Solubility Measurement and Correlation for Îµ-2,4,6 ... - ACS Publications

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Solubility Measurement and Correlation for ε‑2,4,6,8,10,12Hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane in Five Organic Solvents at Temperatures between 283.15 and 333.15 K and Different Chloralkane + Ethyl Acetate Binary Solvents at Temperatures between 283.15 and 323.15 K Chao Cui, Hui Ren,* Yangfei Huang, and Qingjie Jiao* State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, Beijing, China S Supporting Information *

ABSTRACT: The solubility data of ε-2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (ε-HNIW) in five pure solvents (ethyl acetate, N,N-dimethylformamide, acetonitrile, cyclohexanone, N-methylpyrrolidone) at temperatures ranging from 283.15 to 333.15 K at atmospheric pressure were measured by the isothermal method; meanwhile, the solubility behavior of ε-HNIW in four binary solvents (dichloromethane, chloroform, tetrachloromethane, and 1,2-dichloroethane mixed with various mole fractions of ethyl acetate, respectively) was experimentally studied by the equilibrium method at temperatures ranging from 283.15 to 323.15 K. The experimental data in pure solvents were correlated by the van’t Hoff equation and modified Apelblat equation. It was found that both of them could obtain good correlation results according to relative average deviations, root-mean-square deviations, and correlation coefficients (R2). The solubilities of ε-HNIW in binary solvents were correlated with the modified Apelblat equation, the combined nearly ideal binary solvent/Redlich−Kister (CNIBS/R-K) equation, and the Jouyban−Acree model. For the binary solvents studied, all of the models provide a satisfactory correlation. Commercial methods used to generate ε-HNIW crystals and/ or particles with controlled sizes include the cooling of saturated solutions, precipitation, and evaporation often with a solvent/ antisolvent. The recrystallization of ε-HNIW in various solvents was experimentally studied. However, the solubility of ε-HNIW in different organic solvents and binary solvents has seldom been presented.12,13 Also, experimental data reported in the references for ε-HNIW have been compared graphically in Supporting Information. In this work, we present the solubility of ε-HNIW in ethyl acetate, N,N-dimethylformamide, acetonitrile, cyclohexanone, and N-methylpyrrolidone at temperatures ranging from 283.15 to 333.15 K; meanwhile, the solubility of ε-HNIW in four binary solvents (dichloromethane, chloroform, tetrachloromethane, and 1,2-dichloroethane mixed with various mole fractions of ethyl acetate, respectively) were experimentally studied by the equilibrium method at temperatures ranging from 283.15 to 323.15 K at atmospheric pressure. Furthermore, the van’t Hoff equation and modified Apelblat equation were used to correlate the experimental data in pure solvents, respectively, and the modified Apelblat equation, the combined nearly ideal binary solvent/Redlich−Kister (CNIBS/R-K) equation and the

1. INTRODUCTION HNIW, or 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (C6H6N12O12; CAS Registry No. 135285-90-4), shown in Figure 1, has four crystal polymorphs. Among the four

Figure 1. Chemical structure of HNIW.

polymorphs of HNIW, the best energetic performance is obtained with ε-polymorph. The ε-HNIW is the one with the highest density (ρ = 2.04 g·cm−3) and the greatest stability under ambient conditions.1 Thus, ε-HNIW is most desirable for use in propellant and weapon systems.2−5 The sensitivity of energetic materials mostly depends on the crystal size, morphology, purity, internal and external defects, and microstructure of internal crystalline voids as well as the concomitant presence of polymorphic phases,6−11 which are determined in the crystallization condition. © XXXX American Chemical Society

Received: September 2, 2016 Accepted: March 17, 2017

A

DOI: 10.1021/acs.jced.6b00664 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Description of Materials Used in This Paper IUPAC name

CAS RN

source

mass fraction purity

purification method

analysis method

ε-HNIW β-HMX acetone ethyl acetate N,N-dimethylformamide acetonitrile cyclohexanone N-methylpyrrolidone dichloromethane chloroform tetrachloromethane 1,2-dichloroethane deionized water

135285-90-4 2691-41-0 67-64-1 141-78-6 68-12-2c 75-05-8 108-94-1 872-50-4 75-09-2 67-66-3 56-23-5 107-06-2 7732-18-5

Liaoning Qingyang Chemical Industrial Company Gansu Yinguang Chemical Industrial Company Sinopharm Chemical Reagent Beijing Co., Ltd. Sinopharm Chemical Reagent Beijing Co., Ltd. Sinopharm Chemical Reagent Beijing Co., Ltd. Sinopharm Chemical Reagent Beijing Co., Ltd. Sinopharm Chemical Reagent Beijing Co., Ltd. Sinopharm Chemical Reagent Beijing Co., Ltd. Sinopharm Chemical Reagent Beijing Co., Ltd. Sinopharm Chemical Reagent Beijing Co., Ltd. Sinopharm Chemical Reagent Beijing Co., Ltd. Sinopharm Chemical Reagent Beijing Co., Ltd. Sinopharm Chemical Reagent Beijing Co., Ltd.

>0.995 >0.995 >0.995 >0.995 >0.995 >0.995 >0.995 >0.995 >0.995 >0.995 >0.995 >0.995 none

none none none none none none none none none none none none none

HPLCa HPLCa GCb GCb GCb GCb GCb GCb GCb GCb GCb GCb none

a

High-performance liquid chromatography. bGas liquid chromatography. Both the analysis method and the mass fraction purity were provided by the suppliers.

where mA and mi denote the mass of ε-HNIW and the pure solvent, respectively. MA and Mi stand for the molecular mass, respectively. Each solubility point was repeated three times, and the average value was defined as the solubility. The relative uncertainty of the data was less than 0.05. The powder X-ray diffraction (PXRD) analysis was performed to confirm the crystalline structure of the sample during the measurement. The consistent PXRD patterns indicated that there was ε-polymorph sample used during the experiment, which was shown in Figure 2.

Jouyban−Acree model were used to correlate the experimental data in binary solvents, respectively.

