LiquidâLiquid Phase Equilibrium and Heat Capacity of Binary Mixture

Article pubs.acs.org/jced

Liquid−Liquid Phase Equilibrium and Heat Capacity of Binary Mixture 1‑Ethyl-3-methylimidazolium Bis(trifluoromethylsulfonyl)imide + 1‑Propanol Mingjie Wang,†,§ Tianxiang Yin,†,§ Chen Xu,† Zhiyun Chen,† and Weiguo Shen*,†,‡ †

School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China Department of Chemistry, Lanzhou University, Lanzhou, Gansu 730000, China

‡

S Supporting Information *

ABSTRACT: The measurements of the liquid−liquid coexistence curve and the heat capacity for binary mixture {1-ethyl3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C2mim][NTf2]) + 1-propanol} have been precisely performed. The values of the critical exponents α and β in the critical region were obtained and coincided well with the 3DIsing ones. The complete scaling theory was applied to well represent the asymmetric behavior of the diameter of the coexistence curve, indicating an important role of the heat capacity related term in the complete scaling formulizm. A comparison of the reduced critical parameters to those predicted by the restricted primitive model clearly showed the solvophobic criticality of the studied system.

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INTRODUCTION Because room temperature ionic liquids (RTILs) are characterized by high stability, high conductivity, low volatility, large heat capacity, and good dissolving ability,1−4 they have received much attention in both fundamental studies and practical applications in recent decades.5,6 Especially, RTILs as one kind of green solvents have replaced traditional solvents in many chemical engineering applications. Mixed RTILs/organic solvents have been used as a chemical reaction media to facilitate the separation of the products, the solvent, and the catalyst by varying the temperature or composition in the media.7 Therefore, the detailed knowledge of liquid−liquid phase equilibrium of solutions containing RTILs is highly desired.8 Whether the critical behavior of ionic fluids belongs to the Ising universality class was a core problem of ionic fluids criticality.9−11 Nowadays, it is clear that the liquid−liquid phase transition of ionic solutions exhibits 3D-Ising behavior, which has been confirmed by many experimental studies and simulations by using a simple model called the restricted primitive model (RPM) for ionic fluids.8−20 It was pointed out that, for ILs solutions with low permittivity organic solvents, the phase transition observed at ambient temperature might be driven by the Coulombic interaction, while with high permittivity solvents, the phase transition was considered to be driven by a solvophobic mechanism.20 It was found that some IL solutions showed a crossover from the solvophobic character to the Coulombic one, and the solvophobic character of a mixture was usually accompanied by larger critical © XXXX American Chemical Society

amplitudes related to the coexistence curve and the heat capacity,14 and a special bending character of the diameter of the coexistence curve as compared to the Coulombic character. In recent years, Anisimov and co-workers21−23 extended the complete scaling theory24−26 to incompressible and weakly compressible liquid mixtures, which pointed out that scaling fields should be the linear mixtures of all physical fields: the chemical potential of solvent μ1, the difference of chemical potential between solvent and solute Δμ, the temperature T, and the pressure P. The complete scaling theory has been verified by some experiments on binary molecular liquid mixtures;27,28 however, only a few reports involved high-quality coexistence curve and heat capacity data in the critical region for binary RTIL mixtures.29−32 It has been noted that for ionic liquids containing anions [BF4]− and [PF6]−, the compound HF would possibly exist from decomposition or hydrolysis.33,34 In this work, a critical binary solution of a more stable ionic liquid {1-ethyl-3methylimidazolium bis(trifluoromethylsulfonyl)imide ([C2mim][NTf2]) + an alcohol was chosen. We report the liquid−liquid coexistence curve and the heat capacity of {x[C2mim][NTf2] + (1 − x)1-propanol} in this work. These precise experimental results were used to determine the critical exponent α and β and to examine the asymmetric behavior of the diameters of the coexistence curves through the complete Received: April 28, 2014 Accepted: October 17, 2014

