Isothermal VaporâLiquid Equilibria for Binary Mixtures of Methyl

Article pubs.acs.org/jced

Isothermal Vapor−Liquid Equilibria for Binary Mixtures of Methyl Nonafluorobutyl Ether + Acetone, Cyclopentyl Methyl Ether, Ethyl Acetate, n‑Heptane, Methanol, and Toluene Karel Ř ehák,* Martin Klajmon, Martin Strejc, and Pavel Morávek

Department of Physical Chemistry, University of Chemistry and Technology, Prague, 166 28 Prague 6, The Czech Republic S Supporting Information *

ABSTRACT: Measurements of vapor−liquid equilibrium data in binary systems methyl nonafluorobutyl ether + solvent (acetone, cyclopentyl methyl ether, ethyl acetate, nheptane, methanol, and toluene) were carried out at constant temperature (328.15 or 318.15 K) by means of a vapor−liquid equilibrium circulation still. In the most cases, the acquired data satisfied thermodynamic consistency tests. The obtained vapor−liquid equilibrium data were (successfully) correlated by two principally different thermodynamic models: the nonrandom two-liquid equation for the excess Gibbs energy, and the perturbed-chain statistical associating fluid theory equation of state. The latter model was tested also for its predictive capabilities and was found not to be suitable for reliable predictions in the studied binary systems, although it may correctly predict the azeotropic behavior of some systems.

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INTRODUCTION

data for cyclopentyl methyl ether were measured using a specialized static apparatus and the VLE equipment. The obtained data on VLE were processed by the NRTL GE model,15 as well as by the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state. The parameters of NRTL and the adjustable binary interaction parameters of the PC-SAFT were evaluated from the experimental VLE data. The PC-SAFT equation of state, which was originally proposed by Gross and Sadowski,19,20 has been applied to describe vapor−liquid equilibria of the investigated HFE-7100 + solvent binary systems as well as the HFE-7100 pure component properties, namely, liquid density and vapor pressure. VLE calculations using this physically based model were performed both with and without the use of the binary interaction parameters adjusted to the experimental VLE data. This approach allows assessment and comparison of the model’s correlative and predictive capabilities for VLE of the considered systems. The PC-SAFT equation of state has already been applied successfully several times for modeling VLE of systems with fluorinated compounds. For example in the work of Kleiner and Sadowski,21 Aparicio,22 El Ahmar et al.,23 Raabe,24 and in the recently published paper by Fouad and Vega,25 who used the Polar PC-SAFT equation of state26 based on the dipolar term of Jog and Chapman.27

Methyl nonafluorobutyl ether (C5H3F9O) is a substance which belongs to the group of hydrofluoroethers (HFEs). Due to the nontoxic nature of these substances and their relatively favorable environmental parameters, they are suitable substitutes for chlorofluorocarbons, hydrochlorofluorocarbons, and perfluorocarbons.1 HFEs find use as cleaning solvents, refrigerants, blowing agents, and dry etching agents in semiconductor manufacturing. Physicochemical properties of pure HFEs,2−5 high-pressure densities for binary mixtures,6−8 excess molar enthalpies, and excess molar volumes9−14 have been studied. However, data on phase equilibria in binary systems, that are useful for assessment of HFE behavior in mixtures, are rare in literature. Experimental data on liquid− liquid equilibrium in ternary systems containing methyl nonafluorobutyl ether along with correlation by the nonrandom two-liquid (NRTL) model15 were published by Eum et al.16 Shiflett and Yokozeki measured liquid−liquid equilibria in HFEs + ionic liquid systems.17 To provide thermodynamic information on the behavior of HFEs in binary mixtures (e.g., to reveal the possible presence of azeotrope), we decided to measure the vapor−liquid equilibria (VLE) for binary systems containing methyl nonafluorobutyl ether. Five commonly used solvents (acetone, ethyl acetate, methanol, n-heptane, and toluene) and one promising ecofriendly solvent (cyclopentyl methyl ether, abbreviated CPME)18 were selected as the second components of the studied binary systems. VLE data were measured at a constant temperature (328.15 or 318.15 K) by means of a VLE circulation still. In addition to that, saturated vapor pressure © XXXX American Chemical Society

Received: June 30, 2017 Accepted: September 27, 2017

A

DOI: 10.1021/acs.jced.7b00599 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Specifications of the Used Chemicals chemical name, (CAS RN)

source, specification, puritya

purification method

measured mole fraction purity, (water contentb)

analysis method GC KF GC KF GC KF GC, NMR KF GC KF GC KF GC KF

acetone, (67-64-1)

Merck, SeccoSolv, dried, >0.999

stored with molecular sieve

0.9992 (75 × 10−6)

cyclopentyl methyl ether,c (5614-37-9)

Sigma-Aldrich, >0.99

none

0.9990 (20 × 10−6)

ethyl acetate, (141-78-6)

Sigma-Aldrich, anhydrous, >0.998

none

0.9997 (18 × 10−6)

nonafluorobutyl methyl ether,d (163702-07-6, 163702-08-7)



