Temperature and Pressure Dependence of the Viscosities of Krytox

Article pubs.acs.org/jced

Temperature and Pressure Dependence of the Viscosities of Krytox GPL102 Oil and Di(pentaerythritol) Hexa(isononanoate) Kenneth R. Harris* School of Physical, Environmental and Mathematical Sciences, The University of New South Wales, P.O. Box 7916, Canberra BC, ACT 2610, Australia ABSTRACT: This work reports high-pressure viscosity measurements on two viscous liquids that may prove useful as high-temperature, high-viscosity reference materials, Krytox GPL102 and di(pentaerythritol) hexa(isononanoate). The perfluoropolyether oil, Krytox GPL102, is the subject of a round-robin comparison of high-pressure viscosity measurements on a specific sample being made by a group of laboratories worldwide employing a variety of viscometric techniques. Viscosity data are reported between (0 and 95) °C, at pressures to 226 MPa and viscosities between (6 and 4182) mPa·s. For the more viscous di(pentaerythritol) hexa(isononanoate), data are reported between (0 and 90) °C, at pressures to 203 MPa and viscosities between (34 and 2269) mPa·s. Correlations are provided using modified Vogel−Fulcher−Tammann (VFT) equations for both substances, a modified Litovitz equation for Krytox GPL102 and a modified Barlow-Lamb equation for di(pentaerythritol) hexa(isononanoate). Glass temperatures are estimated to be (178.2 and 218.1) K, respectively, based on the Angell equation relating the VFT parameters to Tg. Thermodynamic scaling is applied to both the experimental and reduced viscosities. The scaling parameters found are consistent with previous work on chain molecular compounds and esters.

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INTRODUCTION This work reports high-pressure viscosity measurements on two viscous liquids that may be useful as high-temperature, highviscosity reference materials. The first, the perfluoropolyether oil, Krytox GPL102 is the subject of a round-robin comparison of high pressure viscosity measurements on a specific sample being made by a group of laboratories worldwide employing a variety of viscometric techniques. The need for high-temperature, high-pressure viscosity reference materials to complement existing reference materials (water,1 toluene,2 cyclopentane,3 diisodecyl phthalate,4 and squalane5−8) was identified at an annual meeting of the International Association for Transport Properties in 20099 (Table 1 shows the range of applicability of the water standard and the other reference materials) and a subsequent workshop sponsored by Schlumberger Ltd. and Cambridge Viscosity in 2010.10 This has resulted in an IUPAC project, “International Standard for Viscosity at Temperatures up to 473 K and Pressures below 200 MPa”, of which the round-robin measurements on Krytox GPL102 are part.11 This substance (actually a mixture of polyperfluoroethers,12 with the general formula F[(CF(CF3) CF2O]n] CF2CF3], n ∼ 9.5 to 10)13 approximates the industrial requirement for a reference material with a nominal viscosity of 20 mPa·s at a temperature of 473 K and a pressure of 200 MPa. This may be used to represent light oils under the conditions to be found in deep-water crude-oil deposits.13 It does have the disadvantage that different lots may have different compositions: therefore the round-robin measurements must employ a common lot. As the pressure dependence of the viscosity liquids is usually very little affected by small differences © XXXX American Chemical Society

in composition where the components are isomers of similar chain lengths, it should be possible to normalize a high pressure correlation of the round-robin sample viscosity on to atmospheric pressure viscosities of other samples, measured over a common temperature range, with little error, as has been done for the common commercial viscometer calibrant, S20.14 The second, di(pentaerythritol) hexa(isononanoate) (isononanoic acid, 1,1′-[2-[[3-[(1-oxoisononyl)oxy]-2,2-bis[[(1oxoisononyl)oxy]methyl]propoxy]methyl]-2-[[(1oxoisononyl)oxy]methyl]-1,3-propanediyl] ester or diPEiC9, Figure 1), is a stable ester that does not have the disadvantage above. It has been used as a lubricant component15 and is more viscous than Krytox GPL102 under the same conditions. Measurements were suggested to the author by Professor Josefa Fernández of the University of Santiago de Compostela, Spain, as the pVT data, necessary for the buoyancy correction required by the falling body viscometer employed in this laboratory, have been measured in hers.

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EXPERIMENTAL SECTION Sample details are given in Table 2. The Krytox GPL102 sample (lot K2391), purchased from DuPont (Wilmington, DE, USA), through ChemPoint, (Bellevue, WA, USA), by the National Energy Technology Laboratory, US Department of Energy, Pittsburgh, and Received: February 5, 2015 Accepted: April 1, 2015

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DOI: 10.1021/acs.jced.5b00099 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Viscosity Reference Material Correlations water toluene cyclopentane DIDP squalane squalane squalane squalane a

T range/K

pmax/MPa

η (25 °C, 0.1 MPa)/mPa·s

reference

238 to 1173 213 to 373 220 to 310 293 to 303 273 to 373 278 to 473 243 to 473 293 to 373

300a 250 25 0.1 0.1 200 467 1300

0.890 0.555 0.416 88.5 28.2 28.2 28.2 28.2

1 2 3 4 5 6 7 8

The correlation extends to higher pressures, but the temperature range is then correspondingly reduced.