2. EXPERIMENTAL SECTION 2.1. Material. A detailed description of the chemicals used in this work is given in Table 1. ε -HNIW was purchased from Liaoning Qingyang Chemical Industrial Company. All organic solvents, including ethyl acetate, N,N-dimethylformamide, acetonitrile, cyclohexanone, N-methylpyrrolidone, dichloromethane, chloroform, tetrachloromethane, and 1,2-dichloroethane, were analytical grade and purchased from Sinopharm Chemical Reagent Beijing Co., Ltd. (Beijing, China). All chemicals were employed without further purification. 2.2. Solubility Measurements. Two kinds of methods were used to measure the solubility in different solvent systems, which have been described previously in other researchers’ papers.14,15 The solubility of ε-HNIW in five pure solvents was measured by the isothermal method. A 100 mL curved-bottom glass vessel (Type Easymax 102 Basic, Mettler Toledo, Switzerland) and a focused beam reflectance measurement probe (FBRM, Type Particle track G400, Mettler Toledo, Switzerland) was employed during the measurements. The number of particles was measured at 2 s intervals, and the scan speed was 2 m/s. The temperature can be controlled with ±0.1 K accuracy. A known mass of ε-HNIW and solvent was put into the glass vessel. The solution is unsaturated and kept at the given temperature under agitation for 1 h. Then milligrams of ε-HNIW about (0.002 to 0.005) g was added into the vessel successively under the agitation, until the solute could not dissolve completely within 30 min. The criterion of dissolved completely is that particle cannot be detected by the FBRM probe. Subsequently, the gross mass of the ε-HNIW and solvent were used to calculate the mole fraction solubility. To avoid the evaporation of the solvent, a condensing system was employed. All of the masses in the experiment were weighted by the balance (Type AL104 Mettler Toledo, Switzerland) with an accuracy of ±0.0001 g. The mole fraction solubility of ε-HNIW (xA) in pure solvent is calculated by xA =

mA /MA mA /MA + m i /M i

Figure 2. Powder X-ray diffraction patterns for ε-HNIW and sample.

The solubility of ε-HNIW in binary solvents was measured by gravimetric method. A set of 25 mL test tubes (type Easymax 102 Basic Mettler Toledo, Switzerland) were employed to dissolve the solute during the measurements. An excess amount of ε-HNIW was added to the binary solvent mixtures with various mole fractions of ethyl acetate and kept at the given temperature under agitation for 12 h to ensure the solid−liquid equilibrium. Then the agitation was stopped, and the system was kept still for more than 1 h under the given temperature to allow the undissolved particles to settle down. After that, the upper clear solution was filtered through a membrane filter (0.22 μm) and poured into an aluminum foil dish. Subsequently, the aluminum foil dish was put into a drying oven (type AHX-824FB-1, Nanjing University of Science and Technology, China) at 373.15 K until the mass of the aluminum foil dish did not change. All of

(1) B



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3. RESULTS AND DISCUSSION 3.1. Solubility Data. 3.1.1. Pure Solvents. The mole fraction solubility (xA) data of ε-HNIW in ethyl acetate, N,N-dimethylformamide, acetonitrile, cyclohexanone, and N-methylpyrrolidone at temperatures ranging from 283.15 to 333.15 K at atmospheric pressure was recorded in Table 4 and graphically plotted in Figure 4. At the temperature range from 283.15 to 333.15 K, the sequences of the solubility in five solvents are in the following order: N-methylpyrrolidone > cyclohexanone > N,N-dimethylformamide > ethyl acetate > acetonitrile after a cursory glance at Figure 4. However, at the temperature range from 283.15 to 298.15 K, the solubility in ethyl acetate is slightly higher than in N,N-dimethylformamide. The difference may be caused by the nature of the solvent, the intermolecular interactions between the solute and solvent, hydrogen bonding interaction, and so on. The results suggest that the solubility of ε-HNIW in N,Ndimethylformamide, acetonitrile, and cyclohexanone increases with increasing temperature. Nevertheless, the solubility in ethyl acetate and N-methylpyrrolidone decreases very slightly with increasing temperature. In all of the pure solvents, the temperature dependence is very weak, even the negative correlation. Obviously, cooling crystallization may not be used. In general, drowning-out crystallization is the most popular method. Ethyl acetate is the frequently used solvent because the other solvents molecular can easily form adducts with ε-HNIW molecules. 3.1.2. Binary Solvents. The mole fraction solubility (xA) data of ε-HNIW in binary solvents at temperatures ranging from 283.15 to 323.15 K at atmospheric pressure are recorded in Tables 5−8 and graphically plotted in Figures 5−8. The results suggest that the solubility of ε-HNIW decreases slightly with an increasing temperature at low mole fractions of chloralkane, then increases slightly with increasing temperature when the mole fraction of chloralkane increases to a certain value. The solubility of ε-HNIW decreases monotonically with the increase of the initial mole fraction of chloralkane at different dropping rates. The polarity of the solvent follows the order chloroform > dichloromethane >1,2-dichloroethane > tetrachloromethane. The solubility of ε-HNIW dropping rate increases with the increasing polarity of the solvent. The sequence of dropping rate in binary solvents is listed as follows: chloroform > dichloromethane > 1,2-dichloroethane > tetrachloromethane. The solubility of ε-HNIW in binary solvents may be caused also by the temperature, the composition of the binary solvents, the intermolecular interactions, and so on. 3.2. Correlation of the Solubility Data. 3.2.1. van’t Hoff Equation. The van’t Hoff equation reveals the relationship between the mole fraction solubility of a solute and the absolute temperature for real solutions. The temperature dependence of the solubility of ε-HNIW in pure solvent can be correlated by the following equation

the masses in the experiment were weighted by the balance (type AL104 Mettler Toledo, Switzerland) with an accuracy of ±0.0001 g. The mole fraction solubility of ε-HNIW (xA) in binary solvent mixtures is calculated by xA =

mA /MA mA /MA + mB /MB + mC /MC

(2)

where mA, mB, and mC denote the mass of ε-HNIW, chloralkane, and ethyl acetate, respectively. MA, MB, and MC stand for the molecular mass, respectively. The initial mole fraction (xB0) of chloralkane in binary solvent mixtures is defined as x B0 =

mB /MB mB /MB + mC /MC

(3)

where mB and mC represent the mass of chloralkane and ethyl acetate, respectively. MB and MC represent the same meanings as eq 2. Each solubility point was repeated three times, and the average value was defined as the solubility. The relative uncertainty of the data was less than 0.05. The powder X-ray diffraction (PXRD) analysis was performed to determine the crystalline structure of the sample during the measurement. The consistent PXRD patterns indicated that there was no phase transition during the experiment, which was shown in Figure 3.

