15) ± 0.01 K to achieve equilibrium. The saturated solutions were taken from the samples using syringes and analyzed. The density of the saturated solutions was measured by Anton Paar DM-4500 densimeter with a precision of 1·10−5 g·cm−3. The refractive indices measured using RXA170 (Anton Paar) with a precision of 4·10−5. The concentration of the salts RbCl or CsCl and ILs in the systems RbCl/CsCl + [Cnmim]Cl (n = 2, 4, 6, 8) + H2O can be determined from a calibration curve according to literature.17 There is a relationship between the composition and the physical properties (density, refractive index) within a certain concentration range. For dilute solution, the relationship between density, refractive and the mass fraction of the component in solutions was described by the empirical equation:18,19 nD = a0 + a1ws + a 2wIL (1) ρ = b0 + b1ws + b2wIL

ws

CsCl

1.48039

1.51758 1.51957

ref

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(2)

RESULTS AND DISCUSSION The experimental solubility, density, and refractive index for RbCl and CsCl in pure water and [Cnmim]Cl (n = 2, 4, 6, 8) + H2O

Where nD and ρ are refractive indices and density of the solution, ws and wIL are the mass fraction of the RbCl/CsCl and ionic 727



Article

at T = (288.15, 298.15 and 308.15) K were listed in Table 2 and Table 3. The literature15,20−24 values of RbCl and CsCl in pure water were also given in Table 2 for comparison. The max deviations of the mass fraction, density, and refractive indices were ± 0.0059, 0.00432 g·cm−3 and 0.0004, respectively, which show that the experimental data were well consistent with the literature results. The solubility diagrams for the RbCl + [Cnmim]Cl (n = 2, 4, 6, 8) + H2O ternary systems at 298.15 K were shown in Figure 1a together with the correlation results using the NRTL model. It can be seen that the solubility of RbCl in [Cnmim]Cl (n = 2, 4, 6, 8) + H2O decreased sharply with the increasing of ionic liquid concentration. That is, ionic liquid induced the salting-out effect. This may be attributed to that ionic liquids and inorganic salts compete with each other for water molecules. Furthermore, for a constant mass fraction of ionic liquid, the solubility of RbCl/CsCl in [Cnmim]Cl (n = 2, 4, 6, 8) + H2O mixtures follows the order [C2mim]Cl < [C4mim]Cl < [C6mim]Cl < [C8mim]Cl. It can be interpreted that increasing the number of carbon atoms in the alkyl chain of the cation of ionic liquids increases the hydrophobicity of the ionic liquid1 and thus weakens the interaction between water and the cation of ionic liquids.2 So, the salting-out effect follows the order: [C2mim]Cl > [C4mim]Cl > [C6mim]Cl > [C8mim]Cl. The CsCl + [Cnmim]Cl (n = 2, 4, 6, 8) + H2O ternary systems have a similar trend, which is shown in Figure S2 of the Supporting Information. Figure 1b shows a comparison of the effect of temperature on the solubility for the RbCl + [C8mim]Cl + H2O systems, which indicates little influence of the temperature on the solubility. For RbCl and CsCl in the same ionic liquid−water mixture at the fixed temperature, CsCl has higher solubility than RbCl (Figure 1c). The salting-out ratio R can be evaluated using the following equation: R = (S0 − S)/S0

RbCl + [C2mim]Cl + H2O. A cross point was observed for the systems at different temperatures for both density and refractive index curves. Before the cross point, the higher is the temperature, the larger the values of density and refractive index are. However, after that point, the order is reversed. The concentration of the salt and the temperature are used to account for this trend. Before the cross point, the concentration of the salt is the major factor, and after the cross point the temperature is the major factor. Correlated Results. The NRTL (nonrandom two-liquid) equation was the so-called local-composition models for the solution theory, which was proposed by Renon and Prausnitz.25 The NRTL model was satisfactorily used to correlate the liquid−liquid equilibrium system containing ionic liquids.26−28 For ternary systems, the application of the NRTL model for the ternary system was found to be successful in the published paper in this area. Marcilla and co-worker had correlated the experimental data for H2O + alcohol (ethanol, butanol, and pentanol) + NaCl,29 H2O + acetone + NaCl30 using the NRTL equation and the Gibbs energy of mixing function (gM = (ΔmixG)/RT). Therefore, in this work the NRTL model was used to correlate the experimental data for RbCl/CsCl + [Cnmim]Cl (n = 2, 4, 6, 8) + H2O systems. For the liquid−solid equilibrium data of mixture, the NRTL model with mole fractions for the Gibbs energy was written as29 M G liquid GM GM = solid + RT RT RT c μL μS =s + (1 − s) ∑ xiL i RT RT i=1

⎡ ⎛ Δh ΔCp ⎞⎛ Tf ⎞ ΔCp ⎛ Tf ⎞⎤ = s⎢ − ⎜ f − ln⎜ ⎟⎥ ⎟⎜ − 1⎟ − ⎠ ⎝ T ⎠⎥⎦ ⎢⎣ ⎝ RTf R ⎠⎝ T R