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dx.doi.org/10.1021/je5003779 | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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refractive index, the temperature T, and the temperature distance from the critical point (Tc − T) were ± 0.0001, ± 0.02, and ± 0.002 K, respectively. A differential scanning calorimeter, Micro DSC III (Setaram, France) with special vessels for avoiding the presence of vapor space was used to measure the isobaric heat capacities per unit volumes CPV−1 of a critical binary RTIL solution at diverse temperatures. The calorimeter was calibrated by two liquids, 1butanol and n-heptane. The specific descriptions of the apparatus, the measurement principle, and experimental procedure can be found in our previous articles.27,28,37 The measurements were carried out in the down scanning model. The scanning rates were set at 0.01 K·min−1 in the critical region and 0.1 K·min−1 in the region far away from the critical point. The background noise of Micro DSC III was less than ± 0.2 μW, and the temperature stability was better than ± 0.002 K. The estimated uncertainties in measurement of CPV−1 were ± 0.01 J·cm−3·K−1 and ± 0.001 J·cm−3·K−1 in the critical region and the noncritical region, respectively.

scaling theory. Furthermore, the solvophobic or Coulombic character of the RTIL solution was discussed based on its critical properties.

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EXPRIMENTAL METHODS Materials. Table 1 lists the suppliers, purification methods, and purities of all the chemicals used in the experiments. Table 1. Purities and Suppliers of the Chemicals chemical

supplier

[C2mim][NTf2]

ChengJie Chemical Co. LTD Aladdin

1-propanol

purity, mass fraction 0.99 0.999

dried and stored method dried under vacuum at 328 K for 48 h and then stored in a desiccator over P2O5 0.4 nm molecular sieves

Apparatus and Procedure. The “minimum deviations” technique was used to measure the refractive index n of two coexisting phases to give a plot of temperature against n, which was referred to as a (T, n) coexistence curve.35 The detailed experimental principle, method, and apparatus have been described previously.35−37 The critical mole fraction xc was determined within 0.001 by the visual “equal-volume” observation. The uncertainties in measurements of the

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RESULTS AND DISCUSSION Coexistence Curve. The experimental values of the critical mole fraction xc and the critical temperature Tc for {x[C2mim][NTf2] + (1 − x)1-propanol} were 0.133 ± 0.001 and 295.203

Table 2. Coexistence Curves of (T, n), (T, x), (T, ϕ), (T, ρ̂m) and (T, ρ̂m x) for {x[C2mim][NTf2] + (1 − x)1-Propanol}a (Tc − T)/K

nU

nL

xU

xL

ϕU

ϕL

ρ̂Um

ρ̂Lm

ρ̂Umx

ρ̂Lmx

0.003 0.006 0.012 0.020 0.036 0.054 0.080 0.111 0.152 0.209 0.258 0.334 0.420 0.508 0.638 0.810 1.001 1.203 1.450 1.759 2.142 2.646 3.239 3.953 4.807 5.851 6.854 8.055 9.606 11.557

1.3960 1.3957 1.3955 1.3953 1.3950 1.3947 1.3944 1.3942 1.3939 1.3936 1.3934 1.3931 1.3928 1.3926 1.3923 1.3921 1.3918 1.3916 1.3913 1.3910 1.3908 1.3906 1.3904 1.3902 1.3901 1.3900 1.3901 1.3902 1.3904 1.3907

1.3977 1.3979 1.3981 1.3983 1.3987 1.3990 1.3993 1.3996 1.3999 1.4002 1.4005 1.4009 1.4012 1.4015 1.4019 1.4023 1.4028 1.4033 1.4038 1.4043 1.4049 1.4056 1.4064 1.4073 1.4081 1.4092 1.4101 1.4111 1.4123 1.4137

0.121 0.117 0.115 0.112 0.109 0.105 0.102 0.099 0.096 0.092 0.090 0.087 0.083 0.081 0.077 0.074 0.071 0.068 0.064 0.060 0.057 0.053 0.049 0.045 0.041 0.037 0.034 0.031 0.027 0.023

0.143 0.145 0.148 0.151 0.156 0.160 0.164 0.169 0.173 0.177 0.181 0.187 0.192 0.196 0.202 0.207 0.215 0.223 0.230 0.237 0.246 0.257 0.269 0.283 0.294 0.311 0.324 0.339 0.357 0.377

0.320 0.313 0.308 0.303 0.295 0.288 0.280 0.275 0.267 0.259 0.254 0.245 0.237 0.231 0.223 0.216 0.207 0.200 0.190 0.180 0.171 0.162 0.151 0.139 0.128 0.115 0.108 0.098 0.088 0.076

