Density, Surface Tension, and Kinematic Viscosity of

Article pubs.acs.org/jced

Density, Surface Tension, and Kinematic Viscosity of Hydrofluoroethers HFE-7000, HFE-7100, HFE-7200, HFE-7300, and HFE-7500 Michael H. Rausch,†,‡ Lorenz Kretschmer,‡ Stefan Will,†,‡ Alfred Leipertz,†,‡ and Andreas P. Fröba*,†,‡ †

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Erlangen Graduate School in Advanced Optical Technologies (SAOT), University of Erlangen-Nuremberg, Paul-Gordan-Straße 6, D-91052 Erlangen, Germany ‡ Department of Chemical and Biological Engineering, Institute of Engineering Thermodynamics (LTT), University of Erlangen-Nuremberg, Am Weichselgarten 8, D-91058 Erlangen, Germany ABSTRACT: The liquid density, liquid kinematic viscosity, and surface tension of the segregated hydrofluoroethers (HFEs) HFE7000 (1,1,1,2,2,3,3-heptafluoro-3-methoxy-propane), HFE-7100 (mixture of the isomers 1,1,1,2,2,3,3,4,4-nonafluoro-4-methoxybutane and 1,1,1,2,3,3-hexafluoro-3-methoxy-2-(trifluoromethyl)propane), HFE-7200 (mixture of the isomers 1-ethoxy1,1,2,2,3,3,4,4,4-nonafluorobutane and 1-ethoxy-1,1,2,3,3,3-hexafluoro-2-(trifluoromethyl)propane), HFE-7300 (1,1,1,2,2,3,4,5,5,5-decafluoro-3-methoxy-4-(trifluoromethyl)pentane), and HFE-7500 (3-ethoxy-1,1,1,2,3,4,4,5,5,6,6,6-dodecafluoro-2-(trifluoromethyl)hexane) were studied in dependence on temperature under saturation conditions. A vibrating-tube densimeter was used for the measurement of the saturated-liquid density at temperatures from (273.15 to 363.15) K with a relative expanded uncertainty (k = 2) of 0.02 %. The kinematic viscosity of the liquid phase and surface tension were obtained on the basis of surface light scattering (SLS) measurements for temperatures between (273.15 and 373.15) K with estimated relative expanded uncertainties (k = 2) of (2 and 1.5) %. The measured data could be correlated within their expanded uncertainties (k = 2) by interpolating expressions. Effects of the molecular structures of the studied HFEs on the thermophysical data are discussed. In particular for viscosity and surface tension, comparison with literature data is restricted by their scarce availability.

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compatibility.4 The substances HFE-7000, HFE-7100, HFE7200, HFE-7300, and HFE-7500 examined in this study, for instance, possess GWPs below 530 and ALTs smaller than 5 years.5−9 For comparison, 1,1,1,2-tetrafluoroethane (HFC134a), one of the most popular refrigerants for industrial applications in the past, has a GWP of 1300 and an ALT of 14 years.10 While all studied HFEs can be used as heat transfer fluids, HFE-7100, HFE-7200, and HFE-7300 are also applicable as cleaning solvents and lubricant carriers, and HFE-7000 may be used as a direct expansion refrigerant.5−9 Despite the large number of potential applications, thermophysical property data for HFEs in the literature are very scarce. Therefore, it is the major aim of the present study to provide reliable density, surface tension, and kinematic viscosity data for the investigated substances.

INTRODUCTION Facing today’s challenge of environmental responsibility requires that substances which deplete the ozone layer or contribute to global warming must be restricted or substituted. In this spirit, the United Nations Framework Convention on Climate Change (UNFCCC) has, as a result of their third meeting in Kyoto in 1997, included chlorofluorocarbons (CFCs), hydrochlorofluorocarbons (HCFCs), and perfluorocarbons (PFCs) among others as restricted compounds. Consequently, it was of great importance that alternative compounds were developed. Besides hydrofluorocarbons (HFCs), hydrofluoroethers (HFEs) are also regarded as promising alternatives to CFCs.1,2 While the HFCs have become commonplace in industrial applications, HFEs are still only under consideration in many fields although they seem to have a lower impact on the environment. Most fluorinated, and in particular segregated HFEs where the ether oxygen separates all fluorinated from the nonfluorinated carbons, possess zero ozone depletion potential (ODP), low global warming potentials (GWP over an integrated time horizon of 100 years) and relatively short atmospheric lifetimes (ALT).2,3 In addition, most HFEs exhibit low toxicity, are nonflammable and thermally stable, and thus have excellent environmental © 2015 American Chemical Society