0.9980 (38 × 10−6)

n-heptane, (142-82-5)


none

0.9920 (15 × 10−6)

methanol, (67-56-1)

Merck, SeccoSolv, dried, >0.999


0.9990 (60 × 10−6)

toluene, (108-88-3)

Sigma-Aldrich, anhydrous, >0.998

none

0.9997 (95 × 10−6)

a

As stated by the supplier. bMass fraction. cOther name: methoxycyclopentane. Abbreviated CPME. dMixture of two isomers methyl nonafluorobutyl ether (mole fraction 44.4%) and methyl nonafluoroisobutyl ether (mole fraction 55.6%) with essentially identical properties. Abbreviated HFE-7100 according to the analogous commercial product of 3 M Co.

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EXPERIMENTAL SECTION Materials. Specifications of chemicals used in this work are summarized in Table 1. The purity was determined by our gas chromatography equipment (see below) and by a Metrohm 831 Karl Fischer coulometer. Commercially supplied chemicals called methyl nonafluorobutyl ether are in fact inseparable mixtures of isomers (methyl nonafluoroisobutyl ether and methyl nonafluorobutyl ether) with practically identical properties. For instance, an approximately equimolar mixture of these isomers is available as 3 M Novec engineered fluid HFE-7100. The abbreviation HFE7100 for methyl nonafluorobutyl ether will be used within this work because our sample had a more or less identical composition. Vapor−Liquid Equilibrium Measurement. The measurements were carried out in a VLE circulation still similar to that described in literature.28 Temperatures (328.15 or 318.15 K) of VLE data measurement have been selected so that equilibrium pressures fall into suitable working conditions of the apparatus. The still was connected to devices that allowed a two-stage pressure control and a precise temperature measurement. A scheme of the all arrangement is given in Figure 1. The temperature was measured by means of an AP MKT precision thermometer and a calibrated Pt-100 probe. The pressure control apparatus consisted of an Edwards vacuum pump (model RV3), a HEISE pressure transducer (model DXD, 0− 15 psia), a WIKA Tronic Line pressure transducer (−1 to 3 bar), an Agilent data acquisition/switch unit (model 34970A), two 80 L pressure reservoirs, and two solenoid valves. The apparatus allowed to maintain a constant pressure in range from about 20 to 90 kPa. In the second (final) stage, pressure fluctuations were less than ±0.05 kPa. VLE measurements were performed by the following procedure. A binary mixture (about 50 mL) was loaded into the glass still. An electric power in the heater was manually adjusted to reach a regular boiling and a sufficient flux of the vapor phase. At the same time the system pressure was gradually lowered from its initial value (atmospheric pressure), and the temperature in the still’s head was monitored. The pressure set point was manually changed to reach a desired temperature in the still. When the temperature was stabilized at

Figure 1. Experimental apparatus for VLE measurement. 1, VLE circulation still; 2, cooling trap; 3, buffer tank (80 dm3); 4, pressure transducer; 5, solenoid valve; 6, vacuum pump; 7, temperature probe; 8, thermometer; 9, data acquisition unit; 10, solenoid valve controller; 11, computer.

the given value within fluctuations of ±0.02 K for at least 20 min, the mean value of the monitored pressure was taken as the corresponding system pressure. After that, samples of the liquid phase and condensed vapor phase were taken by syringes and analyzed by an HP 6890 gas chromatograph. The analyses were performed in a split mode on an HP-1 capillary column (25 m × 0.32 mm × 0.52 μm) with an FID detector and helium as the carrier gas. For each binary system, the GC method was tuned to reach an appropriate peak separation. A five-point calibration with binary system compositions regularly spread over the entire concentration range was used for the evaluation of analyses. The estimated standard uncertainty of molar fraction composition determined by the used methods is u(x) = 0.0008. For each binary system, the procedure was repeated with several mixtures differing in composition. The obtained data on VLE for the studied systems are given in Table 2. B



Article

Table 2. Experimental VLE Data for the Studied Systems at Temperature T, Liquid Composition x1, Gas Composition y1, and Pressure pa and Absolute Deviations (Δy1,model and Δpmodel)b of Data Fitted by the NRTL and PC-SAFT Models T/K

p/kPa

x1

318.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15

68.20 77.25 78.85 80.06 80.65 80.15 78.00 76.00 73.10 65.00 60.21

0.000 0.098 0.138 0.204 0.339 0.441 0.577 0.657 0.744 0.916 1.000

328.15 328.15 328.15 328.15 328.15 328.15 328.15 328.15 328.15 328.15

17.34 27.40 31.80 39.80 45.50 65.40 71.20 76.70 82.70 85.75

0.000 0.028 0.047 0.088 0.127 0.404 0.560 0.719 0.900 1.000

328.15 328.15 328.15 328.15 328.15 328.15 328.15 328.15 328.15 328.15 328.15 328.15