Figure 3. Powder X-ray diffraction patterns for ε-HNIW before/after measurement.

To verify the two kinds of methods’ validity, two sets of verification measurements were done in which the mole fraction solubility of HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) in N-methylpyrrolidone and the solubility of HMX in acetone + water were measured. The solubility values and relative deviation of measurement and refs 15−16 are shown in Tables 2 and 3. The results indicated the two methods used in this work have been validated.

ln xA = −

ΔHsoln ΔSsoln + RT R

(4)

Table 2. Experimental Solubility of HMX, xA(exp.), and the Reference Data, xARef 16), in N-Methylpyrrolidone at Different Temperatures and Pressure P = 0.1 MPaa T/K 100xA(exp.) 100xA(ref 15) relative deviation/% a

273.0

288.0

303.0

318.0

333.0

348.0

2.2741 2.1037 8.1

4.0962 3.8863 5.4

6.0014 5.5931 7.3

7.3385 7.5733 −3.1

9.8414 9.4447 4.2

11.9565 12.403 −3.6

The standard uncertainty u is u(T) = 0.1 K; the relative uncertainties ur are ur(xA) = 0.05, ur(p) = 0.05. C



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Table 3. Experimental Solubility of HMX, xA(exp.), and the Reference Data, xA(Ref 16), in Binary Solvent Mixtures of Water (B) + Acetone (C) at Different Temperatures and Pressure P = 0.1 MPaa 103 xA(ref 16)

xB0

103 xA(exp.)

103 xA(ref 16)

xB

RD/%

T = 293.15 K 0 0.1381 0.2871 0.4462 0.5707 0.6682 0.7632 0.8754

4.4879 4.1707 2.7800 1.5823 0.7073 0.3217 0.0951 0.0129

103 xA(exp.)

RD/%

4.8426 4.5390 3.1170 1.7805 0.8618 0.3921 0.1361 0.0214

0.741 0.805 0.850 0.724 0.875 0.773 0.919 0.862

T = 298.15 K 4.5283 4.2016 2.7977 1.5938 0.7134 0.3248 0.0958 0.0130

0.901 0.741 0.636 0.725 0.867 0.963 0.737 0.722

0 0.1381 0.2871 0.4462 0.5707 0.6682 0.7632 0.8754

4.8070 4.5027 3.0907 1.7677 0.8543 0.3891 0.1349 0.0212

a

xB0, xA(ref 16), and xA(exp.) represent the initial mole fraction of water in the binary mixtures, the experimental data, and the reference data, respectively. The standard uncertainty of T is u(T) = 0.1 K. The relative uncertainty of pressure is ur(P) = 0.05. The relative standard uncertainty of the solvent composition is ur(xB0) = 0.005. The relative standard uncertainty of the solubility measurement is ur(xA,exp) = 0.05.

Table 4. Experimental and Correlated Mole Fraction Solubilitiy (xA) of ε-HNIW in Different Pure Solvents at Different Temperature and Pressure p = 0.1 MPaa van’t Hoff equation T/K

a

100xA,exp

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

20.874 20.748 20.632 20.585 20.506 20.416 20.344 20.221 20.156 20.076 20.013

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

15.862 15.900 15.940 15.991 16.031 16.055 16.079 16.094 16.125 16.163 16.201

283.15 288.15 293.15 298.15 303.15

9.161 9.365 9.742 10.188 10.441

100xA,cal

100RD

N-Methylpyrrolidone 20.863 0.056 20.763 −0.073 20.667 −0.172 20.575 0.051 20.486 0.097 20.400 0.081 20.317 0.132 20.238 −0.085 20.161 −0.024 20.086 −0.052 20.015 −0.010 Cyclohexanone 15.871 −0.051 15.908 −0.049 15.944 −0.025 15.979 0.080 16.012 0.117 16.045 0.061 16.077 0.011 16.108 −0.083 16.138 −0.080 16.167 −0.022 16.195 0.039 N,N-Dimethylformamide 9.202 −0.452 9.483 −1.261 9.763 −0.208 10.041 1.447 10.317 1.188

van’t Hoff equation

Apelblat equation 100xA,cal

T/K

100RD

20.854 20.760 20.668 20.579 20.491 20.406 20.322 20.241 20.161 20.083 20.006

0.099 −0.058 −0.177 0.031 0.070 0.052 0.108 −0.100 −0.025 −0.033 0.032

15.869 15.907 15.944 15.980 16.014 16.046 16.078 16.108 16.138 16.166 16.193

−0.038 −0.045 −0.027 0.074 0.109 0.052 0.003 −0.087 −0.079 −0.016 0.053

9.137 9.458 9.770 10.071 10.361

0.259 −0.997 −0.281 1.153 0.771

100xA,exp

308.15 313.15 318.15 323.15 328.15 333.15

10.644 10.895 11.093 11.297 11.623 11.965

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

4.328 4.696 4.981 5.294 5.593 5.790 6.073 6.411 6.842 7.220 7.575

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

9.928 9.901 9.885 9.851 9.812 9.771 9.751 9.713 9.693 9.663 9.641

100xA,cal

100RD

N,N-Dimethylformamide 10.592 0.493 10.865 0.275 11.136 −0.385 11.405 −0.957 11.672 −0.416 11.937 0.240 Acetonitrile 4.374 −1.051 4.656 0.865 4.945 0.718 5.242 0.974 5.546 0.839 5.857 −1.168 6.175 −1.675 6.499 −1.374 6.830 0.178 7.166 0.752 7.508 0.885 Ethyl Acetate 9.941 −0.128 9.906 −0.047 9.872 0.132 9.839 0.119 9.808 0.046 9.777 −0.062 9.748 0.033 9.720 −0.072 9.693 0.003 9.666 −0.033 9.641 0.008