Special Issue: Memorial Issue in Honor of Anthony R. H. Goodwin Received: August 13, 2015 Accepted: November 2, 2015 Published: November 11, 2015 3759

DOI: 10.1021/acs.jced.5b00691 J. Chem. Eng. Data 2015, 60, 3759−3765

Journal of Chemical & Engineering Data

Article

Table 1. Specification of the Studied HFE Samples substance HFE-7000 HFE-7100 HFE-7200 HFE-7300 HFE-7500 a

source 3M 3M 3M 3M 3M

specified mass fraction purity ≥ ≥ ≥ ≥ ≥

a

0.995 0.995c 0.99e 0.99g 0.99h

molecular weight

critical temperature

critical pressure

critical density

dipole moment

M/g·mol−1

Tc/K

pc/MPa

ρc/kg·m−3

μ/D

a

a

200 250c 264e 350g 414h

438.15 468.45c 482.95b 516.45b 534.15h

a

2.48 2.23c 2.007b 1.877b 1.55h

a

553 555c 526f 578f 580h

2.328b 2.4d 2.5d 2.287b 2.7d

Reference 5. bReference 11. cReference 6. dReference 12. eReference 7. fCalculated according to ref 13. gReference 8. hReference 9.

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EXPERIMENTAL SECTION Materials. The segregated hydrofluoroethers HFE-7000 (1,1,1,2,2,3,3-heptafluoro-3-methoxy-propane; GWP 530; ALT 4.9 years), HFE-7300 (1,1,1,2,2,3,4,5,5,5-decafluoro-3-methoxy4-(trifluoromethyl)pentane; GWP 200; ALT 3.8 years), and HFE-7500 (3-ethoxy-1,1,1,2,3,4,4,5,5,6,6,6-dodecafluoro-2(trifluoromethyl)hexane; GWP 90; ALT 2.2 years) as well as the inseparable isomer mixtures HFE-7100 (1,1,1,2,2,3,3,4,4nonafluoro-4-methoxy-butane and 1,1,1,2,3,3-hexafluoro-3-methoxy-2-(trifluoromethyl)propane; GWP 320; ALT 4.1 years) and HFE-7200 (1-ethoxy-1,1,2,2,3,3,4,4,4-nonafluorobutane and 1-ethoxy-1,1,2,3,3,3-hexafluoro-2-(trifluoromethyl)propane; GWP 55; ALT 0.77 years) were provided by 3M Deutschland GmbH. According to the provider’s specifications, HFE-7000 and HFE-7100 had a purity of ≥ 99.5 mass %, whereas HFE-7200, HFE-7300, and HFE-7500 were specified with ≥ 99.0 mass %.5−9 The compositions of the binary isomer mixtures HFE-7100 and HFE-7200 were determined by 19F nuclear magnetic resonance (NMR) analysis (JEOL, ECX +400 spectrometer) with deuterated trichloromethane (CDCl3) as solvent. For HFE-7100, a 1,1,1,2,3,3-hexafluoro-3-methoxy-2(trifluoromethyl)propane mole fraction of 0.623 was found with a standard uncertainty of 0.007. The measured mole fraction of 1-ethoxy-1,1,2,3,3,3-hexafluoro-2-(trifluoromethyl)propane in HFE-7200 was 0.613 with a standard uncertainty of 0.002. All samples were used without further purification prior to the thermophysical property measurements. A summary of the studied compounds and their properties required for data evaluation is given in Table 1. Vibrating-Tube MethodDensity . For the density meter (Anton Paar, DMA 5000) used for measuring the saturated liquid-phase density as a function of temperature, long-term drift is eliminated by a reference oscillator. The temperature of the U-tube is controlled within ± 1 mK and measured by a high-precision platinum resistance probe with an expanded uncertainty (k = 2) of 10 mK. For the density meter calibration, standard water and air were used. The calibration procedure was checked by measuring the liquid density of toluene at atmospheric pressure for temperatures between (278.15 and 343.15) K in intervals of 5 K. Here, the difference between the density values determined by our density meter and those calculated by the equation of state given by Lemmon and Span14 was smaller than 0.01 %, which is equal to the uncertainty of the employed equation of state for the saturated liquid density around 300 K. The relative expanded uncertainty (k = 2) of the present density measurements is estimated to be 0.02 %, for which the calibration error of the apparatus of 0.01 % and the error associated with the applied measurement procedure were taken into account. Before the measurements, the U-tube of the density meter was evacuated and flushed with the investigated HFE. Saturation conditions were ensured by