45.95 58.95 62.82 66.36 68.15 71.60 74.34 78.72 79.97 81.58 84.86 85.75

0.000 0.113 0.155 0.211 0.242 0.326 0.397 0.554 0.603 0.680 0.899 1.000

328.15 328.15 328.15 328.15 328.15 328.15 328.15 328.15 328.15 328.15 328.15 328.15 328.15 328.15

23.04 30.60 39.54 51.90 66.45 71.20 73.55 76.40 82.10 86.60 87.40 87.17 86.90 85.75

0.000 0.018 0.043 0.089 0.192 0.258 0.294 0.366 0.566 0.784 0.849 0.946 0.970 1.000

318.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15

44.86 50.62 58.01 58.21 64.81 70.40 84.65 87.99

0.000 0.005 0.012 0.013 0.022 0.033 0.086 0.140

y1

Δy1,NRTL

HFE-7100 (1) + Acetone (2) 0.000 0.167 −0.011 0.212 −0.004 0.256 −0.006 0.335 −0.001 0.400 0.006 0.494 0.010 0.559 0.010 0.640 0.008 0.859 0.006 1.000 HFE-7100 (1) + CPME (2) 0.000 0.360 0.018 0.457 0.003 0.573 −0.011 0.634 −0.012 0.779 −0.007 0.821 −0.003 0.866 −0.003 0.942 0.000 1.000 HFE-7100 (1) + Ethyl Acetate (2) 0.000 0.281 −0.017 0.342 −0.014 0.408 −0.009 0.435 −0.010 0.500 −0.011 0.556 −0.003 0.659 −0.001 0.687 −0.006 0.741 −0.003 0.910 −0.001 1.000 HFE-7100 (1) + n-Heptane (2) 0.000 0.255 −0.003 0.435 0.004 0.576 0.002 0.694 0.004 0.717 −0.003 0.731 −0.001 0.752 0.002 0.787 0.002 0.841 0.000 0.872 0.001 0.940 0.001 0.965 0.001 1.000 HFE-7100 (1) + Methanol (2) 0.000 0.122 0.010 0.239 0.014 0.241 0.011 0.321 0.001 0.380 −0.003 0.498 −0.002 0.534 0.006 C

ΔpNRTL/kPa

Δy1,SAFT

ΔpSAFT/kPa

0.41 0.48 0.21 −0.11 −0.09 −0.02 0.13 0.23 0.09

−0.013 −0.006 −0.009 −0.004 0.004 0.009 0.010 0.009 0.009

0.47 0.52 0.25 −0.13 −0.17 −0.22 −0.15 −0.12 −0.18

0.97 0.34 −0.29 −0.63 0.01 0.18 0.29 0.11

0.008 −0.008 −0.021 −0.022 −0.008 −0.002 −0.003 −0.002

0.65 −0.17 −1.08 −1.54 −0.16 0.37 0.50 0.08

−0.46 0.14 0.17 0.33 −0.01 0.15 −0.04 0.01 −0.02 −0.08

−0.020 −0.018 −0.014 −0.014 −0.016 −0.008 −0.004 −0.009 −0.005 −0.001

−0.39 0.17 0.16 0.29 −0.10 0.02 −0.23 −0.21 −0.27 −0.38

−0.08 0.14 0.62 −0.20 −0.63 −0.32 −0.45 0.22 0.72 0.71 0.35 0.43

0.003 0.008 0.001 0.000 −0.007 −0.005 −0.001 0.003 −0.001 −0.002 −0.003 −0.002

0.09 0.43 0.80 −0.44 −0.90 −0.54 −0.47 0.70 1.17 1.07 0.10 0.11

0.22 0.43 0.28 −0.50 −1.30 −2.17 −3.00

0.023 0.034 0.031 0.022 0.015 −0.003 −0.007

2.66 3.40 3.31 2.94 2.23 −0.14 −2.64



Article

Table 2. continued T/K

a

p/kPa

x1

318.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15

92.83 93.12 93.92 94.89 94.20 93.70 92.40 90.77 85.55 74.45 60.21

0.229 0.241 0.290 0.511 0.755 0.821 0.878 0.912 0.957 0.980 1.000

328.15 328.15 328.15 328.15 328.15 328.15 328.15 328.15 328.15 328.15

14.96 25.20 36.10 48.75 59.40 68.15 72.83 76.40 80.36 85.75

0.000 0.020 0.059 0.127 0.254 0.484 0.628 0.733 0.844 1.000

y1

Δy1,NRTL

HFE-7100 (1) + Methanol (2) 0.550 0.009 0.559 0.017 0.560 0.014 0.576 0.002 0.602 0.000 0.616 0.006 0.634 0.010 0.653 0.009 0.714 0.003 0.813 0.006 1.000 HFE-7100 (1) + Toluene (2) 0.000 0.413 0.030 0.599 −0.004 0.706 −0.010 0.773 −0.005 0.822 −0.002 0.856 0.002 0.882 0.000 0.920 −0.001 1.000