0.363 0.368 0.373 0.378 0.388 0.396 0.403 0.410 0.417 0.425 0.432 0.441 0.448 0.455 0.464 0.473 0.484 0.496 0.506 0.516 0.529 0.542 0.558 0.575 0.588 0.608 0.623 0.638 0.656 0.676

1.022 1.029 1.034 1.038 1.046 1.053 1.060 1.065 1.072 1.080 1.085 1.093 1.100 1.106 1.114 1.120 1.129 1.136 1.145 1.155 1.164 1.174 1.184 1.196 1.208 1.221 1.229 1.240 1.252 1.266

0.982 0.977 0.973 0.968 0.959 0.952 0.945 0.938 0.931 0.925 0.918 0.909 0.902 0.896 0.888 0.880 0.869 0.859 0.849 0.840 0.829 0.816 0.802 0.786 0.774 0.757 0.743 0.729 0.713 0.696

0.123 0.121 0.119 0.117 0.114 0.111 0.108 0.106 0.103 0.100 0.098 0.095 0.091 0.089 0.086 0.083 0.080 0.077 0.073 0.069 0.066 0.062 0.058 0.054 0.050 0.045 0.042 0.038 0.034 0.029

0.140 0.142 0.144 0.146 0.150 0.152 0.155 0.158 0.161 0.164 0.166 0.170 0.173 0.176 0.179 0.182 0.187 0.191 0.195 0.199 0.204 0.209 0.215 0.222 0.227 0.235 0.241 0.247 0.254 0.262

a Refractive indexes n were measured at wavelength λ = 632.8 nm and xc = 0.133, Tc = 295.203 K. Mole fraction, volume fraction, dimensionless molar density, and dimensionless partial molar density are denoted by x, ϕ, ρ̂m, and ρ̂m x. Superscripts “U” and “L” relate to upper and lower phases, respectively. Standard uncertainties u are u(p) = 10 kPa, u(Tc − T) = 0.002 K, u(n) = 0.0001, u(x) = 0.003, u(ϕ) = 0.003, u(ρ̂m) = 0.001, and u(ρ̂m x) = 0.002.

B



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± 0.001 K, respectively. The phase diagrams containing CnmimNTf2 and alcohols were extensively studied by other groups.38,39 Our results coincide well with these reported values, that is, 0.135 ± 0.003 and 294.87 ± 0.22 K.38 The difference between them may be due to the different sources of chemicals or uncontrollable moisture or other impurities introduced in the preparation of the samples.40 The refractive indexes n were measured for each coexisting phase at the wavelength λ = 632.8 nm and various temperatures, which are listed in columns 2 and 3 of Table 2. The refractive index n of a pure liquid or a mixture may be expressed as a linear function of temperature in a certain temperature range: 0

0

n(T , x) = n(T , x) + R(x)(T − T )

(1)

R(x) = xR1 + (1 − x)R 2

(2)

n(289.423K, x) = 1.3853 + 0.1396x − 0.3179x 2 + 0.4857x 3 − 0.4033x 4 + 0.1346x 5 (3)

and the standard deviation was less than 1·10−4. Equations 1 to 3 were used to convert refractive indexes to mole fractions with the Newton iteration method. The volume fraction ϕ was then calculated from the mole fraction by 1/ϕ = (1 − K ) + K /x

K=

d1M 2 d 2M1

(4)

(5)

where M is the molar mass; d is the mass density; and the subscripts 1 and 2 refer to [C2mim][NTf2] and 1-propanol, respectively. The densities of [C2mim][NTf2] and 1-propanol at different temperatures were measured by a vibrating-tube densimeter (Anton Paar, DMA-5000 M), which gave: d/g·cm−3 = −1.01303·10−3T/K + 1.82081 for [C2mim][NTf2] and d/g· cm−3 = −7.86472·10−4T/K + 1.03697 for 1-propanol. The values of x and ϕ at various temperatures for each coexisting phases are listed in columns 4 to 7 of Table 2. The plot of temperature against mole fraction is shown in Figure 1 and compared with those determined by other authors with different methods,38,42 showing good agreement with our results.