(3)

c

where S0 and S are the solubility of RbCl/CsCl in pure water and in the mixture of ionic liquid + water. The related comparison of the salting-out ratio of the [C4mim]Cl + water system with different alkali metal salts from this work and the literature12 are given in Figure 2. This same phenomenon was also observed in the other experimental system containing the same ionic liquid. It can be seen that the salting-out ratios of alkaline salts are different. We can assume that adding an appropriate ionic liquid might separate RbCl and CsCl in alkaline salts aqueous solutions. The density and refractive index of RbCl and CsCl in the saturated solutions at T = 288 K.15, 298.15 K, and 308.15 K were measured and summarized in Table 2 and Table 3. As depicted in Figure 3a, at a constant temperature, the density of the systems decreases rapidly with the increasing ionic liquid content. However, the refractive index curves monotonically increase with the ionic liquid increasing (Figure 3b). It is important to note that the curves in Figure 3 both panels a and b are almost indistinguishable at the lower concentration of ionic liquids, while the difference can be clearly seen in the higher ionic liquids content. At the lower concentration of ILs, the content of RbCl/CsCl is the main influence factor. But for the mixed solution with high mass fraction of ILs, the solution barely contains RbCl/CsCl and the ionic liquids become a main factor. Moreover, for a constant mass fraction of ionic liquid, the density and refractive index of the saturated solutions decreased with an increase in the alkyl carbon atoms of ionic liquids. Figure 4 panels a and b present the effect of temperature on the density and refractive index for the ternary systems

+ (1 − s) ∑ xiL ln(γi LxiL)

(4)

i=1

where s is the ratio (moles of solid phase)/(moles of mixture), xi denotes the mole fraction of component i in mixture. μS and μiL are the chemical potentials of the pure solid and component i in the liquid phase, and the superscript S and L express the solid phase and the liquid one, respectively. ΔCP is the difference between the liquid and solid heat capacities. Δhf is the enthalpy of fusion at the normal melting temperature; Tf is the normal melting temperature. The Gibbs energy for the anhydrous solid salts is given as26 Tf Δhf ⎛ Tf ⎞ ΔμS 1 ⎜1 − ⎟ + = ΔCP dT RT RTf ⎝ T ⎠ RT T Tf ΔC 1 P − dT R T T ⎛ Δh ΔCp ⎞⎛ Tf ⎞ ΔCp ⎛ Tf ⎞ = −⎜ f − ln⎜ ⎟ ⎟⎜ − 1⎟ − ⎠ ⎝T ⎠ R ⎠⎝ T R ⎝ RTf

∫

g S,E =

∫

(5)

where ΔCP can be calculated by the equation:

728

ΔCP = CP ,L − CP ,S

(5a)

CP,L = aL + bLT + c LT 2 + dLT 3

(5b)

CP,S = aS + bST + cST 2

(5c)


0.4268 0.3518 0.2701 0.1879 0.1098 0.0507 0.0121 0.0031

0.0572 0.1305 0.2161 0.3164 0.4253 0.5471 0.6667 0.7686

1.42833 1.35613 1.28385 1.21459 1.15547 1.12039 1.11532 1.12565

1.41288 1.34258 1.27184 1.20676 1.15003 1.11987 1.12016 1.13115

729

0.5887 0.5078 0.4201 0.3132 0.2023 0.0914 0.0213 0.0041

0.5934 0.5168 0.4274 0.3308

0.0390 0.0993 0.1711 0.2791 0.4123 0.5662 0.6831 0.8003

0.0424 0.0988 0.1716 0.2656

1.81760 1.70203 1.57704 1.44498

1.80680 1.69093 1.56228 1.42945 1.30071 1.19965 1.14445 1.13737

0.4376 1.44378 0.3702 1.36968 0.2931 1.29586 0.2139 1.22242 0.1275 1.16091 0.0633 1.12091 0.0137 1.11011 0.0045 1.12015 CsCl + [C2mim]Cl + H2O

0.4070 0.3285 0.2613 0.1774 0.0983 0.0411 0.0097 0.0023

0.0644 0.1307 0.2115 0.3113 0.4251 0.5461 0.6717 0.7622

ρ/(g/cm3)

RbCl + [C2mim]Cl + H2O

ws

0.0688 0.1373 0.2198 0.3189 0.4334 0.5546 0.6639 0.7632

wIL

1.42084 1.42315 1.42664 1.43209

1.42031 1.42309 1.42624 1.43205 1.44110 1.45486 1.47421 1.49679

1.39355 1.39947 1.40725 1.41717 1.43083 1.44772 1.46814 1.49212

1.39338 1.39959 1.40771 1.41827 1.43208 1.45001 1.47088 1.49501

1.39321 1.39971 1.40817 1.41937 1.43333 1.45228 1.47362 1.49790

nD

0.0410 0.0963 0.1654 0.2620

0.0413 0.0993 0.1711 0.2658 0.3902 0.5564 0.6890 0.7999

0.0478 0.1183 0.1935 0.3093 0.4408 0.5659 0.6951 0.7758

0.0571 0.1285 0.2170 0.3168 0.4432 0.5634 0.6894 0.8001

0.0760 0.1459 0.2297 0.3278 0.4455 0.5690 0.6838 0.7918

wIL

ρ/(g/cm3)

1.42898 1.35746 1.28511 1.21535 1.15138 1.10334 1.08076 1.07920

1.40116 1.33513 1.26872 1.19983 1.14624 1.10168 1.08488 1.08519

0.5987 0.5196 0.4386 0.3446

0.5889 0.5127 0.4302 0.3351 0.2321 0.1184 0.0369 0.0077 1.81907 1.69972 1.58021 1.45146