ΔpNRTL/kPa

Δy1,SAFT

ΔpSAFT/kPa

−0.01 0.14 0.43 −0.28 −0.52 −0.43 −0.35 0.20 2.47 0.46

−0.012 −0.004 −0.007 −0.002 0.005 0.009 0.011 0.016 0.040 0.087

−0.75 −0.64 −0.31 −0.05 −0.26 −0.03 −0.06 −0.28 −1.65 −7.46

1.27 −0.24 −0.36 −0.24 0.13 0.22 0.20 0.18

0.046 0.006 −0.008 −0.007 −0.002 0.002 0.000 −0.003

1.57 0.35 −0.09 −0.45 0.22 0.45 0.40 0.24

Standard uncertainties are u(T) = 0.05 K, u(p) = 0.01p, u(x1) = u(y1) = 0.001. bΔy1,model = (y1 − y1,calc), Δpmodel = (p − pcalc).

Saturated Vapor Pressure Measurement. In addition to the binary mixture VLE measurement, all used pure components were loaded into the VLE still, and their saturated vapor pressures were measured at the given temperatures. Obtained values were compared to saturated vapor pressures taken from other sources. In case of toluene, n-heptane, methanol, ethyl acetate, and acetone, the equations provided by the DIPPR Project 801 database29 have been used for this purpose. In case of HFE-7100, the equation was taken from the work of An et al.3 However, no suitable vapor pressure data were found for CPME in literature. For this reason, the data were measured within this work. Vapor pressures in the range about from 400 to 7400 Pa were experimentally determined by the vapor pressure static apparatus described together with the corresponding measuring procedure elsewhere.30 The pressure was measured by a capacitance diaphragm absolute gage MKS Baratron 631A12TBEM (MKS Instruments Inc., USA). The temperature of the pressure sensor was kept at T = 398 K by a self-controlling temperature system. The upper limit of the pressure measurement was 13 332 Pa, and its uncertainty was 0.25% of the reading as stated by the manufacturer and confirmed by the Czech Metrology Institute. The pressure sensor was connected to a sample cell containing the measured material. The cell was placed in a Lauda RE 206 thermostat (Lauda, Germany) that allowed adjustment of the sample temperature with stability of 0.01 K. The sample temperature was measured by a platinum resistance thermometer Pt100 in a four wire connection. The thermometer was calibrated at the triple point of water and by comparison to standard platinum resistance thermometer (SPRT). This SPRT was calibrated to the ITS-90, and its calibration is traceable to the National Institute of Standards and Technology (NIST). The standard uncertainty of the temperature measurements is estimated to be less than 0.02 K.

The data acquired by the static apparatus were completed by experimental points (at five temperatures) obtained by the VLE apparatus. The consistency of the both data sets was checked by means of the arc test,31 which is capable to visualize even small discrepancies in vapor pressure data. Since it was found that the data are in reasonably good agreement, they were regressed together by the Antoine equation. The resulting relationship for the temperature range 250−370 K is ln(psat /Pa) = 20.79731 −

2985.79 T /K − 57.025

(1)

The experimental vapor pressure data for CPME and the corresponding arc test can be found in the Supporting Information. The normal boiling temperature of CPME calculated from eq 1 is 379.92 K (105.92 °C). This value corresponds well with data found in the REAXYS database.32 For computational VLE data processing, vapor pressures of pure substances measured in our apparatus were used. The only exception was the HFE7100 + CPME system, for which data provided by eq 1 were utilized. Density Measurement. Liquid density data for CPME were needed for an evaluation of its PC-SAFT parameters. Because only little data were found in the literature, our own measurements in the temperature range 288.15−328.15 K were carried out as well. An Anton Paar DMA 5000 vibrating-tube densimeter was used for this purpose. This device was calibrated at each temperature by chemically pure and degassed water obtained from a Milli-Q Water 62 purification system (Millipore, USA), and dry air. Prior to measurements, samples of CPME were loaded into a gastight syringe and partially degassed by repeatedly shaking the syringe and creating a vacuum by pulling the piston down until a noticeable reduction in the number of bubbles produced by the pressure drop. The determined densities that are given in the Supporting Information (Table S1) were combined with data published D



Article

Table 3. Calculated Parameters of the NRTL Model and Root-Mean-Square Deviationsa from Fitted Vapor Phase Mole Fractions (y1) and Pressures (p) system HFE-7100 HFE-7100 HFE-7100 HFE-7100 HFE-7100 HFE-7100

(1) (1) (1) (1) (1) (1)

+ + + + + +

acetone (2) CPME(2) ethyl acetate (2) n-heptane (2) methanol (2) toluene (2)