Viscosities were measured with a falling body viscometer using self-centering sinkers with hemispherical faces of nominal diameters of (6.0 and 6.3) mm with calibrations obtained with Cannon Instruments viscosity standards covering the range (0.3 to 2875) mPa·s as described previously.23−25 (Previous calibrations have demonstrated constancy of the calibration constant up to 10 242 mPa·s, though the calibration constant slowly changes with time due to wear). The working equation relating the fall time, t, to the viscosity, η, is Figure 1. Structure of di(pentaerythritol) hexa(isononanoate), diPEiC9.

η (p , T ) =

distributed to the round-robin laboratories by Professor Bob Enick of the University of Pittsburgh, USA, was used as received. The water content, measured by Karl Fischer coulometric analysis was 10·10−6, as a weight fraction. 19F and 13C NMR spectra obtained with a Varian “Unity Plus” 400 MHz spectrometer were compared with those of similar compounds16 and are consistent with the polyfluoroether structure given above. The di(pentaerythritol) hexa(isononanoate) (C64H118O13) was also dried with molecular sieves. 13C NMR spectra obtained at 100.571 MHz with a Varian “Unity plus” 400 MHz spectrometer which were compared with AIST database spectra17 for pentaerythritol, nonanoic, and 8-methylnonanoic acids, confirmed the isomeric purity of diPEiC9. (This test was found to be necessary by work on the ester diisodecyl phthalate where the alcohol moiety consists of many isomeric forms.18) There appears to be no contamination by the parent acid and alcohol that might affect the viscosity. Spectra for both Krytox GPL102 and diPEiC9 are given as Figure 2. Densities at atmospheric pressure were measured with an Anton-Paar DMA vibrating-tube densimeter with an in-built viscosity correction (previously verified19): the uncertainty is estimated20 as ±0.02%. High-pressure densities were calculated from equations of state based on the results of Comuñas21 for Krytox GPL102 and of Fandiño22 for diPEiC9, normalized on the atmospheric pressure densities of this work.

t(1 − ρ /ρs ) A[(1 + 2αp(θ − θref )][1 − 2βT (p − pref )/3] (1)

(where A is the calibration constant, αp is the coefficient of thermal expansion of the viscometer tube and sinker, θ is the Celsius temperature, and βT the bulk compressibility of the sinker and tube material; θref = 25 °C and pref = 0.1 MPa), so there is a buoyancy factor dependent on the ratio of the density of the fluid ρ to that of the sinker ρs. This varies slightly with temperature and pressure, and its estimation is important when the calibrants and the material under study differ significantly in density. For diPEiC9 under the conditions of the measurements, it ranged from 0.860 to 0.874, values similar to those for the calibrants, but for the denser Krytox GPL102, it lay between 0.711 and 0.763. A platinum resistance thermometer calibrated between (−65 and 100) °C on ITS-90 to a tolerance of ± 8 mK was employed. The viscometer oil-bath temperature was controlled to within ± 0.01 K. The primary pressure gauge (400 MPa Heise CM) has been calibrated against a dead weight tester, and the pressures have an overall uncertainty of ± 0.2 MPa. The fall times are the average of at least three replicates. The combination of the uncertainties in replicate measurements (± 1 %), determined from several measurements at randomly selected state points, the calibration (± 1 %), and the calibrant viscosities in quadrature yields an expanded uncertainty of ± 2 %.

Table 2. Sample Data

Krytox GPL102 diPEiC9

CAS No.

source

812693-47-3

DuPont, Wilmington DE, USAb Croda-Uniqema, Cleveland, UK

127304-08-9

M/g·mol−1 specification 1720c

Lot K2391

1095.6

purity (manufacturer) 1.000 (wt fraction, as polyfluoroethers, no hydrocarbons detectable by IR) 0.95d (mole fraction)

106 w(H2O) 10

a

Weight fraction. bIATP/IUPAC round-robin sample. cApproximate number-average molar mass: see text. dExamination by both 1H (400 MHz) and 13C NMR suggests the purity is better than this. B



Article

Figure 2. NMR spectra: Krytox GPL102, (a) 13C, (b) 19F; 1H diPEiC9, (c) 1H, (d) 13C.The resonances at −171.6 ppm in (b) are from C6F6, used as a solvent and reference, and those at 30 and 206 ppm in (d) are those from the solvent and deuterium lock compound, (CD3)2CO.

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RESULTS AND DISCUSSION The atmospheric pressure densities, ρ0, are listed in Table 3 and can be represented by the polynomials:

the data are in very good agreement with the unpublished measurements of Comuñas.21 The high pressure densities necessary for the viscometer buoyancy correction were calculated for Krytox GPL102 using a Tait equation of state based on Comuñas’ measurements made to 120 MPa between (5 and 125) °C21 and for diPEiC9 using a Hayward equation of state based on Fandiño’s measurements22 made to 70 MPa between (10 and 125) °C. This required extrapolations for the higher pressures used here, but densities need only be known to 1 % for the buoyancy correction. The equations of state were normalized relative to the atmospheric pressure densities of this work. The viscosities are listed in Tables 4 and 5. Atmospheric pressure data were fitted to the Vogel−Fulcher−Tammann (VFT) equation:

Table 3. Atmospheric Pressure Density (ρ) and Expansivity (αp) Dataa Krytox GPL102

diPEiC9

θ/°C

−3

ρ/g·cm

10 αp/K

0.00 10.00 20.00 20.00 25.00 25.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00

1.902 13 1.883 57 1.864 99 1.865 01 1.855 64 1.855 65 1.846 28 1.827 47 1.808 55 1.789 58 1.770 50 1.751 29 1.731 96