1.79657 1.68231 1.56169 1.43261 1.30660 1.19517 1.11887 1.09014

0.4494 1.45459 0.3826 1.37637 0.3119 1.31239 0.2235 1.22983 0.1275 1.15652 0.0705 1.10250 0.0174 1.07664 0.0076 1.07321 CsCl + [C4mim]Cl + H2O

0.4287 0.3576 0.2874 0.2070 0.1137 0.0599 0.0154 0.0043

0.4019 0.3356 0.2659 0.1866 0.1106 0.0493 0.0134 0.0035


ws K 0.0642 0.1326 0.2101 0.3066 0.4165 0.5423 0.6639 0.7737 K 0.0564 0.1262 0.2084 0.3074 0.4182 0.5457 0.6784 0.8003 K 0.0609 0.1162 0.2057 0.2999 0.4274 0.5574 0.6597 0.7737 K 0.0413 0.0960 0.1657 0.2604 0.3787 0.5249 0.6742 0.8000 K 0.0406 0.0917 0.1632 0.2550

288.15 1.42046 1.42348 1.42551 1.43245 1.43977 1.45336 1.47045 1.48968 298.15 1.42142 1.42416 1.42811 1.43374

wIL

288.15 1.39344 1.40081 1.40892 1.41954 1.43291 1.44928 1.46813 1.48684 298.15 1.39375 1.40059 1.40886 1.41915 1.43183 1.44739 1.46618 1.48472 308.15 1.39406 1.40037 1.40840 1.41876 1.43075 1.44550 1.46423 1.47915

nD

ρ/(g/cm3)

1.44143 1.36633 1.29575 1.22036 1.15996 1.10307 1.06318 1.04205

1.42158 1.35414 1.28860 1.21352 1.15565 1.10225 1.06541 1.04961

0.5977 0.5405 0.4562 0.3633

0.5909 0.5247 0.4429 0.3522 0.2595 0.1534 0.0494 0.0102

1.81987 1.71927 1.58915 1.45726

1.79838 1.68640 1.56365 1.43255 1.31136 1.19875 1.09293 1.05207

0.4435 1.44528 0.3903 1.37852 0.3156 1.30290 0.2419 1.22720 0.1586 1.16427 0.0863 1.10389 0.0359 1.06095 0.0081 1.03673 CsCl + [C6mim]Cl + H2O

0.4370 0.3693 0.3056 0.2319 0.1507 0.0803 0.0309 0.0047

0.4110 0.3561 0.2974 0.2242 0.1513 0.0769 0.0249 0.0051


ws

1.42163 1.42569 1.42862 1.43301

1.42094 1.42356 1.42717 1.43185 1.43992 1.44958 1.46374 1.48136

1.39574 1.40276 1.41158 1.42116 1.43019 1.44265 1.45513 1.47176

1.39467 1.40154 1.41041 1.42008 1.42938 1.44336 1.45920 1.47679

1.39290 1.40002 1.40924 1.41900 1.42857 1.44408 1.46301 1.47741

nD

0.0404 0.0867 0.1506 0.2611

0.0422 0.0916 0.1604 0.2511 0.3711 0.5173 0.6689 0.7938

0.0512 0.1149 0.1959 0.2943 0.4210 0.5527 0.6537 0.7607

0.0556 0.1262 0.2049 0.3022 0.4120 0.5387 0.6653 0.7756

0.0653 0.1311 0.2067 0.3071 0.4156 0.5436 0.6635 0.7737

wIL

ρ/(g/cm3)

1.44544 1.37693 1.30565 1.23619 1.16781 1.10189 1.04387 1.01608

1.42404 1.35695 1.29714 1.22918 1.16364 1.09480 1.04230 1.02168

0.6074 0.5427 0.4843 0.3781

0.6004 0.5336 0.4592 0.3719 0.2790 0.1689 0.0639 0.0124

1.83212 1.72028 1.60833 1.46466

1.81506 1.69389 1.57652 1.45072 1.32635 1.20431 1.09067 1.03518

0.4556 1.45476 0.4044 1.39471 0.3326 1.31816 0.2598 1.24720 0.1792 1.17356 0.1007 1.10058 0.0498 1.03936 0.0108 1.01128 CsCl + [C8mim]Cl + H2O

0.4395 0.3811 0.3195 0.2467 0.1697 0.0949 0.0415 0.0082

0.4152 0.3667 0.3097 0.2309 0.1592 0.0864 0.0329 0.0077


ws

1.42257 1.42416 1.42704 1.43180

1.42117 1.42278 1.42583 1.43095 1.43885 1.44766 1.45828 1.47320

1.39680 1.40362 1.41105 1.41929 1.42863 1.43974 1.45116 1.46774

1.39506 1.40234 1.41048 1.41908 1.42879 1.44021 1.45395 1.47134

1.39358 1.40112 1.40991 1.41887 1.42895 1.44068 1.45474 1.47294

nD

Table 3. The Solubility, Density and Refractive Index of RbCl/CsCl + [Cnmim]Cl (n = 2, 4, 6, 8) + H2O Ternary System Solution at T = (288.15, 298.15, 308.15) K