T/K

a12

a21

α

100 RMSD(y1)

100 RMSD(p)

318.15 328.15 328.15 328.15 318.15 328.15

−97.35 133.76 −53.05 277.24 715.95 134.70

512.03 375.10 351.15 369.81 725.70 478.97

0.40 0.40 0.40 0.40 0.48 0.40

0.76 0.92 0.91 0.24 0.87 1.15

0.32 1.43 0.32 0.64 1.39 1.83

0.5 ⎡ ⎛ pexp − pcalc ⎞2 ⎤ N calc 2 0.5 ⎢∑iN= 1 ⎜ i exp i ⎟ /N ⎥ . RMSD(y1) = [∑i = 1 (y1,exp − y ) / N ] , RMSD( p ) = i 1, i ⎠ ⎝ pi ⎥⎦ ⎢⎣

a

by Vogel33 and regressed with a linear temperature dependence. The resulting relationship for the temperature range 280−361 K is

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ρ /(g cm−3) = 1.14528 − 9.6314 × 10−4(T /K)

j). Data in the objective function were weighted according to their standard deviations s(y1) and s(p). Standard uncertainties u(y1) and u(p) were initially used for values of s(y1) and s(p). When necessary, the standard deviations were slightly modified by trial and error during the calculations to obtain coherent fits of both y1 and p. The calculated parameters aij are summarized in Table 3. Parameter α was not treated as an adjustable parameter. It was fixed at a value of α = 0.40 for all systems except the HFE-7100 + methanol system. For this system, α = 0.48 resulted in a significantly better description. Correlation and Prediction of VLE Data by the PCSAFT Equation of State. The PC-SAFT equation of state19,20 is a molecular-based model considering molecules as chains of spherical segments. It is a model for the residual Helmholtz energy that takes into account various contributions: the hardchain contribution, the dispersion contribution, and the association contribution describing the effects of specific association interactions (hydrogen bonding). The association term contributes to the residual Helmholtz energy only when at least one associating component is present in the system. Detailed information about the hard-chain and dispersion terms can be found in the original literature,19 whereas the association term is described in refs 20, 38, and 39. Nonassociating molecules are described within PC-SAFT by three pure component parameters: the number of segments per the i-th molecule mi, the corresponding segment diameter σi, and the segment dispersion energy parameter (ε/k) i . Associating molecules have two additional parameters representing the association interaction, namely, the association energy parameter (εassoc/k)i and the association volume (κassoc)i. These PC-SAFT pure component parameters are usually determined simultaneously by fitting liquid density and vapor pressure data for a pure substance. When considering mixtures, the Lorentz−Berthelot mixing rules for the cross-parameters σij and εij are given by

(2)

COMPUTATIONAL METHODS Correlation of VLE Data by the NRTL Model. The obtained experimental data on VLE were utilized for evaluation of the NRTL GE model15 parameters. “Gamma-phi” equations for VLE were used in the form • pyi φi = xiγi psat, i φsat, F i i

i = 1, 2

(3)

where xi and yi are molar fractions of liquid and vapor phases, respectively, p is the total equilibrium pressure, and psat,i is saturated vapor pressure of pure substance i. Since under our experimental conditions the equilibrium pressures p were close to the pressures psat,i, the Poynting correction factors Fi = 1 were considered. φi is the fugacity coefficient of the i-th component in the gaseous mixture under pressure p, and φ•sat,i is fugacity coefficient of pure component under the pressure psat,i. These coefficients were evaluated by means of the virial equation of state (volume-explicit) truncated at the second virial coefficient. Virial coefficients for the used solvents were calculated according to the relations given in literature.34,29 In the case of CPME, no data were available so that its second virial coefficient was estimated by the Pitzer−Curl equation35 with coefficients by Tsonopoulos.36 Critical data and acentric factor for CPME (Tc = 576.84 K, pc = 3.759 MPa, ω = 0.283) needed were evaluated by estimation methods.37 Cross virial coefficients, which were necessary for calculation of φi, were determined as geometrical means of the corresponding coefficients for pure substances. The used virial coefficients are summarized in Table S2 in the Supporting Information. Activity coefficients γi were described by the NRTL model with parameters aij Gij = exp( −ατij) τij = (T /K) (4)

σij = 1/2(σi + σj)

εiεj (1 − kij)

(6)

where kij is the adjustable binary interaction parameter that can be fitted to experimental data for mixtures to get a better agreement between the theory and experiment. The use of kij = 0 in eq 6 presents pure prediction based only on pure components data. Mixing rules commonly used for the association parameters are those proposed by Wolbach and Sandler.40 However, no mixing rules for the association parameters were applied in the calculations employing PC-SAFT within this work, due to the fact that there was only one associating component (methanol) and no cross-associations between unlike molecules were thus taken into account.