where R1 and R2 are the temperature coefficient of n for [C2mim][NTf2] and 1-propanol, respectively; R(x) is the temperature coefficient for a mixture with a particular composition x. Since the critical anomaly in the refractive index is negligible,35,41 eqs 1 and 2 are valid even if the system approaches the critical point. We measured the refractive indexes for two pure components at various temperatures and for mixtures with various known compositions at T = 296.267 K above the critical point, and these are listed in Table 3. LeastTable 3. Refractive Indexes n at Wavelength λ = 632.8 nm for [C2mim][NTf2] and 1-Propanol at Various Temperatures and for {x[C2mim][NTf2] + (1 − x)1Propanol} with Various Compositions at T = 296.267 Ka T/K

n

285.034 287.165 288.969 290.281

1.4252 1.4246 1.4242 1.4238

284.726 286.914 288.210 x

1.3870 1.3861 1.3856

0.000 0.021 0.056 0.097 0.142

n

T/K

n

[C2mim][NTf2] 291.114 1.4236 292.189 1.4233 293.157 1.4230 294.213 1.4227 1-Propanol 289.238 1.3851 290.257 1.3847 291.260 1.3843 x n

T/K

n

295.176 297.256

1.4225 1.4219

292.590 293.688 296.267

1.3837 1.3833 1.3823

x

{x[C2mim][NTf2] + (1 − x)1-Propanol} 1.3823 0.149 1.3977 0.502 1.3854 0.192 1.4006 0.699 1.3896 0.243 1.4036 0.855 1.3935 0.306 1.4064 1.00 1.3971 0.397 1.4099

Figure 1. Coexistence curves for {x[C2mim][NTf2] + (1 − x)1propanol} plotted as temperature T against mole fraction x.

n 1.4131 1.4174 1.4199 1.4222

With the hypothesis of ideal mixing, the molar volumes V of a mixture in each coexistence phase can be expressed by V U(L) = x U(or L)

a

Standard uncertainties u are u(n) = 0.0001, u(T) = 0.02 K, u(x) = 0.001, and u(p) = 10 kPa.

M1 M + (1 − x U(or L)) 2 d1 d2

(6)

and the molar volume Vc at the critical point can be calculated by Vc = xc

squares linear fittings of the experimental results for the two pure components gave R1 = −2.70·10−4 for [C2mim][NTf2] and R2 = −4.11·10−4 for 1-propanol. The refractive indexes of the binary mixtures with various known compositions at T = 296.267 K were then converted to n (T0, x) by using eqs 1 and 2 with T0 = 289.423 K being the middle temperature of the coexistence curve. These values of n(T0, x) were fitted to a polynomial equation to obtain

M1 M + (1 − xc) 2 d1,c d 2,c

(7)

where the superscripts U and L indicate the upper and the lower phases, respectively; di,c is the density of each pure component at the critical temperature. The dimensionless molar density ρ̂m (ρ̂m = ρm/ρmc = Vc/V, where ρm is the molar density and ρmc is the value of ρm at the critical point), and the dimensionless partial molar density ρ̂mx (the product of ρ̂m and the mole fraction x) were calculated by using the experimental data of (T, n) the coexistence curve and the densities of the two C



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pure components. The values of ρ̂Um, ρ̂Lm, ρ̂Umx and ρ̂Lmx for each temperature are listed in columns 8 to 11 of Table 2. Heat Capacity. We measured the isobaric heat capacities per unit volume of the binary mixture of {x[C2mim][NTf2] + (1 − x)1-propanol} with the critical composition in a wide temperature range. The experimental data are collected and summarized in the Supporting Information and a part of them are listed in Table 4. The critical temperature was determined Table 4. Experimental Isobaric Heat Capacities per unit Volume CpV−1 of Critical Binary Solution {xc[C2mim][NTf2] + (1 − xc)1-Propanol} with xc = 0.133 at Various Temperatures Ta T K 331.001 330.000 329.006 328.005 327.005 326.004 325.003 324.002 323.002 322.001 321.001 320.000 319.000 318.000

CpV−1 −3

T −1

J·cm ·K 2.139 2.134 2.135 2.133 2.131 2.129 2.124 2.125 2.124 2.121 2.117 2.117 2.114 2.113

K 317.005 316.005 315.004 314.003 313.002 312.002 311.001 310.001 309.000 308.000 307.005 306.005 305.004 304.010

CpV−1 −3

J·cm ·K 2.111 2.108 2.108 2.103 2.103 2.102 2.098 2.097 2.098 2.095 2.094 2.090 2.090 2.092

T −1

K 303.001 302.001 301.001 300.000 299.000 298.002 297.002 296.001 295.001 294.000 293.000 292.400

CpV−1 −3

J·cm ·K

Figure 2. Plot of CpV−1 against (T − Tc) for the binary mixture of {x[C2mim][NTf2] + (1 − x) 1-propanol} with the critical composition in the critical region. The inset shows values in the temperature range far away from the critical points.