Apelblat equation 100xA,cal

100RD

10.639 10.907 11.163 11.407 11.639 11.860

0.046 −0.113 −0.630 −0.976 −0.138 0.880

4.392 4.663 4.943 5.233 5.532 5.841 6.161 6.490 6.829 7.179 7.538

−1.471 0.721 0.771 1.160 1.095 −0.893 −1.439 −1.231 0.180 0.572 0.481

9.935 9.904 9.872 9.842 9.811 9.781 9.751 9.722 9.693 9.664 9.636

−0.074 −0.027 0.125 0.095 0.012 −0.098 0.003 −0.091 0.003 −0.009 0.061

The standard uncertainty u is u(T) = 0.1 K; the relative uncertainty ur are ur(xA) = 0.05, ur(p) = 0.05.

where xA is the mole fraction solubility and ΔHsoln and ΔSsoln are the van’t Hoff enthalpy and entropy of solution, respectively.17−19 T is the experimental temperature, and R is the gas constant. Equation 4 can be further simplified as follows ln xA =

a +b T

3.2.2. Modified Apelblat Equation. The modified Apelblat equation is a semiempirical expression for the solubility of a solid in a solution based on solid−liquid equilibrium theory. The relationship between solubility of ε-HNIW and temperature is correlated with the modified Apelblat equation

(5)

ln xA = A +

where a and b are the model constants. D

B + C ln T T

(6) DOI: 10.1021/acs.jced.6b00664 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


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Table 5. Experimental (xA,exp) and Correlated (xA, al) Mole Fraction Solubility Data of ε-HNIW in Binary Solvent Mixtures of Dichloromethane + Ethyl Acetate (P = 0.1 MPa)a 102 xA,cal xB

Figure 4. Mole fraction solubility, xA,exp, of ε-HNIW in pure solvents. ■, N-methylpyrrolidone; ●, cyclohexanone; ▲, N,N-dimethylformamide; ▼, acetonitrile; ◆, ethyl acetate.

where T is the experimental temperature and A, B, and C are the model parameters.20 The values of A and B represent the effect of solution on the solubility. The value of C reflects the effect of temperature on the fusion enthalpy. 3.2.3. CNIBS/R-K Model. The CNIBS/R-K model describes the solubility of solute in binary solvents varies with binary solvent composition, which was suggested by Acree and his co-workers21−24 N

ln xA = x B0 ln(xA )B + xC0 ln(xA )C + x B0xC0 ∑ Si(x B0 − xC0)i i=1

(7)

where xB0 and xC0 refer to the initial mole fraction of the mixtures on the absence of the solute. (xA)B and (xA)C are the solubilities of the solute in pure solvents B and C, respectively. For the binary solvents, N = 2 and eq 4 can be further simplified as eq 8. ln xA = B0 + B1x B0 + B2 (x B0)2 + B3(x B0)3 + B4 (x B0)4

(8)

where B0, B1, B2, B3, and B4 are the model parameters. 3.2.4. Jouyban−Acree Model. The basic Jouyban−Acree model is widely used to describe both composition and temperature effects on the solubility of solute in binary solvents, which was proposed by Jouyban-Gharamaleki and his co-workers.25 The model equation can be written as ln xA,T = x B0 ln(xA )B,T + xC0 ln(xA )C,T N

+

x B0xC0

∑

Ji (x B0 − xC0)i

i=0

T

(9)

where Ji is the model parameter and the other symbols represent the same meanings as eq 8. The solubility of the solute in pure solvents, (xA)B and (xA)C, can be obtained from the modified Apelblat equation ln xA = A +

B + C ln T T

0

2

10 xA,exp

0.00 0.14 0.28 0.40 0.50 0.60 0.70 0.78 0.86

9.9280 7.1560 4.9854 3.1705 1.7575 0.9615 0.4214 0.1439 0.0441

0.00 0.14 0.28 0.40 0.50 0.60 0.70 0.78 0.86

9.9009 7.0696 4.8661 3.1505 1.7540 0.9640 0.4704 0.1741 0.0534

0.00 0.14 0.28 0.40 0.50 0.60 0.70 0.78 0.86

9.8848 7.0560 4.7789 3.0611 1.8105 0.9702 0.4765 0.2089 0.0680

0.00 0.14 0.28 0.40 0.50 0.60 0.70 0.78 0.86

9.8509 7.1013 4.8690 3.1146 1.9031 1.0356 0.5064 0.2243 0.0729

0.00 0.14 0.28 0.40 0.50 0.60 0.70 0.78 0.86

9.8122 7.1632 4.9225 3.1590 2.0142 1.1232 0.5410 0.2440 0.0753

modified Apelblat

CNIBS/R-K

T = 283.15 K 9.9339 7.1516 4.9851 3.1822 1.7184 0.9643 0.4267 0.1437 0.0435 T = 288.15 K 9.9055 7.0777 4.8566 3.1164 1.7819 0.9555 0.4561 0.1759 0.0556 T = 293.15 K 9.8762 7.0584 4.8096 3.0925 1.8465 0.9785 0.4844 0.2049 0.0659 T = 298.15 K 9.8461 7.0896 4.8366 3.1068 1.9121 1.0333 0.5114 0.2279 0.0729 T = 303.15 K 9.8153 7.1688 4.9338 3.1574 1.9788 1.1229 0.5368 0.2428 0.0757

Jouyban−Acree

9.9080 7.2316 4.9119 3.1382 1.8324 0.9411 0.4108 0.1485 0.0437

10.5836 7.4619 4.7952 2.9553 1.7147 0.8983 0.4068 0.1536 0.0471

9.8435 7.2281 4.7942 3.0470 1.8230 0.9825 0.4553 0.1744 0.0537

9.9327 7.2109 4.7686 3.0209 1.8005 0.9693 0.4516 0.1758 0.0557

9.8401 7.1658 4.7429 3.0096 1.8093 0.9955 0.4829 0.2001 0.0692

9.5808 7.0939 4.7857 3.0914 1.8789 1.0323 0.4917 0.1961 0.0639

9.8126 7.2020 4.8158 3.0975 1.8903 1.0546 0.5168 0.2151 0.0741

9.4812 7.0961 4.8440 3.1670 1.9493 1.0861 0.5257 0.2137 0.0711

9.7803 7.2503 4.8630 3.1735 1.9839 1.1335 0.5623 0.2316 0.0767

9.6100 7.2099 4.9422 3.2476 2.0114 1.1297 0.5526 0.2276 0.0771

a

(10)

xB0, xA,exp, and xA,cal represent the initial mole fraction in the binary mixtures, the experimental data, and the calculated data, respectively. The standard uncertainty of T is u(T) = 0.1 K. The relative uncertainty of pressure is ur(P) = 0.05. The relative standard uncertainty of the solvent composition is ur(xB0) = 0.005. The relative standard uncertainty of the solubility measurement is ur(xA,exp) = 0.05.