Using our experimental data on VLE, the binary parameters aij were evaluated by minimizing the objective function ⎛ (y exp − y calc )2 (pjexp − pjcalc )2 ⎞ 1, j 1, j ⎜ ⎟ S=∑ + 2 2 ⎜ ⎟ s ( y ) s ( p ) j=1 ⎝ 1 ⎠

εij =

N

(5)

which utilizes experimental (superscript exp) and calculated (superscript calc) values of vapor phase molar fraction y1 and total equilibrium pressure p for each experimental point (index E



Article

Table 4. PC-SAFT Pure Component Parameters for Substances Considered in This Work component

Mi (g mol−1)

mi

σi/Å

(ε/k)i/K

acetone CPME ethyl acetate methanolb HFE-7100 n-heptane toluene

58.08 100.16 88.11 32.04 250.06 100.20 92.14

2.8912 3.0627 3.5375 1.5255 4.0992 3.4831 2.8149

3.2279 3.6915 3.3079 3.2300 3.6493 3.8049 3.7169

247.42 267.05 230.80 188.90 193.37 238.40 285.69

κiassoc

source

0.035176

ref 47 this worka ref 19 ref 20 this workc ref 19 ref 19

(εassoc/k)i/K

2899.5

a

Average absolute relative deviations of correlated and experimental data are AARD(ρ) = 0.05%, AARD(psat) = 0.54%. bMethanol is assumed to have two association sites (one electron donor and one acceptor). cAverage absolute relative deviations of correlated and experimental data are AARD(ρ) = 0.09%, AARD(psat) = 0.68%.

The use of the PC-SAFT equation of state first requires knowledge of its parameters for pure components. Their values used in this work are summarized in Table 4. The parameters for acetone, toluene, n-heptane, ethyl acetate, and methanol were taken from the literature. Methanol is the only associating component in the study and is described by the two-site association scheme (one electron donor and one electron acceptor).20 Vijande et al.41 have determined the PC-SAFT pure component parameters for HFE-7100 (m = 6.9892, σ = 3.0360 Å, ε/k = 163.98 K) by fitting compressed and saturated liquid densities5 only, because no experimental vapor pressure data for HFE-7100 were available in the literature at that time. Their set of parameters can be successfully used for description of HFE-7100s liquid density, but it fails in estimation of vapor pressure (see Figures S3 and S4 in the Supporting Information), which prevents its use for calculation of VLE of the HFE-7100 containing mixtures. A new set of HFE-7100 pure component parameters have therefore been identified within this work by fitting experimental data on both liquid density4 and vapor pressure.3 The temperature range was 279− 321 K for density and 305−431 K for vapor pressure. The obtained PC-SAFT pure component parameters for HFE-7100 are included in Table 4. They give deviations of 0.09% and 0.68% for liquid density and vapor pressure, respectively. Their performance for the liquid density and vapor pressure description is illustrated in Figures S3 and S4. These new parameters for HFE-7100 were then used for all of the binary VLE calculations employing the PC-SAFT model within this work. For CPME, the PC-SAFT pure component parameters were needed to be also identified within the work because of their unavailability in the literature. The CPME parameters were optimized to fit the Antoine equation for CPME vapor pressure (eq 1) and the liquid density data from Table S1 and ref 33. After the PC-SAFT parameters for pure substances were established, VLE calculations with binary interaction parameters k12 = 0 were performed by the “phi-phi” approach. The acquired data were then demonstrated as VLE pure predictions. To obtain the PC-SAFT correlation of the experimental VLE data in the studied systems, binary interaction parameters k12 were adjusted by a computational procedure utilizing the objective function given by eq 5. The parameters are listed in Table 5.

Table 5. Calculated Binary Interaction Parameters (k12) of the PC-SAFT Equation of State and Root-Mean-Square Deviationsa from Fitted Vapor Phase Mole Fractions (y1) and Pressures (p) system HFE-7100 (1) + acetone (2) HFE-7100 (1) + CPME (2) HFE-7100 (1) + ethyl acetate (2) HFE-7100 (1) + n-heptane (2) HFE-7100 (1) + methanol (2) HFE-7100 (1) + toluene (2) a

T/K

k12

100 RMSD(y1)

100 RMSD(p)

318.15

0.017

0.87

0.36

328.15

0.038

1.19

1.79

328.15

0.016

1.23

0.35

328.15

0.064

0.37

0.95

318.15

0.014

2.79

3.75

328.15

0.038

1.68

2.27

N

RMSD(y1) = [∑i = 1 (y1,exp − y1,calc )2 /N ]0.5, i i

⎤0.5 ⎡ exp calc 2 N ⎛p −p ⎞ RMSD(p) = ⎢∑i = 1 ⎜ i pexp i ⎟ /N ⎥ . ⎠ ⎝ i ⎥⎦ ⎢⎣

(test 2), the point test (test 3). Criteria for the tests were adopted from the work of Kang et al.42 Table 6 shows a summary of test results. As it can be seen from the table, majority of test were satisfied. In cases where tests were not passed, criteria were exceeded only slightly. More detailed information concerning the consistency tests is provided in the Supporting Information. Isothermal p−x1,y1 and x1−y1 phase diagrams for the studied systems are shown in Figures 2−7. They are also completed by corresponding composition dependencies of activity coefficients and relative volatilities that are given in Figures S11 and S12 in the Supporting Information. Data on relative volatilities reveal slight discrepancies between the experimental and the calculated data for the systems containing acetone and ethyl acetate. As it can be seen from Figure S11, a degree of nonideality in systems HFE-7100 + solvent increases in the solvent order: ethyl acetate, acetone, CPME, toluene, nheptane, methanol. The HFE-7100 (1) + ethyl acetate (2) system exhibits low positive deviations from ideal behavior with ∞ limiting activity coefficients of γ∞ 1 = 2.5 and γ2 = 1.7. A degree of nonideality for the HFE-7100 (1) + methanol (2) is quite high indicating that this system is very close to a liquid−liquid phase split. This fact is also documented by composition dependence of the second derivation of the Gibbs energy of mixing with respect of molar fraction (see “Conditions for Thermodynamic Stability” in the Supporting Information). It should be also noted that this system exhibits symmetrical