0.971 0.985 1.000 1.000 1.008 1.008 1.016 1.032 1.048 1.065 1.082 1.099 1.117

3

−1

θ/°C

ρ/g·cm−3

103αp/K−1

0.00 10.00 20.00 25.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00

0.978 83 0.971 90 0.965 02 0.961 59 0.958 18 0.951 35 0.944 52 0.937 84 0.931 14 0.924 45 0.917 76

0.805 0.811 0.817 0.820 0.823 0.828 0.834 0.840 0.846 0.853 0.859

η = exp[A + B /(T − T0)]

In addition, it was found that the Avramov equation, eq 5, fits Krytox GPL102 with n = 3 (Litovitz equation), and diPEiC9 with n = 4 (the Barlow−Lamb equation, which generally fits esters well); these forms may be better than the VFT equation for extrapolation:

a

η = exp[A′ + B′/T n]

Standard uncertainties u are u(T) = 0.01 K, u(ρ) = 0.02 %, u(αp) = 0.02·10−3 K−1. −3

(2)

ρ0 (diPEiC9) = 0.978825 − 0.693782 ·10−3θ − 1.73246 ·10 θ

(5)

Coefficients are given in Table 6. Allowing n to float gives no improvement, and the values are integers within the precision of the fits. The Angell relation between the VFT parameters, δ = B/T0, and the glass transition temperature, Tg

−7 2

ρ0 (Krytox) = 1.90211 − 1.84626· 10 θ − 4.89689· 10 θ

−7 2

(4)

Tg /T0 = 1 + δ /2.303 log10(ηg /η0) (3)

(6)

where the logarithmic term is equal to 17 and allows the estimation of Tg.26 One obtains 178.6 K for Krytox GPL102 and 218.1 K for diPEiC9. For the high-pressure data, there is good agreement between results obtained with the two sinkers in the regions of overlap. Fits were first made to simple polynomials in the pressure for the

(where θ is the temperature in Celsius), both with a standard uncertainty of fit, u, of 0.000 02 g·cm−3. Expansivities, αp, are also listed in the table: (∂αp/∂T) is positive in both cases. There are no previously published measurements for comparison, though C



Article

Table 4. Viscosity (η) Data for Krytox GPL102a slug diameter/mm

θ/°C

p/MPa

t/s

ρ/ρsb

η/mPa·s

Rec

6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.3 6.3

0.00 0.00 0.00 5.00 5.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 20.00 20.00 25.00 25.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 40.00 40.00 40.00 40.00 50.00 50.00 50.00 50.00 50.00 50.00

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 12.5 12.5 25.1 41.7 42.1 59.3 60.3 81.2 81.8 95.5 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 10.6 15.1 15.2 25.3 25.3 49.6 49.7 75.1 75.3 100.0 100.8 101.0 124.5 124.6 126.5 150.7 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

702.6 702.1 701.6 504.0 502.9 372.3 372.7 372.9 365.9 368.6 372.5 632.9 634.4 1079 2049 2088 3967 4091 8656 8702 13868 215.8 215.8 169.4 169.3 134.8 135.5 135.5 134.5 135.3 135.2 133.5 133.6 133.7 133.8 202.0 241.2 241.7 350.1 350.3 790.3 797.3 1750 1758 3689 3713 3738 7242 7237 7590 14668 88.10 88.10 89.33 89.24 61.12 60.91 62.19 62.07 726.6 726.2

0.2608 0.2608 0.2608 0.2596 0.2596 0.2584 0.2584 0.2584 0.2584 0.2584 0.2584 0.2619 0.2619 0.2650 0.2686 0.2687 0.2719 0.2721 0.2756 0.2756 0.2777 0.2559 0.2559 0.2547 0.2547 0.2535 0.2535 0.2535 0.2535 0.2535 0.2535 0.2535 0.2535 0.2535 0.2535 0.2569 0.2582 0.2582 0.2609 0.2609 0.2665 0.2665 0.2712 0.2712 0.2752 0.2753 0.2753 0.2785 0.2786 0.2788 0.2818 0.2510 0.2510 0.2510 0.2510 0.2486 0.2486 0.2486 0.2486 0.2486 0.2486

206.3 206.2 206.0 148.2 147.9 109.6 109.8 109.8 107.8 108.6 109.7 185.5 186.0 315.0 595.1 606.5 1147 1183 2491 2504 3979 63.74 63.76 50.10 50.10 39.93 40.16 40.15 39.86 40.08 40.07 39.55 39.58 39.61 39.64 59.58 71.03 71.15 102.7 102.8 230.1 232.1 506.3 508.5 1062 1068 1075 2074 2073 2173 4182 26.18 26.18 26.54 26.52 18.22 18.15 18.53 18.50 18.30 18.29

0.091 0.091 0.091 0.18 0.18 0.32 0.32 0.32 0.33 0.33 0.32 0.11 0.11 0.039 0.011 0.011 0.0030 0.0028 0.0006 0.0006 0.0003 0.94 0.94 1.5 1.5 2.4 2.3 2.3 2.4 2.4 2.4 2.4 2.4 2.4 2.4 1.1 0.76 0.76 0.37 0.37 0.074 0.073 0.015 0.015 0.0035 0.0035 0.0035 0.0009 0.0009 0.0009 0.0002 5.48 5.49 5.34 5.35 11 11 11 11 1.3 1.4

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Table 4. continued slug diameter/mm