−1

2.087 2.082 2.101 2.103 2.105 2.122 2.118 2.164 2.448 2.407 2.329 2.328

was then fixed in the following data analysis. We used two fitting routings to analyze the capacity data in the critical region τ = (−0.01 to 0.01) by eq 8 in order to reduce the coupling between the critical exponent α and the amplitude ratio A+/A−: first, we fixed the critical exponent α at its theoretical value of 0.110 to determine A+/A−; second, we fixed the amplitude ratio A+/A− at its theoretical value of 0.53 to determine α. The fitting results are summarized in Table 5 and show that both A+/A− and α are in good consistence with the theoretical values. The capacity data measured in the one-phase region by the Micro DSCIII in this work is more reliable than that measured in the two-phase region because the equipment provided no stir operation.45,46 Therefore, we fitted the experimental data in the temperature range of τ = (0 to 0.01) with eq 8 to obtain Cp0 and A+, and the latter gave the value of A− through A+/A− = 0.53. The results are summarized in Table 5. The critical fluctuation induced background term Bcr then calculated by Bcr = Cp0 − Bbg, which was −0.279 ± 0.004 J·cm−3·K−1. It has been pointed that the A+ value is lower for an ionic solution with the lower value of solvent’s permittivity εr.47 The permittivity of the 1-propanol at the critical temperature of the binary mixture of {x[C2mim][NTf2] + (1 − x)1-propanol} was about 21.0, which was much larger than that of diethyl carbonate in the binary mixture of {[C2mim][NTf2] + diethyl carbonate}.48 It is clearly shown in Table 5 that the A+ values are much larger than the A+ = 0.00022 J·cm−3·K−1 of {[C2mim][NTf2] + diethyl carbonate} which showed Coulombic criticality,47 but similar to A+ = (0.013 to 0.015) J·cm−3·K−1 of the nonionic solvophobic {nitrobenzene + alkane} systems,49 indicating a solvophobic character. Asymmetric Behavior of Coexistence Curves. According to the complete scaling theory,21−23 the width ΔZcxc and the diameter Zd of a coexistence curve can be expressed by

Standard uncertainties u are u(T) = 0.002 K, u(CpV−1) = 0.005 J· cm−3·K−1 in the noncritical region, and u(CpV−1) = 0.04 J·cm−3·K−1 in the near critical single phase region. a

during the process of analysis of the heat capacity data by the method we reported previously,27,28 which was 295.450 K. There is a difference of about 0.25 K from that determined by the coexistence curve measurement reported above, which may be ascribed to the uncontrollable moisture or some other impurities during the sample preparation.40 The plot of CPV−1 against (T − Tc) in the temperature region of (T − Tc) = (−3 K to 3 K) is shown in Figure 2 with the inset representing the dependence of CPV−1 on (T − Tc) in the temperature region of (T − Tc) = (26 K to 36 K), which is far away from the critical point. The isobaric heat capacity per unit volume in the critical region can be represented by A± −α |τ | (8) α where “+” and “−” refer to the one-phase region and two-phase region, respectively; α = 0.110 and Δ = 0.50 are the universal exponents in the 3D-Ising universality class;43 Cp0 is the sum of the regular background heat capacity in the noncritical region Bbg and the critical fluctuation induced background heat capacity Bcr: Cp0 = Bbg + Bcr; τ = (T − Tc)/Tc; E|τ| is the noncritical linear term resulting from the regular term of the free energy. The values of Cp0 and E are taken to be the same in the one-phase and the two-phase region.44 The isobaric heat capacity per unit volume in the noncritical region shown in the inset of Figure 2 can be described by CpV−1 = Bbg + E|τ|. Linear least-squares fit gave Bbg = 2.0701 ± 0.0003 J·cm−3·K−1 and E = 0.562 ± 0.003 J·cm−3·K−1. The value of E CpV −1 = Cp0 + E|τ | +

Z Z Z ΔZcxc ≡ (ZL − ZU)/2 ≈ B0̂ |τ | β (1 + B1̂ |τ |Δ + B2̂ |τ |2β )