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RESULTS AND DISCUSSION Experimental data on VLE for studied systems are given in Table 2. Consistencies of the individual data sets were tested by three consistency tests: the area test (test 1), the Van Nest test F



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Table 6. Summary of Consistency Testsa and Pure Component Vapor Pressures Comparisons. T − Temperature of Isothermal VLE Data, N − Number of Experimental Data Points, Test 1−the Area Test, Test 2−the Van Ness Test, Test 3−the Point Test, Δpi0 − Relative Difference of Pure Component Vapor Pressuresb system HFE-7100 HFE-7100 HFE-7100 HFE-7100 HFE-7100 HFE-7100

(1) (1) (1) (1) (1) (1)

+ + + + + +

acetone (2) CPME (2) ethyl acetate (2) n-heptane (2) methanol (2) toluene (2)

T/K 318.15 328.15 328.15 328.15 318.15 328.15

N

test 1

9 8 10 12 17 8

+ + − + + +

test 2 + + + + + −

test 3 + − + + − +

100Δp01 c

0.79 0.09c 0.09c 0.09c 0.79c 0.09c

100Δp01 0.00d 2.37e 0.30d 0.10d 0.82d 0.96d

The + sign: data set passed a test, the−sign: data set failed a test. bΔp0i = |(p0i,exp − p0i,ref)/p0i,ref| where p0i,exp and p0i,ref are pure component vapor pressures measured and that from an independent source, respectively. cp01,ref from ref 3. dp02,ref from ref 29. ep02,ref from eq 1. a

Figure 2. Isothermal (T = 318.15 K) p−x1,y1 and x1−y1 VLE diagrams for the HFE-7100 (1) + acetone (2) system. ■, ●, ⧫, experimental data; solid line, data calculated by the NRTL model; dashed line, data calculated by the PC-SAFT equation (k12 = 0.017); dotted line, data predicted by the PCSAFT equation (k12 = 0). Coordinates of azeotrope (by the NRTL model): x1,az = 0.33, paz = 80.7 kPa.

Figure 3. Isothermal (T = 328.15 K) p−x1,y1 and x1−y1 VLE diagrams for the HFE-7100 (1) + CPME (2) system. ■, ●, ⧫, experimental data; solid line, data calculated by the NRTL model; dashed line, data calculated by the PC-SAFT equation (k12 = 0.038); dotted line, data predicted by the PCSAFT equation (k12 = 0).

composition dependencies of activity coefficients. Their ∞ limiting values are γ∞ 1 = 21.0 and γ2 = 20.4. It is apparent from Figures 2, 5, and 6 that three systems exhibit maximum pressure azeotropes. They are those containing solvent methanol (x1,az = 0.58, paz = 95.3 kPa), acetone (x1,az = 0.33, paz = 80.7 kPa), and n-heptane (x1,az = 0.91, paz = 86.9 kPa). Pressure elevation is significant especially in the HFE-7100 (1) + methanol (2) and HFE-7100 (1) + acetone (2) systems. It can be estimated that normal boiling temperatures of azeotropes would be about 320 K for the former system and about 325 K for the latter one.

Apart from the experimental data, curves modeled using the NRTL and PC-SAFT equations are displayed in Figures 2−7. In the case of PC-SAFT, the data predicted using the parameters of pure substances only are shown as well. From these images, and the deviations between experimental and calculated data (see Table 2), it is obvious that both models provide a comparable description of the studied systems. The PC-SAFT correlations based on the fitted k12 values are generally in very good agreement with the experimental VLE data for all systems and are almost identical to the results of the NRTL equation. This reflects ability of the PC-SAFT model to G



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Figure 4. Isothermal (T = 328.15 K) p−x1,y1 and x1−y1 VLE diagrams for the HFE-7100 (1) + ethyl acetate (2) system. ■, ●, ⧫, experimental data; solid line, data calculated by the NRTL model; dashed line, data calculated by the PC-SAFT equation (k12 = 0.016); dotted line, data predicted by the PC-SAFT equation (k12 = 0).

Figure 5. Isothermal (T = 328.15 K) p−x1,y1 and x1−y1 VLE diagrams for the HFE-7100 (1) + n-heptane (2) system. ■, ●, ⧫, experimental data; solid line, data calculated by the NRTL model; dashed line, data calculated by the PC-SAFT equation (k12 = 0.064); dotted line, data predicted by the PC-SAFT equation (k12 = 0). Coordinates of azeotrope (by the NRTL model): x1,az = 0.91, paz = 86.9 kPa.