Journal of Chemical & Engineering Data Article


0.6026 0.5319 0.4418 0.3483 0.2393 0.1174 0.0385 0.0072

0.2284 0.1064 0.0353 0.0067

ws

nD 1.44066 1.45391 1.47257 1.49489 1.42187 1.42321 1.42604 1.43023 1.44022 1.45296 1.47093 1.49299

ρ/(g/cm3)

1.31392 1.20280 1.14439 1.13297

1.82840 1.71313 1.59180 1.46051 1.31813 1.20595 1.14433 1.12857

0.0382 0.0929 0.1644 0.2573 0.3769 0.5182 0.6711 0.7994

0.3815 0.5249 0.6717 0.7990

wIL

0.6060 0.5386 0.4583 0.3612 0.2581 0.1494 0.0527 0.0081

0.2475 0.1361 0.0434 0.0078

ws

1.83777 1.71713 1.59773 1.46684 1.33858 1.21607 1.12323 1.06936

1.32312 1.20562 1.12105 1.08755

ρ/(g/cm3) 298.15 1.44148 1.45247 1.46797 1.48558 308.15 1.42188 1.42484 1.42769 1.43348 1.44119 1.45158 1.46649 1.48375

nD K 0.3629 0.5032 0.6593 0.7968 K 0.0382 0.0898 0.1591 0.2475 0.3569 0.4964 0.6542 0.7901

wIL

0.6089 0.5424 0.4741 0.3858 0.2957 0.1813 0.0768 0.0165

0.2745 0.1625 0.0594 0.0133

ws

1.83656 1.72814 1.61265 1.48902 1.36012 1.21561 1.10341 1.04445

1.34496 1.20718 1.09767 1.04836

ρ/(g/cm3)

1.42342 1.42716 1.43054 1.43552 1.44144 1.44964 1.46002 1.47791

1.44032 1.44961 1.46238 1.48006

nD

wIL

0.0391 0.0848 0.1524 0.2377 0.3449 0.4813 0.6408 0.7804

0.3578 0.4942 0.6524 0.7889

The expanded uncertainties of temperature, mass fraction, density, and refractive indexes measurements are 0.003 K, 5·10−4, 5·10−5 g·cm−3, and 4.1·10−5.

0.0395 0.0929 0.1644 0.2622 0.3902 0.5449 0.6875 0.7998

0.3968 0.5513 0.6951 0.8003

wIL

Table 3. continued

0.6127 0.5608 0.4984 0.4132 0.3205 0.2172 0.0983 0.0195

0.3008 0.1879 0.0786 0.0158

ws

1.83622 1.75667 1.64981 1.51360 1.38578 1.25628 1.11930 1.03299

1.35417 1.21325 1.09421 1.03409

ρ/(g/cm3)

1.42336 1.42615 1.42872 1.43235 1.43955 1.44656 1.45590 1.46954

1.43920 1.44711 1.45709 1.47137

nD

Journal of Chemical & Engineering Data Article

Figure 1. The solubility of RbCl + [Cnmim]Cl (n = 2, 4, 6, 8) + H2O at 298.15 K.

where CP,L and CP,S denote liquid and solid heat capacities, aL, bL, cL, dL, aS, bS, and cS are the parameters which can be obtained from the literature.31 The values of Δhf for RbCl and

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Article

Figure 2. Comparison of the salting-out ratio of [C4mim]Cl on alkali metal salts at T = 298.15 K.

Figure 4. The effect of temperature on the density (a) and refractive index (b) for RbCl + [C2mim]Cl systems.

CsCl were obtained from the literature.32 The Gibbs energy of pure CsCl and RbCl solid were are as follows: gS,E 288.1K(RbCl) = S,E −12.24, gS,E 298.1K(RbCl) = −11.27, and g308.1K(RbCl) = −10.36; S,E S,E gS,E 288.1K(CsCl) = −8.11, g298.1KCsCl) = −7.60, and g308.1K(CsCl) = −7.11. The activity coefficient (γ) for any component i is written as ln γi =

∑j τjiGjixj ∑j Gjixj

+

∑ j

⎡ ∑ xτ G ⎤ ⎢τij − k k kj kj ⎥ ∑k Gkjxk ⎥⎦ ∑k Gkjxk ⎢⎣ xjGji

(6)

where the quantities τij and Gij are given by Gij = exp( −αijτij)

τij =

Δgij

=

(7)

Aij

(8) RT T where αij is a fitting parameter, the parameter value of αij = 0.2 is often used in published papers.33,34 gij is an energy parameter characteristic of the i−j interaction; Aij is the binary parameter obtained from the correlation of the equilibrium data. For this

Figure 3. Densities curves (a) and refractive indexes (b) of RbCl + [Cnmim]Cl (n = 2, 4, 6, 8) + H2O at 298.15 K. 731



Article

Table 4. Correlation Result Using the NRTL (α = 0.2) Model for the RbCl/CsCl + [Cnmim]Cl (n = 2, 4, 6, 8) + H2O Ternary System at T = (288.15, 298.15, 308.15) K system 288.15 298.15 308.15 288.15 298.15 308.15 288.15 298.15 308.15 288.15 298.15 308.15 288.15 298.15 308.15 288.15 298.15 308.15 288.15 298.15 308.15 288.15 298.15 308.15