(9) L

U

Z +Z − Zc 2 − ⎞ Z Z ⎛ Â ≈ D̂2 |τ |2β + D1̂ ⎜ 0 |τ |1 − α − Bcr̂ |τ |⎟ ⎝1 − α ⎠

ΔZd ≡

(10)

where the subscript “c” denotes the value at the critical point; β, α, and Δ are universal critical exponents;43 Z is the physical D



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Table 5. Critical Parameters in Equation 8 for the Binary Mixture of {x[C2mim][NTf2] + (1 − x)1-Propanol}. The Parameters in the Brackets are Fixed in the Fittings range of τ −0.01−0.01 −0.01−0.01 0− 0.01

A−

A+

Cp0 −3

J·cm ·K

−1

−3

J·cm ·K

1.842 ± 0.002 1.825 ± 0.004 1.791 ± 0.004

−1

0.0173 ± 0.0002 0.0183 ± 0.0002 0.0203 ± 0.0002

J·cm−3·K−1

α

A+/A−

std. dev.

0.0326 ± 0.0004 0.0334 ± 0.0002

0.110 ± 0.001 (0.110) (0.110)

(0.53) 0.54 ± 0.01

0.025 0.024 0.017

Table 6. Values of Critical Amplitudes B̂ Z0 and B̂ Z1 and Critical Exponent β for Coexistence Curves of (T, n), (T, x), (T, ϕ), (T, ρ̂m), and (T, ρ̂m x) of {x[C2mim][NTf2] + (1 − x)1-Propanol}. The Parameters in the Brackets are Fixed in the Fittings Tc − T < 1 K B̂ Z0

order parameter n x ϕ ρ̂m ρ̂mx

0.0345 0.46 0.87 −0.82 0.336

± ± ± ± ±

Tc − T < 1 K B̂ Z0

β 0.0007 0.01 0.02 0.02 0.006

0.323 0.327 0.324 0.324 0.324

± ± ± ± ±

0.003 0.003 0.003 0.003 0.003

0.035 0.457 0.888 −0.832 0.342

density, such as the mole fraction x, the dimensionless molar density ρ̂m, or the dimensionless partial molar density ρ̂mx; Â − = A−Vc/αR is the dimensionless critical amplitude corresponding to the heat capacity in the two-phase region, and B̂ cr = BcrVc/R is the dimensionless critical background of the heat capacity with R being the gas constant. The scaling amplitudes D̂ Z2 and D̂ Z1 are given by B0̂ m = (a1 + a3)B0 |τ0| β

ρ̂ x

B0̂ m = (1 + a3xc)B0 |τ0| β x D̂2 = −

x a1(B0̂ )2 1 − a1xc

ρ̂ D̂2 =

ρ̂ a3(B0̂ m )2 a1 + a3

(11) ρ ̂x D̂2 =

ρ̂ x a3(B0̂ m )2 1 + a3xc

(12) x D1̂ = (b2xc − b4)|τ0|−1

ρ̂ D1̂ m = −(b2 + b3)|τ0|−1

ρ̂ x D1̂ m = −(b4 + b3xc)|τ0|−1

0.001 0.001 0.002 0.002 0.001

β (0.326) (0.326) (0.326) (0.326) (0.326)

(0.035) (0.457) (0.888) (−0.832) (0.342)