allowing for the presence of a HFE vapor phase in the dosing system outside the measurement volume. The precision or repeatability of the instrument in the present study was better than 0.001 %. Surface Light ScatteringSurface Tension and Kinematic Viscosity. Liquid kinematic viscosity and surface tension of the HFEs under saturation conditions were measured simultaneously by using surface light scattering (SLS). The noninvasive SLS technique probes the dynamics of surface fluctuations on phase boundaries such as liquid surfaces. For the probed HFEs showing low viscosities, the frequency ω and damping Γ of surface fluctuations is, in a first order approximation, governed by the surface tension and the liquid kinematic viscosity. In SLS, the intensity of scattered light emerging from the interaction between the incident light and the fluctuating surface structure is analyzed on a temporal basis by using photon correlation spectroscopy (PCS). The kinematic viscosity of the liquid phase ν′ (= η′/ρ′) and the surface tension σ were determined under saturation conditions by means of an exact numerical solution of the dispersion relation for surface waves.15 In addition to the information on the dynamics of surface fluctuations at a given wave vector q⃗ obtained from the SLS experiment, reference data for the density of both phases and the dynamic viscosity of the vapor phase under saturation conditions were utilized for this purpose. A more detailed description of the SLS method in connection with the determination of viscosity and surface tension can be found in refs 16 to 18. The experimental SLS setup including the sample cell used in the present study is the same as that employed in our former investigations for numerous pure refrigerants and refrigerant mixtures. For details, refs 16 17, and 19 are recommended. In the following, only the experimental conditions for the present investigations of the HFEs are summarized. The cleaned sample cell was filled with liquid HFE under atmospheric conditions, closed, and evacuated with an oilsealed vacuum pump at about 50 Pa. With this procedure, also degassing of the samples could be ensured. The temperature of the sample cell, which was placed inside an insulated housing, was regulated through resistance heating and measured by calibrated 100 Ω platinum resistance probes with an expanded uncertainty (k = 2) of 15 mK. For sample temperatures below room temperature, the insulating housing was cooled by a lab thermostat connected to cooling coils to about 10 K below the desired temperature in the sample cell. The HFEs were investigated in the temperature range from (273.15 to 383.15) K in steps of 10 K. For each temperature point, typically six single measurements were performed at different angles of incidence, where the laser was irradiated from either side with respect to the axis of observation in order to avoid a possible misalignment. The temperature stability was better than ±2 mK during each experimental run. 3760



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Table 2. Liquid Density ρ′ of HFE-7000, HFE-7100, HFE7200, HFE-7300, and HFE-7500 for T = (273.15 to 363.15) K under Saturation Conditionsa

The data directly obtained from SLS for the dynamics of surface waves are their frequency ωq (relative standard uncertainty Δωq/ωq = 0.0005) and damping Γ (relative standard uncertainty ΔΓ/Γ = 0.005) at a defined wave vector q⃗ (relative standard uncertainty of the modulus of the wave vector Δq/q = 0.001). These data have been combined with our experimental data for density of the liquid phase ρ′ (relative standard uncertainty Δρ′/ρ′ = 0.0001) as well as reference data for the density of the vapor phase ρ″ (relative standard uncertainty Δρ″/ρ″ = 0.005) and for the dynamic viscosity of the vapor phase η″ (relative standard uncertainty Δη″/η″ = 0.05) to determine the surface tension σ and liquid kinematic viscosity ν′ of the studied HFEs under saturation conditions by an exact numerical solution of the equation of dispersion for surface waves according to ref 16. The required ρ″ data were obtained by the Chen equation.20 This equation is a universal p,v,T equation for gases at saturation conditions on the basis of the corresponding-states principle and has been checked for different working fluids including polar substances, for which, in comparison with data recommended in the literature, an absolute average deviation of 0.43 % is reported.20 The dynamic viscosity of the saturated vapor phase η″ was obtained according to a method detailed in refs 21 and 22. In both cases, the properties of the HFEs summarized in Table 1 as well as the correlations for the vapor pressure specified by the provider5−9 were employed for calculating the theoretical values. From the data evaluation, the surface tension σ and the liquid kinematic viscosity ν′ of the studied HFEs at saturation conditions could be determined with estimated relative expanded uncertainties (k = 2) of (1.5 and 2.0) %, respectively.