K K K K K K K K K K K K K K K K K K K K K K K K

RbCl+[C2mim]Cl+H2O RbCl+[C2mim]Cl+H2O RbCl+[C2mim]Cl+H2O RbCl+[C4mim]Cl+H2O RbCl+[C4mim]Cl+H2O RbCl+[C4mim]Cl+H2O RbCl+[C6mim]Cl+H2O RbCl+[C6mim]Cl+H2O RbCl+[C6mim]Cl+H2O RbCl+[C8mim]Cl+H2O RbCl+[C8mim]Cl+H2O RbCl+[C8mim]Cl+H2O CsCl+[C2mim]Cl+H2O CsCl+[C2mim]Cl+H2O CsCl+[C2mim]Cl+H2O CsCl+[C4mim]Cl+H2O CsCl+[C4mim]Cl+H2O CsCl+[C4mim]Cl+H2O CsCl+[C6mim]Cl+H2O CsCl+[C6mim]Cl+H2O CsCl+[C6mim]Cl+H2O CsCl+[C8mim]Cl+H2O CsCl+[C8mim]Cl+H2O CsCl+[C8mim]Cl+H2O

τ12

τ21

τ13

τ31

τ23

τ32

OF

2.2766 2.2281 2.2604 1.6444 1.8500 1.8839 1.8399 1.8053 1.9037 1.6658 1.7563 1.8829 2.6287 2.5478 2.6421 2.4271 2.6567 2.7461 2.3946 2.4012 2.3409 2.5367 2.5281 2.5197

2.8256 2.7152 2.7355 2.3918 2.2377 2.2272 2.1823 2.1228 2.1889 1.9328 2.0102 2.1205 3.0551 9.3761 3.0269 2.7851 2.9985 3.0782 2.6943 2.6645 2.5862 2.8054 2.7719 2.7511

−1.3643 −1.3417 −1.3634 −1.0527 −1.1119 −1.1763 −1.1738 −1.1197 −1.2400 −1.0990 −1.1654 −1.2922 −1.5865 1.6332 −1.5721 −1.5002 −1.6778 −1.7262 −1.5579 −1.5829 −1.5458 −1.7221 −1.7321 −1.7323

−1.6097 −1.5640 −1.5826 −1.2881 −1.3028 −1.3653 −1.3658 −1.2965 −1.4157 −1.2663 −1.3335 −1.4588 −1.7622 −3.8769 −1.7394 −1.6807 −1.8510 −1.8998 −1.7248 −1.7428 −1.6946 −1.9000 −1.8998 −1.8985

0.1351 0.1017 0.3474 0.0631 −0.4178 −0.0292 0.3317 −0.2149 0.6378 0.4925 0.7354 1.5210 0.7916 3.3043 0.5987 1.0415 1.5030 1.5829 1.8631 2.0265 1.7309 3.4200 3.3714 3.4234

−11.7374 −10.8040 −10.2240 −11.6526 −10.3116 −9.8500 −11.8702 −10.5355 −10.3521 −11.9648 −11.2479 −10.8579 −8.5980 −9.0705 −7.6035 −8.7040 −8.4683 −8.1193 −9.0708 −8.6474 −8.1406 −9.5286 −9.0646 −8.6929

0.0660 0.0774 0.0847 0.0903 0.0956 0.0883 0.0207 0.0333 0.0203 0.0045 0.0342 0.0995 0.0978 0.0295 0.0853 0.0789 0.0575 0.0608 0.0711 0.0572 0.0514 0.0716 0.0373 0.0941

OF (LS) = ∑nnLS= 1∑i 3= 1[((xi)n,L)exp − ((xi)n,L)cal]2 where (xi)n denotes the molar fraction of component i on tie-line n.

Table 5. Values of Parameters of eq 9 at T = (288.15, 298.15, 308.15) K A

system 288.15 288.15 288.15 288.15 298.15 298.15 298.15 298.15 308.15 308.15 308.15 308.15 288.15 288.15 288.15 288.15 298.15 298.15 298.15 298.15 308.15 308.15 308.15 308.15


RbCl + [C2mim]Cl + H2O RbCl + [C4mim]Cl + H2O RbCl + [C6mim]Cl + H2O RbCl + [C8mim]Cl + H2O RbCl + [C2mim]Cl + H2O RbCl + [C4mim]Cl + H2O RbCl + [C6mim]Cl + H2O RbCl + [C8mim]Cl + H2O RbCl + [C2mim]Cl + H2O RbCl + [C4mim]Cl + H2O RbCl + [C6mim]Cl + H2O RbCl + [C8mim]Cl + H2O CsCl + [C2mim]Cl + H2O CsCl + [C4mim]Cl + H2O CsCl + [C6mim]Cl + H2O CsCl + [C8mim]Cl + H2O CsCl + [C2mim]Cl + H2O CsCl + [C4mim]Cl + H2O CsCl + [C6mim]Cl + H2O CsCl + [C8mim]Cl + H2O CsCl + [C2mim]Cl + H2O CsCl + [C4mim]Cl + H2O CsCl + [C6mim]Cl + H2O CsCl + [C8mim]Cl + H2O