θ/°C

p/MPa

t/s

ρ/ρsb

η/mPa·s

Rec

6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.3 6.3 6.3 6.3 6.0 6.0 6.0 6.3 6.3 6.0 6.0 6.3 6.3 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0

50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 60.00 60.00 60.00 60.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00

9.7 11.0 26.0 26.0 50.2 50.4 76.0 76.1 95.4 95.7 124.1 124.8 151.3 151.4 175.7 175.8 199.7 200.6 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.34 0.35 10.2 10.3 10.5 12.2 12.3 25.71 25.73 25.78 26.2 26.2 49.8 50.59 50.60 75.61 75.68 88.2 88.5 100.5 100.6 125.2 125.4 151.8 152.4 173.2 174.1 200.8 202.0 207.6

87.94 92.32 153.3 152.6 319.0 320.7 641.8 642.4 1053 1061 2136 2166 4023 4045 7044 7071 12185 12223 527.6 525.9 521.4 522.6 33.30 32.66 32.74 396.7 396.4 33.70 33.77 391.7 390.2 33.20 33.11 47.47 45.64 46.51 49.83 49.81 77.76 77.82 77.95 75.32 75.09 152.8 154.6 154.9 287.1 287.6 386.8 388.5 507.1 509.2 865.1 868.7 1508 1520 2290 2324 3878 4008 4471

0.2521 0.2525 0.2571 0.2571 0.2630 0.2630 0.2681 0.2681 0.2714 0.2714 0.2756 0.2757 0.2791 0.2791 0.2819 0.2819 0.2845 0.2845 0.2461 0.2461 0.2461 0.2461 0.2436 0.2436 0.2436 0.2436 0.2436 0.2436 0.2436 0.2436 0.2436 0.2437 0.2437 0.2478 0.2478 0.2479 0.2485 0.2485 0.2530 0.2530 0.2530 0.2531 0.2532 0.2594 0.2596 0.2596 0.2649 0.2649 0.2672 0.2672 0.2692 0.2693 0.2730 0.2730 0.2765 0.2766 0.2791 0.2792 0.2821 0.2822 0.2828

26.09 27.37 45.18 44.97 93.27 93.74 186.3 186.5 304.5 306.7 613.7 622.5 1151 1157 2007 2014 3459 3469 13.32 13.28 13.17 13.20 9.983 9.793 9.82 10.05 10.04 10.11 10.12 9.922 9.884 9.954 9.927 14.16 13.61 13.87 14.84 14.84 23.02 23.04 23.08 22.30 22.23 44.87 45.37 45.48 83.66 83.80 112.4 112.9 146.9 147.5 249.3 250.4 432.4 435.9 654.6 664.1 1104 1141 1271

5.5 5.0 1.9 1.9 0.45 0.44 0.11 0.11 0.043 0.042 0.011 0.010 0.0030 0.0030 0.0010 0.0010 0.0003 0.0003 2.5 2.5 2.6 2.6 37 38 38 4.4 4.4 36 36 4.5 4.6 37 37 19 20 19 17 17 7.1 7.1 7.1 7.6 7.6 1.9 1.9 1.9 0.56 0.55 0.31 0.31 0.18 0.18 0.064 0.063 0.021 0.021 0.009 0.009 0.003 0.003 0.003

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Table 4. continued slug diameter/mm

θ/°C

p/MPa

t/s

ρ/ρsb

η/mPa·s

Rec

6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.0 6.0 6.0 6.0 6.0 6.3 6.0 6.0 6.3 6.0 6.0 6.3 6.3 6.3 6.0 6.3 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.3 6.3

80.00 80.00 80.00 80.00 80.00 80.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 95.00 95.00

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 11.35 11.38 30.7 35.0 35.7 41.2 41.2 41.5 45.4 50.3 50.4 60.2 74.7 75.0 79.9 80.0 99.7 99.9 100.1 100.2 100.6 101.1 124.4 124.4 124.7 125.0 125.4 150.3 150.3 150.9 151.0 175.2 175.7 198.7 200.4 219.4 222.7 225.5 0.1 0.1

300.3 300.0 298.7 297.3 302.2 302.3 241.1 241.0 239.1 239.1 238.6 344.6 345.5 611.0 57.82 59.25 67.55 67.55 66.25 890.0 85.65 85.84 1269 149.2 149.6 1977 1987 2972 259.0 2996 260.2 256.2 257.0 400.0 399.4 416.6 418.5 412.8 643.5 643.6 671.1 672.5 1035 1043 1558 1586 2164 2293 2421 215.1 215.4

0.2410 0.2410 0.2410 0.2410 0.2410 0.2410 0.2385 0.2385 0.2385 0.2385 0.2385 0.2438 0.2438 0.2507 0.2520 0.2522 0.2538 0.2538 0.2538 0.2549 0.2561 0.2562 0.2585 0.2616 0.2617 0.2627 0.2627 0.2663 0.2663 0.2663 0.2664 0.2664 0.2665 0.2702 0.2702 0.2702 0.2703 0.2703 0.2738 0.2738 0.2739 0.2739 0.2769 0.2770 0.2796 0.2797 0.2817 0.2820 0.2823 0.2372 0.2372

7.630 7.621 7.589 7.553 7.678 7.681 6.145 6.142 6.093 6.093 6.081 8.722 8.745 15.32 17.13 17.55 19.97 19.97 19.58 22.19 25.24 25.29 31.49 43.65 43.76 48.79 49.02 72.99 75.29 73.58 75.63 74.47 74.67 115.6 115.5 120.4 121.0 119.3 185.2 185.2 193.1 193.5 296.6 298.9 444.7 452.7 615.8 652.4 688.4 5.490 5.496