When combining them with eq 11 and substituting xC0 with (1 − xB0), a new equation (called Apel-JA equation) can be obtained and further simplified by introducing a set of constants as follows:26 E



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Table 6. Experimental (xA,exp) and Correlated (xA,cal) Mole Fraction Solubility Data of ε-HNIW in Binary Solvent Mixtures of Chloroform + Ethyl Acetate (P = 0.1 MPa)a 102 xA,cal 2

xB0

10 xA,exp

0.00 0.12 0.23 0.34 0.45 0.55 0.65 0.74 0.83

9.9280 7.0960 4.9257 2.7430 1.4944 0.6515 0.2197 0.0613 0.0125

0.00 0.12 0.23 0.34 0.45 0.55 0.65 0.74 0.83

9.9009 7.0882 4.7948 2.9222 1.4139 0.6625 0.2372 0.0622 0.0131

0.00 0.12 0.23 0.34 0.45 0.55 0.65 0.74 0.83

9.8848 7.0830 4.7580 2.9049 1.5056 0.6362 0.2425 0.0680 0.0142

0.00 0.12 0.23 0.34 0.45 0.55 0.65 0.74 0.83

9.8509 7.0883 4.7676 2.8949 1.4631 0.6418 0.2447 0.0731 0.0163

0.00 0.12 0.23 0.34

9.8122 7.0925 4.7669 2.9883

modified Apelblat T= 9.9323 7.0929 4.8988 2.8278 1.4808 0.6613 0.2285 0.0613 0.0125 T= 9.9037 7.0900 4.8266 2.8394 1.4588 0.6424 0.2284 0.0636 0.0132 T= 9.8743 7.0883 4.7796 2.8622 1.4549 0.6385 0.2334 0.0669 0.0142 T= 9.8443 7.0878 4.7556 2.8956 1.4677 0.6481 0.2432 0.0714 0.0156 T= 9.8136 7.0883 4.7527 2.9394

102 xA,cal 0

2

Jouyban−Acree

xB

9.9125 7.1770 4.7747 2.8492 1.4761 0.6402 0.2239 0.0609 0.0125

10.0724 7.2608 4.7800 2.8307 1.4652 0.6393 0.2260 0.0622 0.0128

0.45 0.55 0.65 0.74 0.83

1.4801 0.6661 0.2487 0.0777 0.0167

9.8710 7.1716 4.7598 2.8435 1.4846 0.6524 0.2315 0.0637 0.0130

10.0307 7.2011 4.7306 2.8017 1.4543 0.6384 0.2280 0.0637 0.0134

0.00 0.12 0.23 0.34 0.45 0.55 0.65 0.74 0.83

9.7714 7.0883 4.7819 2.9799 1.5295 0.6933 0.2683 0.0823 0.0203

9.9739 7.1570 4.7078 2.7975 1.4605 0.6469 0.2339 0.0665 0.0143

9.9739 7.1570 4.7078 2.7975 1.4605 0.6469 0.2339 0.0665 0.0143

0.00 0.12 0.23 0.34 0.45 0.55 0.65 0.74 0.83

9.7514 7.0944 4.8103 2.9693 1.6099 0.7844 0.3133 0.0924 0.0217

9.7976 7.1992 4.7585 2.8217 1.4731 0.6581 0.2433 0.0719 0.0164

9.9031 7.1272 4.7094 2.8162 1.4830 0.6644 0.2439 0.0706 0.0156

0.00 0.12 0.23 0.34 0.45 0.55 0.65 0.74 0.83

9.7129 7.0959 4.8362 3.0089 1.7038 0.8308 0.3435 0.1033 0.0258

9.7465 7.2154 4.7953 2.8616

9.8198 7.1107 4.7339 2.8568

0.00 0.12 0.23 0.34 0.45 0.55 0.65 0.74 0.83

9.6930 7.0978 4.9349 3.3595 1.7620 0.9089 0.3871 0.1191 0.0315

CNIBS/R-K

10 xA,exp

modified Apelblat

283.15 K

288.15 K

293.15 K

298.15 K

303.15 K

T= 1.4966 0.6711 0.2582 0.0772 0.0174 T= 9.7823 7.0898 4.7696 2.9932 1.5414 0.7078 0.2789 0.0844 0.0196 T= 9.7506 7.0922 4.8051 3.0571 1.6025 0.7596 0.3062 0.0932 0.0225 T= 9.7185 7.0955 4.8585 3.1310 1.6806 0.8284 0.3413 0.1041 0.0262 T= 9.6859 7.0996 4.9294 3.2149 1.7771 0.9173 0.3858 0.1173 0.0308

CNIBS/R-K

Jouyban−Acree

303.15 K 1.5057 0.6782 0.2525 0.0748 0.0170

1.5213 0.6911 0.2581 0.0763 0.0173

9.7495 7.1260 4.8061 2.9144 1.5477 0.7018 0.2655 0.0821 0.0204

9.7250 7.1065 4.7802 2.9189 1.5757 0.7274 0.2769 0.0838 0.0195

9.7467 7.1182 4.7845 2.9559 1.6372 0.7816 0.3069 0.0943 0.0216

9.6199 7.1139 4.8474 3.0023 1.6467 0.7741 0.3009 0.0933 0.0223

9.7283 7.0746 4.8185 3.0315 1.7100 0.8318 0.3343 0.1062 0.0256

9.5057 7.1321 4.9352 3.1074 1.7354 0.8323 0.3310 0.1054 0.0259

9.6761 7.1261 4.9863 3.2158 1.8463 0.9106 0.3725 0.1224 0.0313

9.3834 7.1606 5.0432 3.2351 1.8433 0.9037 0.3683 0.1205 0.0306

308.15 K

313.15 K

318.15 K

323.15 K

a 0 xB , xA,exp, and xA,cal represent the initial mole fraction in the binary mixtures, the experimental data, and the calculated data, respectively. The standard uncertainty of T is u(T) = 0.1 K. The relative uncertainty of pressure is ur(P) = 0.05. The relative standard uncertainty of the solvent composition is ur(xB0) = 0.005. The relative standard uncertainty of the solubility measurement is ur(xA,exp) = 0.05.