0.4693 0.4696 0.4657 0.4674 0.4868 0.4846 0.4857 0.4853 0.5033 0.5016 0.5023 0.5032 0.6429 0.6450 0.6443 0.6475 0.6521 0.6514 0.6512 0.6519 0.6628 0.6615 0.6601 0.6622

288.15 288.15 288.15 288.15 298.15

K K K K K

RbCl RbCl RbCl RbCl RbCl

1.4832 1.4806 1.4839 1.4807 1.4951

+ + + + +

[C2mim]Cl [C4mim]Cl [C6mim]Cl [C8mim]Cl [C2mim]Cl

+ + + + +

H2O H2O H2O H2O H2O

B mass fraction −0.9913 −0.9360 −0.8120 −0.7614 −1.0920 −0.9881 −0.9116 −0.8162 −1.0520 −1.0622 −0.9897 −0.9244 −1.3907 −1.3870 −1.3044 −1.2629 −1.4324 −1.3830 −1.2646 −1.2362 −1.4510 −1.3526 −1.2774 −1.1821 density −1.1442 −1.1130 −1.0893 −0.9674 −1.1795 732

C

D

SD

0.0410 0.1013 −0.0591 −0.1499 0.3644 0.2211 0.1475 0.0107 0.2529 0.4467 0.3816 0.3342 0.7246 0.8877 0.7771 0.7567 0.9070 0.8403 0.5552 0.6933 0.8216 0.7544 0.7175 0.6191

0.5974 0.4267 0.4349 0.4723 0.3056 0.3291 0.3033 0.3311 0.3497 0.1270 0.0886 0.0371 0.0084 −0.1960 −0.1821 −0.2268 −0.1625 −0.1565 0.0275 −0.1912 −0.0417 −0.1123 −0.1728 −0.2088

0.0033 0.0013 0.0019 0.0014 0.0012 0.0029 0.0022 0.0013 0.0019 0.0029 0.0023 0.0020 0.0061 0.0045 0.0062 0.0052 0.0052 0.0062 0.0048 0.0061 0.0029 0.0043 0.0054 0.0039

0.8462 0.8283 0.7696 0.4525 0.9026

0.0678 −0.0679 −0.1196 0.0342 0.0103

0.0023 0.0014 0.0029 0.0036 0.0017



Article

Table 5. continued A

system 298.15 298.15 298.15 308.15 308.15 308.15 308.15 288.15 288.15 288.15 288.15 298.15 298.15 298.15 298.15 308.15 308.15 308.15 308.15

K K K K K K K K K K K K K K K K K K K

RbCl + [C4mim]Cl + H2O RbCl + [C6mim]Cl + H2O RbCl + [C8mim]Cl + H2O RbCl + [C2mim]Cl + H2O RbCl + [C4mim]Cl + H2O RbCl + [C6mim]Cl + H2O RbCl + [C8mim]Cl + H2O CsCl + [C2mim]Cl + H2O CsCl + [C4mim]Cl + H2O CsCl + [C6mim]Cl + H2O CsCl + [C8mim]Cl + H2O CsCl + [C2mim]Cl + H2O CsCl + [C4mim]Cl + H2O CsCl + [C6mim]Cl + H2O CsCl + [C8mim]Cl + H2O CsCl + [C2mim]Cl + H2O CsCl + [C4mim]Cl + H2O CsCl + [C6mim]Cl + H2O CsCl + [C8mim]Cl + H2O

1.4940 1.4902 1.4900 1.5183 1.5133 1.5169 1.5141 1.8902 1.8900 1.8900 1.8959 1.9155 1.9131 1.9130 1.9133 1.9315 1.9342 1.9306 1.9338

288.15 288.15 288.15 288.15 298.15 298.15 298.15 298.15 308.15 308.15 308.15 308.15 288.15 288.15 288.15 288.15 298.15 298.15 298.15 298.15 308.15 308.15 308.15 308.15


RbCl + [C2mim]Cl + H2O RbCl + [C4mim]Cl + H2O RbCl + [C6mim]Cl + H2O RbCl + [C8mim]Cl + H2O RbCl + [C2mim]Cl + H2O RbCl + [C4mim]Cl + H2O RbCl + [C6mim]Cl + H2O RbCl + [C8mim]Cl + H2O RbCl + [C2mim]Cl + H2O RbCl + [C4mim]Cl + H2O RbCl + [C6mim]Cl + H2O RbCl + [C8mim]Cl + H2O CsCl + [C2mim]Cl + H2O CsCl + [C4mim]Cl + H2O CsCl + [C6mim]Cl + H2O CsCl + [C8mim]Cl + H2O CsCl + [C2mim]Cl + H2O CsCl + [C4mim]Cl + H2O CsCl + [C6mim]Cl + H2O CsCl + [C8mim]Cl + H2O CsCl + [C2mim]Cl + H2O CsCl + [C4mim]Cl + H2O CsCl + [C6mim]Cl + H2O CsCl + [C8mim]Cl + H2O

1.3871 1.3872 1.3871 1.3865 1.3883 1.3887 1.3891 1.3886 1.3886 1.3891 1.3888 1.3896 1.4181 1.4180 1.4181 1.4181 1.4189 1.4196 1.4196 1.4199 1.4202 1.4202 1.4203 1.4207