ρ′/kg·m−3 HFE-7000

HFE-7100

HFE-7200

HFE-7300

HFE-7500

1471.16 1458.15 1444.94 1431.58 1418.04 1404.30 1390.35 1376.15 1361.67 1346.91 1331.89 1316.54 1300.86 1284.82 1268.38 1251.45 1234.05 1216.87 1199.54

1579.23 1566.86 1554.37 1541.76 1529.03 1516.15 1503.18 1490.04 1476.74 1463.23 1449.50 1435.61 1421.48 1407.13 1392.52 1377.65 1362.50 1347.04 1331.24

1478.05 1467.14 1456.15 1445.07 1433.94 1422.65 1411.31 1399.85 1388.27 1376.56 1364.66 1352.68 1340.45 1328.09 1315.57 1302.85 1289.93 1276.74 1263.25

1714.26 1702.92 1691.49 1680.02 1668.48 1656.86 1645.14 1633.38 1621.44 1609.41 1597.29 1585.05 1572.65 1560.14 1547.49 1534.67 1521.68 1508.51 1495.16

1670.60 1660.59 1650.49 1640.35 1630.17 1619.92 1609.61 1599.24 1588.77 1578.28 1567.69 1557.00 1546.20 1535.30 1524.31 1513.21 1501.99 1490.64 1479.16

a

The combined expanded uncertainties Uc are Uc(T) = 0.01 K and Uc(ρ′) = 0.0002 ρ′ (level of confidence = 0.95).

The data for HFE-7000 reported by Ohta et al.23 were measured with a magnetic density meter with an uncertainty of 2 kg·m−3, that is, relative uncertainties up to 0.17 %. Thus, agreement within combined uncertainties with our data can be concluded. For the two values reported by Sekiya and Misaki,1 which are smaller than our results, neither the applied measurement technique nor the uncertainty is given. Also Klomfar et al.24 measured the density of HFE-7000. They used the single-sinker buoyancy method and state a combined expanded uncertainty (k = 2) of 0.5 kg·m−3, that is, a relative expanded uncertainty up to 0.036 % in context with the studied HFE at 0.1 MPa. Thus, good agreement can be concluded with our data. Qi et al.25 measured the densities of HFE-7000 and HFE-7100 as a function of temperature and pressure with a vibrating-tube instrument. The data reported for about 0.1 MPa, which are used for comparison here, are specified with relative expanded uncertainties (k = 2) of 0.036 %. While their data for HFE-7000 are in excellent agreement with our data, deviations outside combined uncertainties can be found for HFE-7100. The densities for HFE-7100 and HFE-7200 published by Piñeiro et al.26 were obtained in the compressed-liquid phase as a function of temperature and pressure with a vibrating-tube density meter with an uncertainty of 0.1 kg·m−3, that is, relative deviations smaller than 0.01 %, which seems to be somewhat underestimated. For comparison with our data, their values obtained at the smallest investigated pressure of 0.1 MPa were chosen. According to Figure 1, agreement within combined uncertainties with our data can only be found for a few data points, which may be related to the use of different samples. Fang et al. used the same measurement instrument and procedure as Qi et al.25 to determine the density of HFE-720027 and HFE-7500.28 The data reported for 0.1 MPa are specified with expanded uncertainties (k = 2) of (0.033 and 0.028) % for the two HFEs. Agreement with our data within combined uncertainties can be found for most of