x0 (x 0)2 V2 + V3 ln T + V4x B0 + V5 B + V6 B T T T 0 3 0 4 (x ) (x ) + V7 B + V8 B + V9x B0 ln T (11) T T

The relative deviations (RD) between the experimental values and the calculated values are also presented in Table 4. The RD is calculated by

ln xA = V1 +

RD =

where V1, V2, V3, V4, V5, V6, V7, V8, and V9 are the model

xexp − xcal xexp

(12)

The relative average deviation (ARD) is employed to evaluate the error of different models and is defined as

parameters. F



Article

Table 7. Experimental (xA,exp) and Correlated (xA,cal) Mole Fraction Solubility Data of ε-HNIW in Binary Solvent Mixtures of Tetrachloromethane + Ethyl Acetate (P = 0.1 MPa)a xA,cal

xA,cal xB0

xA,exp

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

9.9280 8.5315 6.7993 5.2567 3.8028 2.5413 1.4167 0.6053 0.1372

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

9.9009 8.5149 6.6524 5.1767 3.7373 2.5592 1.4383 0.6240 0.1451

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

9.8848 8.2836 6.7025 5.1315 3.7340 2.4891 1.4328 0.6358 0.1541

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

9.8509 8.1888 6.6549 5.1156 3.7056 2.4952 1.4463 0.6503 0.1687

0.00 0.10 0.20 0.30

9.8122 8.0640 6.6062 4.8600


Jouyban−Acree

xB0

xA,exp

9.8730 8.6412 6.8153 5.1641 3.7883 2.5659 1.4504 0.5869 0.1385

10.2074 8.7330 6.7950 5.1109 3.7380 2.5343 1.4407 0.5902 0.1425

0.40 0.50 0.60 0.70 0.80

3.6485 2.4814 1.4902 0.6646 0.1769

9.8683 8.5628 6.7108 5.0776 3.7425 2.5632 1.4728 0.6077 0.1463

9.9665 8.5499 6.6815 5.0504 3.7138 2.5349 1.4552 0.6055 0.1498

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

9.7714 8.0134 6.6129 4.8579 3.6375 2.5398 1.4922 0.6460 0.1820

9.8011 8.4732 6.6564 5.0439 3.7115 2.5353 1.4613 0.6150 0.1558

9.7888 8.4122 6.5960 5.0053 3.6969 2.5377 1.4695 0.6201 0.1570

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

9.7514 8.0192 6.5729 4.8232 3.6705 2.4984 1.5024 0.6957 0.1793

9.7711 8.3739 6.6003 5.0259 3.7054 2.5321 1.4680 0.6328 0.1703

9.6672 8.3151 6.5358 4.9744 3.6868 2.5426 1.4834 0.6341 0.1640

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

9.7129 8.1866 6.4998 4.9071 3.7293 2.6026 1.4978 0.6940 0.1865

9.7404 8.2666 6.4439 4.8855

9.5964 8.2548 6.4986 4.9565

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

9.6930 8.2910 6.6029 5.1159 3.7756 2.6144 1.5539 0.7172 0.1924

CNIBS/R-K

modified Apelblat T= 3.6631 2.4972 1.4711 0.6575 0.1736 T= 9.7823 8.0924 6.5662 4.9064 3.6673 2.5122 1.4868 0.6706 0.1799 T= 9.7506 8.1031 6.5508 4.9160 3.6861 2.5379 1.5036 0.6842 0.1847 T= 9.7185 8.1488 6.5419 4.9517 3.7188 2.5740 1.5213 0.6984 0.1880 T= 9.6859 8.2279 6.5389 5.0124 3.7648 2.6203 1.5399 0.7130 0.1899

283.15 K

288.15 K

293.15 K

298.15 K

303.15 K

CNIBS/R-K

Jouyban−Acree

303.15 K 3.6243 2.5177 1.4928 0.6566 0.1777

3.6829 2.5494 1.4971 0.6474 0.1708

9.7313 8.1627 6.4235 4.9261 3.6654 2.5274 1.4813 0.6506 0.1817

9.5722 8.2283 6.4826 4.9507 3.6848 2.5581 1.5106 0.6601 0.1774

9.6654 8.2482 6.4096 4.8510 3.6157 2.5408 1.5275 0.6768 0.1809

9.5912 8.2331 6.4864 4.9561 3.6922 2.5685 1.5237 0.6722 0.1838

9.6983 8.2244 6.4617 4.9471 3.6988 2.5819 1.5364 0.6805 0.1874

9.6511 8.2673 6.5087 4.9720 3.7048 2.5805 1.5367 0.6837 0.1900

9.6535 8.3716 6.6095 5.0499 3.7682 2.6348 1.5766 0.7026 0.1937

9.7500 8.3295 6.5486 4.9979 3.7223 2.5941 1.5494 0.6945 0.1959

308.15 K

313.15 K

318.15 K

323.15 K


ARD =

1 N

N

∑ i=1

xAexp − xAcal xAexp

⎡1 RMSD = ⎢ ⎢⎣ N

(13)

Furthermore, the root-mean-square deviation (RMSD) is used to evaluate the accuracy and predictability of the models and is defined as

⎤1/2

N

∑ i=1

(xAexp

−

xAcal)2 ⎥ ⎥⎦

(14)

where xexp denotes the experimental solubility valves, xcal stands for the calculated solubility values, and N is the number of experimental points. The correlation results of the models mentioned G