B

C

density −1.1565 −1.6225 −1.4716 −1.2554 −1.2311 −1.2915 −1.1416 −2.2040 −2.3001 −2.3129 −2.3188 −2.3433 −2.3490 −2.2671 −2.2360 −2.4528 −2.4500 −2.2934 −2.2022 refractive index 0.0958 0.0898 0.1023 0.1330 0.0872 0.0381 0.1680 0.1885 0.0908 0.1106 0.1378 0.1444 0.0552 0.0566 0.0620 0.0567 0.0539 0.0498 0.0627 0.0505 0.0365 0.0491 0.0841 0.0618

D

SD

0.9109 2.3001 1.8446 0.9839 1.0507 1.2956 0.9083 2.1212 2.4528 2.4356 2.4951 2.3707 2.4170 2.1233 2.0846 2.6222 2.7192 2.1613 2.0948

−0.1443 −1.2213 −0.9392 −0.0294 −0.2567 −0.5600 −0.3750 −0.6879 −1.0427 −1.0787 −1.1947 −0.8374 −0.9733 −0.8123 −0.8514 −1.0227 −1.2688 −0.8676 −0.9703

0.0021 0.0054 0.0058 0.0010 0.0036 0.0041 0.0055 0.0069 0.0044 0.0066 0.0082 0.0043 0.0066 0.0073 0.0097 0.0089 0.0077 0.0097 0.0078

−0.0264 0.0091 −0.0197 −0.1363 −0.0059 0.0896 −0.1957 −0.2882 −0.0379 −0.0904 −0.1588 −0.2087 −0.0605 −0.0489 −0.0519 −0.0314 −0.0570 −0.0142 −0.0494 −0.0131 −0.0082 −0.0066 −0.1203 −0.0508

0.1189 0.0464 0.0511 0.1395 0.0940 0.0168 0.1537 0.2273 0.1247 0.1254 0.1542 0.2022 0.1435 0.1125 0.0910 0.0586 0.1338 0.0693 0.0822 0.0395 0.0944 0.0554 0.1335 0.0657

0.0003 0.0035 0.0010 0.0007 0.0004 0.0048 0.0006 0.0078 0.0009 0.0004 0.0006 0.0002 0.0005 0.0006 0.0004 0.0007 0.0007 0.0002 0.0005 0.0007 0.0007 0.0003 0.0006 0.0006

2 1/2 sd = ((∑ni (Yexp - Ycal i i ) /n)) , where the superscripts “exp” and “cal” are experimental and calculated using eq 10.

parameters τij and the objective function (OF) according to eq 9 were listed in Table 4. For comparison, both the experimental data and calculated data for the studied systems at 298.15 K are both depicted in Figure 1a. It can be observed that the NRTL model well represents the RbCl/CsCl + [Cnmim]Cl (n = 2, 4, 6, 8) (1) + H2O system. In this work, the reliability of the measured mass fraction, density, and refractive index of the saturated solutions were also correlated using an empirical equation:35

work, the objective function (OF) is used in the optimization of the parameters Aij. The OF is given as nLS

OF (LS) =

3

∑ ∑ [((xi)n,L )exp − ((xi)n,L )cal ]2 n=1 i=1

(9)

where, (xi)n is the molar fraction of component i on tie-line n, nLS is the number of tie-lines in the LS region. The subscript L represents the liquid phases. The subscripts exp and cal are the experimental and calculated data, respectively. The experimental equilibrium data obtained for RbCl/CsCl + [Cnmim]Cl (n = 2, 4, 6, 8) + H2O were used to estimate the NRTL binary interaction parameters τij. The values of

Y = A + BwIL + CwIL 2 + DwIL 3

(10)

where wIL is the mass fraction of ionic liquids in saturated solution, Y represents the mass fraction of RbCl/CsCl, density, 733