7.6 7.6 7.7 7.7 7.5 7.5 12 12 12 12 12 5.9 5.8 1.9 13 12 9.5 9.5 9.8 0.94 6.0 5.9 0.47 2.0 2.0 0.20 0.20 0.089 0.69 0.088 0.68 0.70 0.70 0.29 0.29 0.27 0.27 0.28 0.12 0.12 0.11 0.11 0.045 0.045 0.020 0.020 0.011 0.009 0.009 14 14

a

Standard uncertainties u are u(T) = 0.01 K, u(p) = 0.2 MPa above 0.1 MPa, u(t) = 0.1 %, u(ρ/ρs) = 0.3 %; combined expanded uncertainty for the viscosity, Uc(η) = 2 %. bρs(T,p) is the sinker density: the buoyancy correction factor in eq 1 is (1 − ρ/ρs). cReynolds number for annular flow: Re ≅ 2r12ρv/((r2 − r1)η) where v is the terminal velocity of the sinker and r1 and r2 are the radii of the sinker and tube, respectively.22

experimental isotherms and then to the modified forms of the VFT equation used in previous high-viscosity work (MVFT1 and MVFT2)16 for both substances, the modified Litovitz equation25 for Krytox GPL102 and the modified Barlow−Lamb equation (MBL)27 for diPEiC9. The fits to eq 7, 8 and 9 yielded similar standard uncertainties to the isothermal polynomial fits, giving

confidence in the temperature dependences employed in the former. Coefficients are given in Tables 7 and 8, and selected deviation plots are shown as Figures 3 and 4 (MVFT1 for Krytox GPL102 and MBL for diPEiC9). F



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Table 5. Viscosity (η) Data for diPEiC9a,b θ/°C

p/MPa

t/s

ρ/ρs

η/mPa·s

Re

θ/°C

p/MPa

t/s

ρ/ρs

η/mPa·s

Re

20.00 20.00 25.00 25.00 30.00 40.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 60.00 60.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.1 9.6 11.0 21.1 30.1 40.6 50.6 61.7 70.4 81.6 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 9.9 19.8 30.3 40.3 50.3 50.8

5973.6 5971.9 3756.3 3755.0 2428.9 1137.0 583.5 585.7 585.5 600.3 591.5 591.6 589.9 590.1 606.2 799.3 816.3 1104.2 1432.1 1913.7 2530.8 3421.3 4315.8 5860.2 334.7 334.6 205.6 205.4 213.2 212.1 212.9 210.3 210.3 207.9 209.7 209.2 275.0 355.2 460.2 586.0 742.2 737.3

0.1324 0.1324 0.1320 0.1320 0.1316 0.1307 0.1298 0.1298 0.1298 0.1298 0.1298 0.1298 0.1298 0.1298 0.1299 0.1307 0.1308 0.1317 0.1325 0.1333 0.1340 0.1347 0.1353 0.1360 0.1289 0.1289 0.1281 0.1281 0.1281 0.1281 0.1281 0.1281 0.1281 0.1281 0.1281 0.1281 0.1291 0.1300 0.1310 0.1318 0.1326 0.1326

2077.7 2077.1 1307.0 1306.5 845.4 396.0 203.4 204.1 204.1 209.2 206.6 206.7 206.1 206.1 211.7 278.3 284.8 384.9 498.8 665.8 879.9 1188.4 1498.2 2032.7 116.7 116.7 71.74 71.69 74.42 74.02 74.29 73.56 73.57 72.73 73.35 73.18 95.86 123.7 160.1 203.7 257.7 256.6

0.0005 0.0005 0.0014 0.0014 0.0032 0.015 0.055 0.055 0.055 0.052 0.054 0.053 0.054 0.054 0.051 0.030 0.028 0.016 0.0093 0.0053 0.0030 0.0017 0.0011 0.0006 0.17 0.17 0.44 0.44 0.41 0.41 0.41 0.42 0.42 0.43 0.42 0.42 0.25 0.15 0.089 0.056 0.035 0.035

70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 70.00 75.00 80.00 80.00 80.00 80.00 80.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00

61.1 69.4 81.0 91.0 100.3 111.5 125.6 140.9 150.7 150.8 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 10.1 20.1 30.4 40.2 50.5 60.5 70.1 80.4 90.4 100.6 120.0 138.8 161.2 180.5 200.2

948.4 1152.2 1465.6 1866.1 2262.6 2814.2 3812.2 5241.6 6577.6 6519.7 163.94 134.2 134.3 134.3 137.4 137.0 96.31 96.26 94.57 94.50 93.68 92.61 122.7 154.7 194.8 240.6 297.5 363.1 440.6 538.0 654.5 805.1 1147.0 1616.5 2355.8 3297.6 4707.8

0.1333 0.1339 0.1346 0.1352 0.1358 0.1364 0.1371 0.1378 0.1382 0.1382 0.1277 0.1272 0.1272 0.1272 0.1272 0.1272 0.1264 0.1264 0.1264 0.1264 0.1264 0.1264 0.1275 0.1285 0.1295 0.1304 0.1312 0.1320 0.1326 0.1333 0.1340 0.1346 0.1356 0.1365 0.1375 0.1382 0.1389