B̂ Z0 −0.24 0.53 −0.09 −0.04 −0.05

± ± ± ± ±

0.02 0.02 0.01 0.01 0.01

expressed with the consideration of the correction-to-scaling term B̂ Z1 |τ|Δ. The parameter B̂ Z1 was obtained by fitting the experimental values to eq 9 with β and Δ being fixed at their theoretical values of 0.326 and 0.50 and the values of B̂ Z0 being fixed at the values listed in column 4 of Table 6, respectively. The values of B̂ Z1 are summarized in column 7 of Table 6. Since the binary mixture we studied is incompressible or weakly compressible, this results in a3 ≈ 0 and hence D̂ ρ̂2m ≈ 0 and D̂ ρ̂2mx ≈ 0 from eq 12. Therefore, the experimental data of the diameter for the (T, ρ̂m) and (T, ρ̂mx) coexistence curves were fitted to eq 10 with the D̂ Z2 |τ|2β term being neglected, where Â − and B̂ cr were calculated from the values of A− and Bcr determined in the heat capacity measurements. The obtained values of D̂ ρ̂2m and D̂ ρ̂2mx were −0.145 ± 0.008 and 0.098 ± 0.004, which were then used to calculate the values of D̂ x1 by the ρ̂ x ρ̂ relation of D̂ x1 = D̂ 2m − D̂ 2mxc derived from eq 13. The obtained x value D̂ 1 was 0.117 ± 0.004 and was fixed in fitting the experimental values of the diameter of (T, x) coexistence curves with eq 10 to determine D̂ x2, which gave D̂ x2 = 0.414 ± 0.006. The experimental values of xd and the fitting results from eq 10 are compared in Figure 3, indicating a good agreement with each other. It is proposed that the contribution of the heat capacity related term played an important role in the description of the asymmetric behavior of the diameter of the coexistence curve.27,28 Thus, to verify the important contribution of heat

ρ̂

x

B0̂ = (1 − a1xc)B0 |τ0| β

± ± ± ± ±

Tc − T < 15 K B̂ Z0

(13)

where ai and bi are coefficients in the relations between the physical fields and scaling fields;26 B0 is a constant, and τ0 = 1 − b2(a2/a1). In the region sufficiently close to the critical temperature, the coexistence curve width can be represented by eq 9 with the correction terms being neglected. The width of general density variables n, x, ϕ, ρ̂m, and ρ̂mx in the temperature range |T − Tc| < 1 K were fitted to eq 9 with B̂ Z1 |τ|Δ term and B̂ Z2 |τ|2β term being neglected to get the values of B̂ Z0 and β, which are listed in Table 6. As shown in Table 6, in the temperature range |T − Tc| < 1 K, the values of β of all the order parameters agree well with the theoretical prediction of 0.326, confirming the Ising criticality. Moreover, to get a more precise value of the critical amplitude in the critical region, we fixed the value of β at 0.326 to obtain the values of B̂ Z0 by repeating the fitting procedure for the experimental data in the temperature range |T − Tc| < 1 K with eq 9, which are also listed in Table 6. It shows that the value of B̂ x0 is much higher than that of {[C2mim][NTf2] + diethyl carbonate} (B̂ x0 = 0.08), while being similar to that of ionic solutions with more polar solvents showing solvophobic criticality.47 To better describe coexistence curves in the whole temperature range, the coexistence curve width should be

Figure 3. Plot of diameter xd of coexistence curve (T, x) against τ for {x[C2mim][NTf2] + (1 − x)1-propanol}. The points are experimental data and the line is calculated by eq 10. E



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Table 7. Values of the Asymmetric Parameters a1 system

a1,theoa

a1,exp1b

a1,exp2c

a1,exp3d

[C2mim][NTf2] + 1-propanol

−2.43 ± 0.01

−3.8 ± 0.3

−2.43 ± 0.01

−2.68 ± 0.32

a

a1,theo is the asymmetric parameters a1 calculated by eq 17. ba1,exp1 is the asymmetric parameters a1 calculated by eq 16 without the consideration of heat capacity related term. ca1,exp2 is the asymmetric parameters a1 calculated by eq 15. da1,exp2 is the asymmetric parameters a1 calculated by eq 16 with the consideration of heat capacity related term.

capacity in ionic systems, the experimental data of xd were fitted to eq 10 with a simplified version: x xd ≈ xc + D̂2 |τ |2β

(14)

which was used to analyze the coexistence-curve data when the capacity data were unavailable. The values of D̂ x2 acquired from fitting the experimental data of xd to eq 14 was 0.530 ± 0.008, significantly larger than that considering the contribution of the heat capacity. The hypothesis of the incompressible liquid mixtures results in a3 ≈ 0, hence from eqs 11 and 12, the asymmetric coefficient a1 can be calculated by

Figure 4. Plots of asymmetry coefficient a1 against the solute/solvent molar volume ratio V01,c/V02,c at the critical temperature: ■, calculated from eq 16 with consideration of the heat capacity related term for previously reported systems, □, calculated from eq 16 without consideration of heat capacity related term for previously reported systems; these previously reported systems include {dimethyl carbonate + n-alkane}, {nitrobenzene+ n-alkane}, {benzonitrile + nalkane}, and {dimethyl adipate + n-alkane} reported in references 27, 28, and 50−52; ★, calculated from eq 16 with consideration of the heat capacity related term for {x[C2mim][NTf2] + (1 − x)1propanol}; ☆, calculated from eq 16 without consideration of heat capacity related term for {x[C2mim][NTf2] + (1 − x) 1-propanol}. The solid line refers to the values calculated by eq 17.