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RESULTS AND DISCUSSION The saturated-liquid densities ρ′ of the investigated HFEs measured in the temperature range from (273.15 to 363.15) K are summarized in Table 2. They are represented well as a function of temperature by the polynomial ′ = ρ0′ + ρ1′T + ρ2′T 2 + ρ3′T 3 ρcalc

T/K 273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15

(1)

The corresponding fit parameters ρ′0, ρ′1, ρ′2, and ρ′3 as well as the standard percentage deviations (rms) of the measured ρ′ data to the fit, which are always smaller than 0.013, are given in Table 3. The measured saturated-liquid density data, the correlations according to eq 1, and available literature data are illustrated in the upper part of Figure 1. In the lower part of the figure, the deviation of the experimental and literature data from eq 1 is shown. The deviation of our experimental data from the fit is clearly smaller than the combined relative expanded measurement uncertainty (k = 2) of 0.02 %, except for a few data points for HFE-7000 at higher temperatures. Here, the comparatively high vapor pressure of the HFE caused some experimental challenges which may have affected the results at higher temperatures. The rms values for HFE-7000 are, however, still smaller than the expanded uncertainty (k = 2). The densities of HFE-7300 and HFE-7500, which are more strongly branched and possess larger molecular weight, are larger than those of the other HFEs, which exhibit a more linear structure. It seems that the stronger branching allows for a denser packing of the molecules in the liquid phase. Among the members of these two HFE groups, however, no clear structural effect on the density can be found. 3761



Article

Table 3. Coefficients of eq 1 for the Density of HFE-7000, HFE-7100, HFE-7200, HFE-7300, and HFE-7500 Listed in Table 2 ρ0′ /kg·m−3 ρ1′ /kg·m−3·K−1 ρ′2·102/kg·m−3·K−2 ρ′3·105/kg·m−3·K−3 rmsa a

HFE-7000

HFE-7100

HFE-7200

HFE-7300

HFE-7500

2280.63 −4.68360 1.11496 −1.77696 0.013

2510.64 −5.68904 1.32655 −1.80161 0.001

2280.24 −4.72535 1.03330 −1.38567 0.002

2471.72 −4.04355 0.74486 −1.02405 0.001

2318.18 −3.28417 0.53555 −0.73631 0.001

Standard percentage deviation of measured ρ′ data to the fit.

liquid kinematic viscosity ν′ as well as the surface tension σ of the studied HFEs reported in the same table. The employed ρ′ data were obtained from eq 1, whereas ρ″ and η″ were calculated on a theoretical basis.20−22 The obtained ν′ data were correlated according to the equation ′ = ν0′ exp[ν1′T −1 + ν2′T + ν3′T −2] νcalc

(2)

The corresponding fit parameters ν′0, ν′1, ν′2, and ν′3 as well as the standard percentage deviation (rms) of the experimental ν′ data to the fit, which is clearly smaller than the estimated relative expanded uncertainty (k = 2) of 2 % for all HFEs, are given in Table 5. Figure 2 shows the experimental ν′ data, the corresponding fit curves, as well as the relative deviation of the measured values from the fit. It demonstrates that this deviation is smaller than the estimated expanded uncertainty (k = 2) for all data points. The viscosity for a given temperature increases from HFE-7000 to HFE-7100, which could be related to the increasing length of the fluorinated alkyl chain from 3 to 4 carbon atoms. In contrast, the increasing length of the nonfluorinated alkyl chain from methyl (HFE-7100) to ethyl (HFE-7200) hardly affects the viscosity. HFE-7300 and HFE7500, which are more strongly branched than the other studied HFEs and possess higher molar weight, show larger viscosities, which may be attributed to molecule entanglement. Here, the longer nonfluorinated alkyl chain (ethyl instead of methyl) and especially the longer fluorinated side branch with three instead of two C atoms seem to be the reason for the higher viscosity of HFE-7500. The literature datum for HFE-7000 at 296.15 K reported by Sekiya and Misaki1 without providing information on the measurement method and uncertainty is 5.8% larger compared to the result from eq 1. Marchionni et al.29 reported dynamic viscosity and density data for HFE-7100, HFE-7200, and HFE7500 at 298 K which can be combined to obtain kinematic viscosities. Their viscosities were measured with a Cannon viscometer, but no uncertainties are reported. The resulting kinematic viscosity data are (2.1, 3.4, and 8.7) % larger than those calculated from eq 2 for HFE-7100, HFE-7200, and HFE7500, respectively. Warrier and Teja30 measured the dynamic viscosity of HFE-7200 at 297.8 K and atmospheric pressure with a Cannon−Fenske viscometer and state a maximum relative uncertainty of 0.16 %, which seems to be clearly underestimated. Combination of their dynamic viscosity datum with their related density result yields a kinematic viscosity which is 6.4 % smaller than the corresponding value obtained from eq 2. The deviations of the correlations provided by the producer of the HFEs in the corresponding datasheets5−9 from eq 2 for a temperature of 298.15 K range from 3.4 % for HFE7500 up to 16.9 % for HFE-7100. Also here, the source and uncertainty of the given correlations is unknown.