329.0 399.5 507.7 646.0 782.8 975.1 1319.9 1813.3 2269.4 2254.4 57.36 46.88 46.89 46.91 48.09 47.96 33.66 33.64 33.12 33.10 32.81 32.43 42.84 53.93 67.84 83.71 103.4 126.1 152.9 186.5 226.8 278.7 396.7 558.4 813.0 1137.0 1622.0

0.022 0.015 0.0091 0.0056 0.0039 0.0025 0.0014 0.0007 0.0005 0.0005 0.68 1.0 1.0 1.0 1.0 1.0 2.0 2.0 2.0 2.0 2.1 2.1 1.2 0.77 0.49 0.33 0.21 0.14 0.099 0.067 0.045 0.030 0.015 0.0076 0.0036 0.0019 0.0009

a Standard uncertainties u are u(T) = 0.01 K, u(p) = 0.2 MPa above 0.1 MPa, u(t) = 0.1 %, u(ρ/ρs) = 0.3 %; combined expanded uncertainty for the viscosity, Uc(η) = 2 %. b6.0 mm slug.

MVFT1:

Table 6. Coefficients of Best Fit to Viscosity Equations 4 and 5 VFT eq 3 a

A B/K T0/K standard uncertainty of fit/% δ (= B/T0) predicted Tg/K Avramov eq 4 A′a 10−9 B′/Kn n standard uncertainty of fit/% a

Krytox GPL102

η = exp[a + bp + cp2 + (d + ep + fp2 + gp3 )

diPEiC9

−2.8800 ± 0.037 982.2 ± 12 153.49 ± 0.93 0.8 6.40 178.6

−2.5199 ± 0.088 1030.8 ± 23 191.76 ± 1.5 1.3 5.38 218.1

−0.78901 ± 0.0041 0.124605 ± 0.00012 3 (Litovitz) 0.8

0.44916 ± 0.0082 53.1603 ± 0.097 4 (Barlow−Lamb) 1.3

/(T − T0)]

(7)

MVFT2: η = exp{a′ + b′p + c′p2 + δ′T0(p)/[T − T0(p)]} T0(p) = w + xp + yp2 + zp3

(8)

ML, n = 3; MBL, n = 4: η = exp[a″ + b″p + c″p2 + (d″ + e″p + f ″p2 + g ″p3 ) / T n]

η in mPa·s.

(9) 28

Figure 3 also shows a comparison with the results of Bair for the Krytox GPL102 sample at (40 and 70) °C. His data show a G



Article

Table 7. Coefficients of Best Fit to the Polynomials η = exp(α + βp + γp2 + δp3) ϑ/°C

pmax/MPa

ηmin/mPa·s

ηmax/mPa·s

102 β/MPa−1

α

10 30 50 70 90

95.5 150.7 200.6 207.6 225.5

110 40 18 10 6.1

3979 4182 3469 1271 688

4.6906 3.6825 2.9109 2.2955 1.8149

50 70 90

81.6 150.8 200.2

203 71 34

2033 2269 1622

5.3252 4.2917 3.5012

Krytox GPL102 4.3258 3.9292 3.6018 3.3757 3.1513 diPEiC9 3.0109 2.7280 2.4484

105 γ/MPa−2 5.8943 8.5779 8.4395 8.4723 8.0902 −2.5891 5.1676 4.2272

107 δ/MPa−3

standard uncertainty/%

2.0047 1.7697 1.6776 1.5164

0.8 0.7 1.2 1.5 1.5

1.4347 0.84847

0.8 1.1 1.1

Table 8. Coefficients of Best Fit to Viscosity Equations 7, 8, and 9a MVFT1 (eq 7) a b·103/MPa−1 c·106/MPa−2 d/K e/(K·MPa−1) f·103/(K·MPa−2) g·106/(K·MPa−3) T0/K standard uncertainty of fit/% δ (= d/T0) MVFT2, eq 8 a′ b′·103/MPa−1 c′·106/MPa−2 δ′ w/K x·103/(K·MPa−1) y·106/(K·MPa−2) y·106/(K·MPa−3) standard uncertainty of fit/% a″ b″·103/MPa−1 c″·106/MPa−2 d″·10−9/Kn e″·10−6/(Kn·MPa−1) f ″·10−3/(Kn·MPa−2) g″/(Kn·MPa−3) n standard uncertainty of fit/% a

Krytox GPL102

diPEiC9

−2.6427 ± 0.041 10.493 ± 0.36 −46.01 ± 2.3 908.70 ± 12 4.2446 ± 0.073 −6.601 ± 0.38 29.28 ± 1.0 159.25 ± 1.0 1.4 5.71

−2.4221 ± 0.077 3.134 ± 0.96 −21.60 ± 8.6 1005.3 ± 20 3.620 ± 0.13 −3.560 ± 1.1 14.98 ± 2.3 193.31 ± 1.3 1.3 5.20

−2.9608 ± 0.042 18.495 ± 0.26 −43.90 ± 1.4 6.695 ± 0.14 151.00 ± 1.1 232.92 ± 2.9 −670.4 ± 24 2.0257 ± 0.062 1.4 ML, eq 9 −0.77512 ± 0.0062 18.351 ± 0.23 −43.89 ± 1.5 0.12409 ± 0.00019 0.61002 ± 0.0072 −1.4847 ± 0.060 6.302 ± 0.22 3 1.4

−2.4740 ± 0.070 12.443 ± 0.51 −25.21 ± 4.5 5.297 ± 0.13 192.42 ± 1.2 181.34 ± 5.9 −382.6 ± 53 1.149 ± 0.10 1.2 MBL, eq 9 0.45150 ± 0.0071 12.979 ± 0.50 −26.35 ± 4.4 53.1073 ± 0.084 198.09 ± 5.9 −272.7 ± 48 1501 ± 210 4 1.2

Figure 3. Residuals (experimental−calculated values) for the fit to the MVFT1 equation, eq 7, for the viscosities of Krytox GPL102. This work, expanded uncertainty of the fit, ± 2.8 % (dashed lines, k = 2): ●, 10 °C; ■, 30 °C; ▲, 50 °C; ▼, 70 °C; ⧫, 90 °C. Bair,28 □, 40 °C; ▽, 70 °C; ◊, 110 °C.