ρ̂

a1 =

a1 =

B0̂ m ρ̂ x

B0̂ m

(15) x D̂2

x x D̂2 xc − (B0̂ )2

(16)

With the obtained values of B̂ ρ̂0m, B̂ ρ̂0mx, B̂ x0, and D̂ x2, the values of a1 were calculated by eqs 15 and 16 and are listed in Table 7. According to the complete scaling theory, asymmetric coefficients a1 was related to the ratio of molar volume of two components: 23 0 0 a1 ≈ 1 − V1,c /V 2,c

T* =

(17)

ρ* =

where V01,c and V02,c are the molar volumes of pure [C2mim][NTf2] and 1-propanol at the critical temperature of the binary mixture. The theoretical value of a1 calculated from eq 17 is also listed in Table 7. By comparison of the values of a1 listed in Table 7, it was found that the calculated value based on fitting eq 14 with the contribution of the heat capacity being neglected is significantly larger than the others, while the value calculated from eq 16 with the consideration of heat capacity contribution is in much better consistence with the theoretical one calculated by using eq 17 and the value calculated by eq 15, which confirms that the heat capacity related term plays an important role in describing the asymmetric criticality of the coexistence curve in ionic solutions as what we’ve proved for molecular solutions.27,28 Figure 4 shows the comparison between the values of a1 with and without the consideration of the heat capacity contribution for the systems studied in this work and {dimethyl carbonate + n-alkane}, {nitrobenzene+ n-alkane}, { benzonitrile + n-alkane}, and { dimethyl adipate + n-alkane} reported previously,27,28,50−52 which indicates the significant contribution of heat capacity to the critical asymmetry and the successful application of the complete scaling theory to both molecular and ionic solutions. For the RPM, the thermodynamic state is completely specified by a reduced temperature T* and a reduced ion density ρ*:

4πkTε0εrσ q2 2x ILσ 3NA x ILVIL + (1 − x IL)VS

(18)

(19)

where k is the Boltzmann’s constant, σ = 5.4 Å is the collision diameter for [C2mim][NTf2],53 ε0 is vacuum permittivity, εr is relative permittivity: εr = a + bT + cT2 + dT3 where a, b, c, and d were obtained from CRC Handbook of Chemistry and Physics,48 q is the charge of the ions, NA is the Avogadro number, xIL is the mole fraction of the ionic liquid (IL), VIL and VS are the molar volumes of the IL and the solvent, respectively. Although the RPM is only a crude model of a real ionic solution, it is well applied in distinguishing the solvophobic criticality from the Coulombic criticality.54,55 The calculated values of the critical parameters in terms of the reduced RPM variables for the studied system were Tc* = 0.20 and ρc* = 0.25, which shows significant deviations from Tc* ≈ 0.05 and ρc* ≈ (0.05 to 0.08) for the RPM12 and indicates the solvophobic criticality of the studied system.

■

CONCLUSION We measured the liquid−liquid coexistence curve and the heat capacity for ionic system {x[C2mim][NTf2] + (1 − x)1propanol}. The values of the critical exponents α and β obtained in the critical region confirmed the 3D-Ising universality. The experimental data were used to study the asymmetry of diameter of the coexistence curves in terms of the complete scaling theory. The results suggested that the heat capacity makes an important contribution in describing the F



Article

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asymmetric behavior of the coexistences curve. Moreover, the large values of the critical amplitudes B̂ x0 and A+, and the high RPM reduced critical temperature and density indicated a solvophobic criticality for the studied system.

■

ASSOCIATED CONTENT

S Supporting Information *

The experimental data of heat capacity of {x[C2mim][NTf2] + (1 − x)1-propanol} with concentration in both the critical and noncritical regions. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +86 21 64250804. Fax: +86 21 64250804. E-mail: [email protected] Author Contributions §

M.W. and T.Y. contributed equally to this work as first authors. Funding

This work was supported by the National Natural Science Foundation of China (Projects 21173080, 21373085 and 21303055). Notes

The authors declare no competing financial interest.

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REFERENCES

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