Article

Table 8. Experimental (xA,exp) and Correlated (xA, cal) Mole Fraction Solubility Data of ε-HNIW in Binary Solvent Mixtures of 1,2-Dichloroethane + Ethyl Acetate (P = 0.1 MPa)a 102 xA,cal 2

xB0

10 xA,exp

0.00 0.12 0.24 0.35 0.45 0.55 0.65 0.74 0.83

9.9280 7.7944 5.9665 4.5008 3.3006 2.1732 1.1577 0.4571 0.1067

0.00 0.12 0.24 0.35 0.45 0.55 0.65 0.74 0.83

9.9009 7.7066 5.8493 4.1969 2.8263 1.8172 0.9229 0.3721 0.0806

0.00 0.12 0.24 0.35 0.45 0.55 0.65 0.74 0.83

9.8848 7.7047 5.8131 4.1555 2.7662 1.7504 0.8780 0.2839 0.0703

0.00 0.12 0.24 0.35 0.45 0.55 0.65 0.74 0.83

9.8509 7.5756 5.7294 4.0938 2.7672 1.6539 0.8166 0.2867 0.0618

0.00 0.12 0.24 0.35

9.8122 7.4942 5.6987 4.0745


102 xA,cal 0

2

Jouyban−Acree

xB

9.8957 7.8753 5.9291 4.4755 3.2967 2.1878 1.1721 0.4479 0.1075

9.1520 7.7919 6.1094 4.6932 3.4532 2.2576 1.1805 0.4382 0.1021

0.45 0.55 0.65 0.74 0.83

2.7855 1.6120 0.7715 0.2660 0.0633

9.8094 7.9412 5.7444 4.0989 2.8676 1.8294 0.9520 0.3542 0.0821

9.6580 7.8051 5.8319 4.2809 3.0187 1.8991 0.9612 0.3480 0.0798

0.00 0.12 0.24 0.35 0.45 0.55 0.65 0.74 0.83

9.7714 7.5629 5.7802 4.1348 2.7943 1.6707 0.8479 0.3122 0.0707

9.8876 7.7342 5.7360 4.1587 2.8539 1.7272 0.8411 0.2979 0.0693

10.0124 7.8120 5.6531 4.0266 2.7614 1.6953 0.8415 0.3009 0.0688

0.00 0.12 0.24 0.35 0.45 0.55 0.65 0.74 0.83

9.7514 7.5959 5.8635 4.2043 2.8373 1.7391 0.9116 0.3745 0.0831

9.7984 7.7139 5.6522 4.0557 2.7754 1.6817 0.8155 0.2824 0.0622

10.2087 7.8130 5.5587 3.8977 2.6356 1.5997 0.7885 0.2818 0.0649

0.00 0.12 0.24 0.35 0.45 0.55 0.65 0.74 0.83

9.7129 7.6534 5.9840 4.3057 2.9992 1.9493 1.0927 0.4477 0.1190

9.7991 7.5385 5.6452 4.1029

10.2484 7.8084 5.5396 3.8757

0.00 0.12 0.24 0.35 0.45 0.55 0.65 0.74 0.83

9.6930 7.7456 6.1489 4.5435 3.6772 2.3531 1.3835 0.5910 0.1594

CNIBS/R-K

10 xA,exp

283.15 K

288.15 K

293.15 K

298.15 K

303.15 K

modified Apelblat T= 2.6939 1.6107 0.7937 0.2807 0.0637 T= 9.7823 7.5629 5.7802 4.1130 2.7719 1.6659 0.8405 0.3057 0.0711 T= 9.7506 7.5959 5.8635 4.2026 2.9281 1.7893 0.9387 0.3583 0.0864 T= 9.7185 7.6534 5.9840 4.3406 3.1700 1.9909 1.1018 0.4496 0.1136 T= 9.6859 7.7342 6.1418 4.5286 3.5119 2.2897 1.3549 0.6017 0.1609

CNIBS/R-K

Jouyban−Acree

303.15 K 2.7706 1.6255 0.7657 0.2667 0.0633

2.6173 1.5899 0.7873 0.2842 0.0666

9.7044 7.7374 5.6896 4.0818 2.7982 1.7111 0.8479 0.3053 0.0714

10.1397 7.7987 5.5903 3.9519 2.6975 1.6589 0.8342 0.3073 0.0741

9.6362 7.8864 5.7422 4.0912 2.8407 1.7977 0.9345 0.3528 0.0850

9.8964 7.7841 5.7080 4.1254 2.8786 1.8114 0.9345 0.3547 0.0886

9.6369 7.8715 5.8365 4.2579 3.0344 1.9848 1.0838 0.4420 0.1198

9.5366 7.7651 5.8926 4.4026 3.1735 2.0639 1.1027 0.4352 0.1137

9.6650 7.8339 6.0364 4.6647 3.5298 2.4339 1.3849 0.5813 0.1604

9.0807 7.7419 6.1462 4.7964 3.6071 2.4475 1.3664 0.5653 0.1556

308.15 K

313.15 K

318.15 K

323.15 K


van’t Hoff equation and the modified Apelblat equation can be used for model research. From Tables S3−5, the calculated data obtained from the modified Apelblat equation, the CNIBS/R-K equation, and the Jouyban−Acree model are in good agreement with the measured data. For the binary solvents, the modified Apelblat equation, CNIBS/R-K equation, and the Jouyban−Acree model all were found to provide a satisfactory correlation.

above and the values of the ARD and RMSD are listed in Supporting Information, Tables S1, S2, S3, S4, and S5, respectively. From Tables S1 and S2, the calculated data obtained from the van’t Hoff equation and modified Apelblat equation are in good agreement with the measured data according to small ARDs, RSMDs, and correlation coefficients (R2). Therefore, both the H



Article

Figure 5. Mole fraction solubility, xA,exp, of ε-HNIW in dichloromethane−ethyl acetate: ■, 0; ●, 0.14; ▲, 0.28; ▼, 0.4; ◆, 0.5; ◀, 0.6; ▶, 0.7; ⬢, 0.78; ★, 0.86 in mole fraction of dichloromethane.

Figure 8. Mole fraction solubility, xA,exp, of ε-HNIW in 1,2-dichloroethane−ethyl acetate: ■, 0; ●, 0.12; ▲, 0.24; ▼, 0.35; ◆, 0.45; ◀, 0.55; ▶, 0.65; ⬢, 0.74; ★, 0.83 in mole fraction of 1,2-dichloroethane.