Figure 1. Liquid density of HFEs under saturation conditions as a function of temperature in comparison with literature data (, eq 1 using coefficients from Table 3): ◊, HFE-7000, this work; ◆, HFE7000, Ohta et al.;23 crossed diamond, HFE-7000, Sekiya and Misaki;1 starred diamond, HFE-7000, Klomfar et al.;24 black and white diamond, HFE-7000, Qi et al.;25 ○, HFE-7100, this work; ●, HFE7100, Piñeiro et al.;26 ◐, HFE-7100, Qi et al.;25 □, HFE-7200, this work; ■, HFE-7200, Piñeiro et al.;26 ◧, HFE-7200, Fang et al.;27 △, HFE-7300, this work; ▽, HFE-7500, this work; ⧨, HFE-7500, Fang et al.28

their results. Marchionni et al.29 used a pycnometer to measure densities for HFE-7100, HFE-7200, and HFE-7500 at 298 K and atmospheric pressure, which deviate (−1.38, − 0.09, and +1.15) % from the results from eq 1. For these data, which are not included in Figure 1 to ensure legibility of the deviation plot, no uncertainties are stated. Also not included in Figure 1 for the same reason is the value reported by Warrier and Teja30 for HFE-7200 at 297.8 K and atmospheric pressure, which is 0.45 % smaller compared to eq 1. They used a pycnometer and state an uncertainty of 1 kg·m−3, that is, a relative deviation of about 0.07 % in context with the published datum, which seems to be clearly underestimated. It should be mentioned that the producer of the HFEs also provides temperature-dependent liquid-density correlations in the corresponding datasheets.5−9 The source and uncertainty of these correlations is, however, unknown. Exemplary comparison with our correlation according to eq 1 at 298.15 K yields relative deviations from 0.04 % for HFE-7300 up to 2.3 % for HFE-7100. Table 4 summarizes the ρ′, ρ″, and η″ data combined with the directly measured values for frequency and damping of surface waves at defined wave vectors to obtain the saturated3762



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Table 4. Liquid Density ρ′, Vapor Density ρ″, Dynamic Viscosity of the Vapor Phase η″, Kinematic Viscosity of the Liquid Phase ν′, and Surface Tension σ of HFE-7000, HFE-7100, HFE-7200, HFE-7300, and HFE-7500 for T = (273.15 to 373.15) K at Saturation Conditionsa T

ρ′

ρ″

η″

ν′

σ

T

ρ′

ρ″

η″

ν′

σ

K

kg·m−3

kg·m−3

μPa·s

mm2·s−1

mN·m−1

K

kg·m−3

kg·m−3

μPa·s

mm2·s−1

mN·m−1

273.15 283.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15

1471.04 1444.98 1418.14 1390.39 1361.65 1331.79 1300.72 1268.33 1234.51 1199.15 1162.16

0.4218 0.3651 0.3296 0.2902 0.2636 0.2374 0.2198 0.2015 0.1798 0.1661 0.1535

14.49 13.31 12.33 11.23 10.27 9.23 8.28 7.36 6.38 5.48 4.62

373.15

1235.79

0.2225

7.19

273.15 283.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15

1579.26 1554.35 1529.03 1503.19 1476.73 1449.53 1421.50 1392.52 1362.48 1331.27 1298.80