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(7) Liu, W.; Hou, Y.; Wu, W.; Ren, S.; Jing, Y.; Zhang, B. Solubility of Glucose in Ionic Liquid + Antisolvent Mixtures. Ind. Eng. Chem. Res. 2011, 50, 6952−6956. (8) Trindade, J. R.; Visak, Z. P.; Blesic, M.; Marrucho, I. M.; Coutinho, J. A.; Canongia Lopes, J. N.; Rebelo, L. P. Salting-Out Effects in Aqueous Ionic Liquid Solutions: Cloud-Point Temperature Shifts. J. Phys. Chem. B 2007, 111, 4737−4741. (9) Cláudio, A. F. M.; Ferreira, A. M.; Shahriari, S.; Freire, M. G.; Coutinho, J. A. Critical Assessment of the Formation of Ionic-LiquidBased Aqueous Two-Phase Systems in Acidic Media. J. Phys. Chem. B 2011, 115, 11145−11153. (10) Ventura, S. P.; Sousa, S. G.; Serafim, L. S.; Lima, S.; Freire, M. G.; Coutinho, J. A. Ionic Liquid Based Aqueous Biphasic Systems with Controlled pH: The Ionic Liquid Cation Effect. J. Chem. Eng. Data 2011, 56, 4253−4260. (11) Passos, H.; Ferreira, A. R.; Cláudio, A. F. M.; Coutinho, J. A.; Freire, M. G. Characterization of Aqueous Biphasic Systems Composed of Ionic Liquids and a Citrate-Based Biodegradable Salt. Biochem. Eng. J. 2012, 67, 68−76. (12) Ren, Y.; Wang, Y.; Liu, G.; Peng, C.; Liu, H.; Hu, Y. Solubilities of MCl (M = Na, K) in Aqueous Systems Containing the Ionic Liquid [Bmim]Cl from (298.15 to 343.15) K. J. Chem. Eng. Data 2011, 56, 1341−1347. (13) Peng, X. M.; Hu, Y. F.; Jin, C. W. Solubilities of ImidazoliumBased Ionic Liquids in Aqueous Salt Solutions at 298.15 K. J. Chem. Thermodyn. 2011, 43, 1174−1177. (14) Zhao, W. X.; Hu, M. C.; Jiang, Y. C.; Li, S. N. Solubilities, Densities, and Refractive Indices of Rubidium Chloride or Cesium Chloride in Ethanol Aqueous Solutions at Different Temperatures. Chin. J. Chem. 2007, 25, 478−483. (15) Zhou, Y. H.; Li, S. N.; Zhai, Q. G.; Jiang, Y. C.; Hu, M. C. Solubilities, Densities and Refractive Indices for the Ternary Systems Ethylene Glycol + MCl + H2O (M = Na, K, Rb, Cs) at (15 and 35)°C. J. Chem. Thermodyn. 2010, 42, 764−772. (16) Hu, M.; Zhai, Q.; Liu, Z.; Xia, S. Liquid−Liquid and Solid− Liquid Equilibrium of the Ternary System Ethanol + Cesium Sulfate + Water at (10, 30, and 50)°C. J. Chem. Eng. Data 2003, 48, 1561−1564. (17) Yin, G.; Li, S.; Zhai, Q.; Jiang, Y.; Hu, M. Phase Behavior of Aqueous Two-Phase Systems Composed of 1-Alkyl-3-Methylimidazolium Bromide + Rb2CO3/Cs2CO3 + Water. Thermochim. Acta 2013, 566, 149−154. (18) Ho-Gutierrez, I. V.; Cheluget, E. L.; Vera, J. H.; Weber, M. E. Liquid−Liquid Equilibrium of Aqueous Mixtures of Poly(ethylene glycol) with Na2SO4 or NaCl. J. Chem. Eng. Data 1994, 39, 245−248. (19) Cheluget, E. L.; Gelinas, S.; Vera, J. H.; Weber, M. E. Liquid− Liquid Equilibrium of Aqueous Mixtures of Poly(propylene glycol) with Sodium Chloride. J. Chem. Eng. Data 1994, 39, 127−130. (20) Apelblata, A.; Korin, E. The Vapour Pressures of Saturated Aqueous Solutions of Sodium Chloride, Sodium Bromide, Sodium Nitrate, Sodium Nitrite, Potassium Iodate, And Rubidium Chloride at Temperatures from 227K to 323K. J. Chem. Thermodyn. 1998, 30, 59− 71. (21) Lide, D. CRC Handbook of Chemistry and Physics, 89th ed.; CRC Press: Boca Raton, Fl, 2009. (22) Meng, R.; Li, S.; Zhai, Q.; Jiang, Y.; Lei, H.; Zhang, H.; Hu, M. Solubilities, Densities, and Refractive Indices for the Ternary Systems Glycerin + MCl + H2O (M = Na, K, Rb, Cs) at (298.15 and 308.15) K. J. Chem. Eng. Data 2011, 56, 4643−4650. (23) Apelblat, A.; Korin, E. The Molar Enthalpies of Solution and Vapour Pressures of Saturated Aqueous Solutions of Some Cesium Salts. J. Chem. Thermodyn. 2006, 38, 152−157. (24) Qiao, Z.; Li, Y.; Dang, Y.; Xie, H. Phase Equilibria of the Systems of CsCl + ErCl3 + H2O and CsCl + ErCl3 + HCl (∼10.7%, ∼14.4%) + H2O at T = 298.15 K and the Standard Molar Enthalpies of Formation of Solid Phase Compounds. J. Chem. Thermodyn. 2014, 68, 275−280. (25) Renon, H.; Prausnitz, J. M. Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures. AIChE J. 1968, 14, 135−144.

and refractive index. A, B, C, and D are parameters obtained by optimizing the experimental data and given in Table 5 with the corresponding standard deviations less than 0.01. On the basis of the standard deviation we can be seen that eq 10 could correlate the experimental solubility data, density, and refractive index of the systems well.

■

CONCLUSION In this work, the solid−liquid equilibrium of RbCl/CsCl + [Cnmim]Cl (n = 2, 4, 6, 8) + H2O ternary systems were investigated at T = (288.15, 298.15, and 308.15) K. The solubility and density decrease with the ILs content increasing in the mixtures, and the refractive index values exhibit an opposite trend. The NRTL model was successfully utilized to correlate the experimental solubility data. Moreover, the solubility, density, and refractive index for the saturated ternary solutions were also fitted by the empirical equation.

■

ASSOCIATED CONTENT

S Supporting Information *

Data for calibration curves for the studied systems; additional figures as described in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-29-81530767. Fax: +86-29-81530727. E-mail: [email protected]; [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (21171111, 21301114), the Fundamental Research Funds for the Central Universities (2010ZYGX027), and Natural Science Foundation of Shaanxi Province (2013JQ2009).

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REFERENCES

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