Figure 6. Mole fraction solubility, xA,exp, of ε-HNIW in chloroform− ethyl acetate: ■, 0; ●, 0.12; ▲, 0.23; ▼, 0.34; ◆, 0.45; ◀, 0.55; ▶, 0.65; ⬢, 0.74; ★, 0.83 in mole fraction of chloroform.

4. CONCLUSIONS The solubility data of ε-HNIW in ethyl acetate, N,N-dimethylformamide, acetonitrile, cyclohexanone, and N-methylpyrrolidone have been measured at temperatures ranging from 283.15 to 333.15 K; meanwhile, the solubility data in four kinds of chloralkane + ethyl acetate binary solvents (dichloromethane, chloroform, tetrachloromethane, and 1,2-dichloroethane mixed with various mole fractions of ethyl acetate, respectively) have been measured over the temperatures ranging from 283.15 to 323.15 K. The following conclusions were obtained: (1) the solubility of ε-HNIW in N,N-dimethylformamide, acetonitrile, and cyclohexanone increases with increasing temperature; the solubility in ethyl acetate and N-methylpyrrolidone decreases very slightly with increasing temperature; (2) in all of the pure solvents, the temperature dependence is very weak, even having a negative correlation; (3) at the temperature range from 293.15 to 333.15 K, the sequences of the solubility in five solvents are in the general trend: N-methylpyrrolidone > cyclohexanone > N,N-dimethylformamide > ethyl acetate > acetonitrile. However, at the temperature range from 283.15 to 298.15 K, the solubility in ethyl acetate is slightly higher than in N,N-dimethylformamide; (4) the experimental data were correlated by the van’t Hoff equation and modified Apelblat equation, and the corresponding parameters were derived; both of the van’t Hoff Equation, modified Apelblat equation can be used for model research; (5) in all of the binary solvents, the solubility of ε-HNIW decreases slightly with increasing temperature at low mole fractions of chloralkane, then increasing slightly with increasing temperature when the mole fraction of chloralkane increasing to a certain value; (6) in all of the binary solvents, the solubility of ε-HNIW decreases monotonically with the increase of the initial mole fraction of chloralkane at different dropping rates. The sequences of the dropping rate in binary solvents are listed as follows: chloroform > dichloromethane > 1,2-dichloroethane > tetrachloromethane; (7) the modified Apelblat equation, CNIBS/R-K equation, and the Jouyban−Acree model all were found to provide a satisfactory correlation. The modified Apelblat equation was found to be best.

■

ASSOCIATED CONTENT

S Supporting Information *

Figure 7. Mole fraction solubility, xA,exp, of ε-HNIW in tetrachloromethane−ethyl acetate: ■, 0; ●, 0.1; ▲, 0.2; ▼, 0.3; ◆, 0.4; ◀, 0.5; ▶, 0.6; ⬢, 0.7; ★, 0.8 in mole fraction of tetrachloromethane.

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00664. I



■

Article

(16) Chen, L.; Zhang, J.; Wang, W.; Diao, Y. Solubility of β-HMX in Acetone + Water Mixed Solvent Systems at Temperatures from 293.15 to 313.15 K. J. Solution Chem. 2012, 41, 1265−1270. (17) Aldabaibeh, N.; Jones, M. J.; Myerson, A. S.; Ulrich, J. The solubility of orthorhombic lysozyme crystals obtained at high pH. Cryst. Growth Des. 2009, 9, 3313−3317. (18) Nordström, F. L.; Rasmuson, Å. C. Prediction of solubility curves and melting properties of organic and pharmaceutical compounds. Eur. J. Pharm. Sci. 2009, 36, 330−344. (19) Song, L.; Gao, Y.; Gong, J. Measurement and Correlation of Solubility of Clopidogrel Hydrogen Sulfate (Metastable Form) in Lower Alcohols. J. Chem. Eng. Data 2011, 56, 2553−2556. (20) Apelblat, A.; Manzurola, E. Solubilities ofo-acetylsalicylic, 4aminosalicylic, 3,5-dinitrosalicylic, andp-toluic acid, and magnesiumDL-aspartate in water fromT = (278 to 348) K. J. Chem. Thermodyn. 1999, 31, 85−91. (21) Acree, W. E. Mathematical representation of thermodynamic properties. Thermochim. Acta 1992, 198, 71−79. (22) Acree, W. E.; McCargar, J. W.; Zvaigzne, A. I.; Teng, I. L. Mathematical Representation of Thermodynamic Properties. Carbazole Solubilities in Binary Alkane + Dibutyl Ether and Alkane + Tetrahydropyran Solvent Mixtures. Phys. Chem. Liq. 1991, 23, 27−35. (23) Acree, W. E.; Zvaigzne, A. I. Thermodynamic properties of nonelectrolyte solutions. Thermochim. Acta 1991, 178, 151−167. (24) Jouyban-Gharamaleki, A.; Valaee, L.; Barzegar-Jalali, M.; Clark, B.; Acree, W. Comparison of various cosolvency models for calculating solute solubility in water−cosolvent mixtures. Int. J. Pharm. (Amsterdam, Neth.) 1999, 177, 93−101. (25) Jouyban, A. Review of the cosolvency models for predicting solubility of drugs in water-cosolvent mixtures. J. Pharm. Pharm. Sci. 2008, 11, 32−58. (26) Wei, T.; Wang, C.; Du, S.; Wu, S.; Li, J.; Gong, J. Measurement and Correlation of the Solubility of Penicillin V Potassium in Ethanol + Water and 1-Butyl Alcohol + Water Systems. J. Chem. Eng. Data 2015, 60, 112−117.

Correlation results of the models mentioned above and the values of the ARD listed in Tables S1, S2, S3, S4, and S5, respectively, and experimental data reported in references for ε-HNIW compared graphically in Figures S1 and S2 (PDF)

AUTHOR INFORMATION

Corresponding Authors

*Tel.: 86-10-68918060. Fax: +86-10-68914863. E-mail: renhui@ bit.edu.cn. *E-mail: [email protected]. ORCID

Chao Cui: 0000-0003-3384-2581 Hui Ren: 0000-0002-7940-6630 Notes

The authors declare no competing financial interest.

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REFERENCES

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