Figure 6. Isothermal (T = 318.15 K) p−x1,y1 and x1−y1 VLE diagrams for the HFE-7100 (1) + methanol (2) system. ■, ●, ⧫, experimental data; solid line, data calculated by the NRTL model; dashed line, data calculated by the PC-SAFT equation (k12 = 0.014); dotted line, data predicted by the PC-SAFT equation (k12 = 0). Coordinates of azeotrope (by the NRTL model): x1,az = 0.58, paz = 95.3 kPa.

association interactions (hydrogen bonding of methanol molecules) for which the association term has to be applied to the residual Helmholtz energy. In contrast to the successful correlation, the PC-SAFT pure predictions using k12 = 0 give rather unsatisfactory results, with the exception of the HFE-7100 + methanol mixture.

provide safe correlations using a single adjustable binary interaction parameter k12. The lowest absolute value of k12 was obtained for the HFE-7100 + methanol mixture (Figure 6). This is quite interesting finding when taking into account that this system shows the largest deviation from ideality (see Figure S11 in the Supporting Information), likely due to the specific H



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Figure 7. Isothermal (T = 328.15 K) p−x1,y1 and x1−y1 VLE diagrams for the HFE-7100 (1) + toluene (2) system. ■, ●, ⧫, experimental data; solid line, data calculated by the NRTL model; dashed line, data calculated by the PC-SAFT equation (k12 = 0.038); dotted line, data predicted by the PCSAFT equation (k12 = 0).

Considering the systems HFE-7100 + n-heptane, toluene, and CPME, the PC-SAFT equation predicts nearly ideal behavior obeying the Raoult’s law. For the systems HFE-7100 + acetone and HFE-7100 + methanol, the predictions reveal successfully the azeotropic behavior and provide a realistic estimate of the azeotropic composition as well as the phase diagram shape. The azeotropic behavior of the HFE-7100 + n-heptane mixture is not predicted qualitatively at all. The presented modeling results show that, despite the good correlative capabilities, the PC-SAFT predictions are generally far from reliability for the investigated systems. This could potentially be improved by taking into account the dipolar interactions. Using the Gaussian quantum mechanics software43 at the B3LYP/6-311++G(3df,2p) level of theory, we calculated the value of the dipole moment for HFE-7100 to be 2.98 D, which classifies this hydrofluoroether as a moderately polar compound. In addition, some of the solvents used in this work have considerable values of the dipole moment, for example, 2.88 D in case of acetone.44 The effects of the dipolar interactions appearing in the HFE-7100 + solvent mixtures can be explicitly captured by employing a polar version of PCSAFT, such as that used by Dominik et al.,26 or the PCP-SAFT model developed by Gross and Vrabec.45 Another option to improve the PC-SAFT predictions of phase equilibria of systems containing fluorous compounds could potentially be the use of different and more complex mixing rules for the cross-parameters εij and σij instead of the Lorentz−Berthelot ones (eqs 6), as discussed by Song et al.46 and Aparicio22 for perfluoroalkane + alkane systems. This is due to the finding that the geometric mean used for εij in the Lorentz−Berthelot rules is not suitable for description of the weak unlike intermolecular interactions between fluorous and nonfluorous molecules.

pressure. This suggests that relatively volatile (normal boiling temperature around 323 K) azeotropic mixed solvents could be prepared. The work also demonstrates predictive and correlative capabilities of the PC-SAFT equation of state for VLE of the investigated systems. While the PC-SAFT correlations using optimized binary interaction parameters describe the experimental VLE data accurately, the pure predictions are generally unsatisfactory, suggesting that there is still room for improvement in the model formulation.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00599. Saturated vapor pressure and liquid density data for cyclopentyl methyl ether (CPME), the arc method of vapor pressure data screening for pure cyclopentyl methyl ether (CPME), PC-SAFT description of saturated vapor pressure and liquid density of HFE7100, second virial coefficients of the used compounds, consistency tests for isothermal vapor−liquid equilibrium data, composition dependences of activity coefficients in the studied systems, description of relative volatilities, and conditions for thermodynamic stability (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Address for correspondence: Department of Physical Chemistry, University of Chemistry and Technology, Prague, Technická 5, 166 28 Prague 6, The Czech Republic. Tel.: +420 2 2044 4039. ORCID

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Karel Ř ehák: 0000-0003-3238-1648

CONCLUSIONS The isothermal vapor−liquid equilibrium data for six binary systems of a type methyl nonafluorobutyl ether (HFE-7100) + solvent have been determined and described by two thermodynamic models. HFE-7100 is a material that is also used as a special cleaning solvent. The results reveal the thermodynamic behavior of this substance with different types of other solvents. For example, it was found that the two systems (namely, HFE-7100 + methanol and HFE-7100 + acetone) form an azeotrope with significant maximum in

Funding

Financial support is acknowledged from specific university research (MSMT no. 20/2014). Notes

The authors declare no competing financial interest.

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