0.6638 0.5702 0.4841 0.4284 0.3810 0.3377 0.3059 0.2772 0.2464 0.2284 0.2088

15.82 14.82 13.80 12.89 11.92 11.00 10.06 9.13 8.16 7.32 6.46

273.15 283.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15

1714.27 1691.50 1668.48 1645.15 1621.44 1597.31 1572.67 1547.48 1521.67 1495.18 1467.95

1.0103 0.8494 0.7370 0.6312 0.5562 0.4916 0.4355 0.3947 0.3518 0.3150 0.2883

16.56 15.81 14.97 14.15 13.43 12.61 11.79 11.03 10.16 9.43 8.64

273.15 283.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15

1478.07 1456.13 1433.91 1411.31 1388.26 1364.68 1340.47 1315.57 1289.87 1263.31

0.6631 0.5563 0.4824 0.4292 0.3822 0.3429 0.3125 0.2826 0.2564 0.2382

16.03 14.90 14.01 13.21 12.33 11.42 10.56 9.67 8.84 7.99

273.15 283.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15

1670.63 1650.49 1630.17 1609.62 1588.81 1567.68 1546.20 1524.32 1501.99 1479.18 1455.83

1.1383 0.9376 0.8044 0.6913 0.6109 0.5378 0.4709 0.4277 0.3884 0.3520 0.3170

16.92 16.23 15.52 14.75 14.07 13.30 12.65 11.89 11.13 10.40 9.66

HFE-7000 1.97 10.75 3.03 11.17 4.54 11.60 6.64 12.04 9.50 12.48 13.33 12.92 18.43 13.36 25.14 13.79 33.94 14.23 45.32 14.70 59.90 15.25 HFE-7100 0.98 9.78 1.53 10.15 2.30 10.54 3.38 10.93 4.85 11.33 6.82 11.74 9.40 12.15 12.76 12.55 17.08 12.96 22.58 13.35 29.55 13.75 HFE-7200 0.61 9.33 0.96 9.68 1.47 10.03 2.18 10.40 3.15 10.77 4.47 11.15 6.22 11.53 8.50 11.91 11.44 12.30 15.19 12.68

HFE-7200 19.94 13.05 HFE-7300 0.27 8.40 0.44 8.71 0.69 9.02 1.06 9.34 1.60 9.67 2.37 10.01 3.44 10.36 4.92 10.72 6.92 11.09 9.61 11.46 13.20 11.84 HFE-7500 0.11 7.72 0.18 8.01 0.30 8.29 0.48 8.58 0.74 8.87 1.12 9.17 1.64 9.47 2.36 9.78 3.32 10.10 4.59 10.43 6.25 10.76

a

Directly measured values for frequency and damping at a defined wave vector of surface waves were combined with calculated data for ρ′, ρ″, and η″ according to eq 1, ref 20, and refs 21 and 22, respectively, to derive ν′ and σ by an exact numerical solution of the dispersion relation. The combined expanded uncertainties for the employed properties are 0.02 % for the liquid density, 1 % for the vapor density, and 10 % for the dynamic viscosity of the vapor phase. The combined expanded uncertainties Uc are Uc(T) = 0.015 K, Uc(ν′) = 0.02 ν′ and Uc(σ) = 0.015 σ (level of confidence = 0.95).

Table 5. Coefficients of eq 2 for the Saturated-Liquid Kinematic Viscosity of HFE-7000, HFE-7100, HFE-7200, HFE-7300, and HFE-7500 Listed in Table 4 2 −1

ν0′ /mm ·s ν′1/K ν2′ /K−1 ν3′ /K2 rmsa a

HFE-7000

HFE-7100

HFE-7200

HFE-7300

HFE-7500

114.05 −1789.54 −0.010228 279155 0.87

85.44 −1859.59 −0.009152 332097 0.68

53.49 −2016.02 −0.007409 373692 0.69

129.19 −1719.29 −0.010018 311765 0.50

75.23 −1883.93 −0.008190 368525 0.68

Standard percentage deviation of measured ν′ data to the fit.