Figure 4. Residuals (experimental−calculated values) for the fit to the MBL equation, eq 9, for the viscosities of diPEiC9. This work, expanded uncertainty of the fit, ± 2.4 % (dashed lines, k = 2): ▲, 50 °C; ▼, 70 °C; ⧫, 90 °C.

η in mPa·s.

standard deviation of 6 % from those of this work, with maximum deviations of 5.4 % (40 °C, 25 MPa) and −17 % (70 °C, 250 MPa). Most points in this region are within the combined uncertainties of 3 % (Bair) and 2 % (this work), respectively: the fitting equations extrapolated to 110 °C are also consistent with Bair’s data [maximum deviations (3.2 and −6.3) % for MVFT1]. The results of Baled et al.,13 which are for a different, unspecified lot of Krytox GPL102 at (37.9 and 98.9) °C, lie on average some 20 % higher than those reported here, between limits of (6 and 31) %. Evidently the effect of composition differences in lots may be significant for Krytox GPL102, but this will require confirmation from the other studies being carried out for this substance in other laboratories.

It is now common to apply thermodynamic or density scaling to the transport properties of dense fluids.29−31 In brief, the analysis makes use of the hypothesis that the transport properties of fluids other than those with directional bonding are primarily governed by the repulsive component of the intermolecular forces. Scaling assumes an intermolecular potential varying to the power 3γ

U ∼ (1/r )3γ H

(10) DOI: 10.1021/acs.jced.5b00099 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

with the parameter γ being a material specific, thermodynamic state independent quantity that can be used to scale structural relaxation times and the viscosity η(T , V ) = f (TV γ )

Department of Energy, Pittsburgh, PA, USA, for providing this laboratory with a sample of Krytox GPL 102.

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(1) Huber, M. L.; Perkins, R. A.; Laesecke, A.; Friend, D. G.; Sengers, J. V.; Assael, M. J.; Metaxa, I. N.; Vogel, E.; Mares, R.; Miyagawa, K. New International Formulation for the Viscosity of H2O. J. Phys. Chem. Ref. Data 2009, 38, 101−125. (2) Assael, M. J.; Avelino, H. M. T.; Dalaouti, N. K.; Fareleira, J. M. N. A.; Harris, K. R. Reference Correlation for the Viscosity of Liquid Toluene from 213 to 373 K at Pressures to 250 MPa. Int. J. Thermophys. 2001, 22, 789−799. (3) Assael, M. J.; Bauer, H.; Dalaouti, N. K.; Harris, K. R. Reference Correlation for the Viscosity of Liquid Cyclopentane from 220 to 310 K at Pressures to 25 MPa. Int. J. Thermophys. 2004, 25, 13−20. (4) Caetano, F. J. P.; Fareleira, J. M. N. A.; Fröba, A. P.; Harris, K. R.; Leipertz, A.; Oliveira, C. M. B. P.; Trusler, J. P. M.; Wakeham, W. A. An Industrial Reference Fluid for Moderately High Viscosity. J. Chem. Eng. Data 2008, 53, 2003−2011. (5) Comuñas, M. J. P.; Paredes, X.; Gaciño, F. M.; Fernández, J.; Bazile, J.-P.; Boned, C.; Daridon, J.-L.; Galliero, G.; Pauly, J.; Harris, K. R.; Assael, M. J.; Mylona, S. K. Reference Correlation of the Viscosity of Squalane from 273 to 373 K at 0.1 MPa. J. Phys. Chem. Ref. Data 2013, 42, 033101. (6) Mylona, S. K.; Assael, M. J.; Comuñas, M. J. P.; Paredes, X.; Gaciño, F.; Fernández, J.; Bazile, J.-P.; Boned, C.; Daridon, J.-L.; Galliero, G.; Pauly, J.; Harris, K. R. Reference Correlations for the Density and Viscosity of Squalane from 278 to 473 K at pressures to 200 MPa. J. Phys. Chem. Ref. Data 2014, 43, 013104. (7) Schmidt, K. A. G.; Pagnutti, D.; Curran, M. D.; Singh, A.; Trusler, J. P. M.; Maitland, G. C.; McBride-Wright, M. New Experimental Data and Reference Models for the Viscosity and Density of Squalane. J. Chem. Eng. Data 2015, 60, 137−150. (8) Schmidt, K. A. G.; Pagnutti, D.; Trusler, J. P. M. Reply to “Comment on ‘New Experimental Data and Reference Models for the Viscosity and Density of Squalane.’". J. Chem. Eng. Data 2015, 60, 1213− 1214. (9) Minutes, 9th IATP Meeting, Boulder, CO, USA, June 20th, 2009. http://transp.eng.auth.gr/index.php/iatp/2009. Accessed Mar 4, 2014. (10) HPHT Viscosity Standards Workshop Executive Summary, Jan 22, 2010. http://www.slb.com/services/characterization/reservoir/ core_pvt_lab/fluid_lab_services/hpht_pvt_studies/hpht_viscosity_ standards.aspx. Accessed Mar 4, 2014. (11) Project 2012-051-1-100. International standard for viscosity at temperatures up to 473 K and pressures below 200 MPa. http://www. iupac.org/nc/home/projects/project-db/project-details.html?tx_ wfqbe_pi1[project_nr]=2012-051-1-100. Accessed Mar 4, 2014. (12) Bamgbade, B. A.; Wu, Y.; Burgess, W. A.; McHugh, M. A. Experimental density and PC-SAFT modeling of Krytox (perfluoropolyether) at pressures to 275 MPa and temperatures to 533 K. Fluid Phase Equilib. 2012, 332, 159−164. (13) Baled, H. O.; Tapriyal, D.; Morreale, B. D.; Soong, Y.; Gamwo, I.; Krukonis, V.; Bamgbade, B. A.; Wu, Y.; McHugh, M. A.; Burgess, W. A.; Enick, R. M. Exploratory Characterization of a Perfluoropolyether Oil as a Possible Viscosity Standard at Deepwater Production Conditions of 533 K and 241 MPa. Int. J. Thermophys. 2013, 34, 1845−1864. (14) Kandil, M. E.; Harris, K. R.; Goodwin, A. R. H.; Hsu, K.; Marsh, K. N. Measurement of the Viscosity and Density of a Reference Fluid with a Nominal Viscosity at T = 298 K and p = 0.1 MPa of 29 mPa·s, at Temperatures between (273 and 423 K) and Pressures below 275 MPa. J. Chem. Eng. Data 2006, 51, 2185−2196. (15) Garcia, J.; Naccoul, R. A.; Fernández, J.; Razzouk, A.; Mokbel, I. Vapor-Pressure Measurements and Modeling of Dipentaerythritol Ester Lubricants. Ind. Eng. Chem. Res. 2011, 50, 4231−4237. (16) Persico, D. F.; Lagow, R. J. Synthesis of Branched Perfluoro Ethers by Direct Fluorination. Copolymers Based on Hexafluoroacetone. Macromolecules 1985, 18, 1383−1387. (17) SDBSWeb: http://sdbs.db.aist.go.jp (National Institute of Advanced Industrial Science and Technology, March 24, 2015).