In the upper part of Figure 3, the experimental σ data, the corresponding fit curves according to eq 3, and literature data are presented. The relative deviation of the measured and literature data from the fit equation are illustrated in the lower part of the figure. The deviation of our experimental data from the fit is always smaller than the estimated expanded uncertainty (k = 2). The trend among the HFEs for a given temperature is similar to that found for the kinematic viscosity. Also here, the tendencies may be related to the differences in chain lengths and degree of branching. A more detailed

For correlation of the surface tension data, the modified van der Waals-type equation σ = σ0(1 − TR )1.26 [1 + σ1(1 − TR )0.5 ]

(3)

was used. Here, TR = T/Tc is the reduced temperature, where the Tc data given in Table 1 were employed. The fit parameters σ0 and σ1 are given in Table 6 together with the standard percentage deviations (rms) of the experimental σ data to the fit, which are clearly smaller than the estimated relative expanded uncertainty (k = 2) of 1.5 % for all studied HFEs. 3763



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Figure 3. Surface tension of HFEs under saturation conditions as a function of temperature from SLS in comparison with literature data (, eq 3 using coefficients from Table 6): ◊, HFE-7000, this work; ◆, HFE-7000, Wilhelmy plate method, Klomfar et al.;24 black and white diamond, HFE-7000, Du Noüy ring method, Klomfar et al.;24 starred diamond, HFE-7000, Sekiya and Misaki;1 ○, HFE-7100, this work; □, HFE-7200, this work, △, HFE-7300, this work; ▽, HFE7500, this work.

Figure 2. Liquid kinematic viscosity of HFEs under saturation conditions as a function of temperature from SLS (, eq 2 using coefficients from Table 5): ◊, HFE-7000; ○, HFE-7100; □, HFE7200; △, HFE-7300; ▽, HFE-7500.

Table 6. Coefficients of eq 3 for the Surface Tension of HFE7000, HFE-7100, HFE-7200, HFE-7300, and HFE-7500 Listed in Table 4

σ0/mN·m−1 σ1 rmsa a

HFE7000

HFE7100

HFE7200

HFE7300

HFE7500

53.109 −0.1147 0.37

49.351 −0.0527 0.29

48.973 −0.1066 0.35

46.540 −0.1134 0.40

52.165 −0.2832 0.30

temperature range at saturation conditions. The new data were correlated with appropriate fit equations and improve the scarce data situation for HFEs, especially with respect to viscosity and surface tension. Tendencies on how chain lengths and the degree of branching in the HFE structures affect the studied properties could be identified.

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Standard percentage deviation of measured σ data to the fit.

explanation approach on a molecular basis, however, seems to be rather speculative. Klomfar et al.24 measured the surface tension of HFE-7000 by using both the Wilhelmy plate method and the Du Noüy ring technique. For both methods, an expanded combined uncertainty (k = 2) of 0.1 mN·m−1 is stated, which is less than 0.8 % related to the measured data. The relative deviation of their data from those obtained from eq 3 are in the range from (1.6 to 5.9) % for the Wilhelmy plate results and from (2.1 to 3.0) % for the Du Noüy ring method. It can be speculated that the deviations are caused by the use of different samples and/or the presence of air at the liquid surface during the experiments of Klomfar et al.24 Sekiya and Misaki1 reported one surface tension datum for HFE-7000 at 296.15 K, but do not provide information on the applied method and the resulting uncertainty. Their datum deviates 3.2 % from the corresponding value obtained from eq 3. The uncommented correlations provided in the datasheets of the HFEs5−9 yield relative deviations of 0.3 % for HFE-7300 up to 7.1 % for HFE-7500 at T = 298.15 K and are not included in Figure 3.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +49-9131-85-29789. Funding

This work was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) by funding the Erlangen Graduate School in Advanced Optical Technologies (SAOT) within the German Excellence Initiative. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank 3M Deutschland GmbH for providing all HFE samples. The authors also thank Dr. Peter Schulz from the Department of Chemical and Biological Engineering, Institute of Chemical Reaction Engineering, University of ErlangenNuremberg for performing the 19F NMR analysis of HFE-7100 und HFE-7200.

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REFERENCES

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CONCLUSIONS Accurate liquid densities, liquid kinematic viscosities, and surface tensions of five segregated HFEs, which represent a promising option to CFCs in many fields of application, were measured with the vibrating-tube method and SLS over a broad 3764



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Density, Surface Tension, and Kinematic Viscosity of

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