The function f is not known. To evaluate γ, it is sufficient to fit lnη to simple polynomials in (TVγ), choosing γ such that the isotherms fall on a common curve with minimized residuals. The fits are not perfect, tending to be poorer for higher viscosities, but given the simplicity of the approach and that there is only one disposable parameter, the quality and utility of the model are quite good. One obtains γ values of (6.08 ± 0.02) and (4.20 ± 0.03), with standard uncertainties of the fits of (4.2 and 4.1) %, for Krytox GPL102 and diPEiC9, respectively. These values are typical of chain molecules and esters.32 Fragiadakis and Roland33 have shown that where the intermolecular potential can be approximated by an inverse power law, scaling is more appropriately done used reduced variables, though the IPL model, lacking the van der Waals attractive term in the potential, cannot have low-pressure liquid states. Nevertheless it has been shown from computer simulation that van der Waals liquids show “hidden” scale invariance of most thermodynamic and transport properties34 and that such scaling with reduced variables is more consistent with isomorph theory.35 It is of interest that such reduced variables have been used in matching transport properties of simple fluids with those of the hard sphere fluid in past years.36−38 The practical success of thermodynamic scaling over the hard-sphere theory for a wide variety of liquid types is due in part to the use of the actual molar or molecular volumes rather than the hard-sphere reduced volume (V/V0). For the hard sphere fluid, the reduced transport properties (e.g., fluidity) are approximately linear in (V/V0), whereas for anything other than the simplest molecules, the dependence is distinctly nonlinear,37 though empirical extensions of the hard-sphere correlation approach can be employed within certain limitations,39,40 as has been done recently for squalane.6 The current approaches to density scaling have been reviewed recently by López and Fernández.31 For the viscosity the reduced property is η* = ηv 2/3/ mkT

(12)

where m is the molecular mass and v the molecular volume (V/ NA). For Krytox GPL102 and diPEiC9, one obtains values of the scaling parameter, γ*, of (5.55 ± 0.05) and (3.99 ± 0.05) with (improved) standard uncertainties of fit of (3.2 and 2.6) %, respectively. As is usual for the viscosity,31 γ* < γ.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS It is a pleasure to thank Dr. Marı ́a Comuñas and Dr. Olivia Fandiño of the University of Santiago de Compostela, Spain, for kindly allowing the use of their unpublished pVT data, and Professor Josefa Fernández (USC) and Professor Scott Bair (Georgia Institute of Technology, Atlanta, GA) for their interest in this work. Dr. Barry Gray (UNSW Canberra) kindly assisted with the measurement of the NMR spectra. The author would like to thank the National Energy Technology Laboratory, I



Article

(18) Harris, K. R.; Bair, S. Temperature and Pressure Dependence of the Viscosity of Diisodecyl Phthalate at Temperatures between (0 and 100) °C and at Pressures to 1 GPa. J. Chem. Eng. Data 2007, 52, 272− 278. (19) Harris, K. R.; M. Kanakubo, M.; Woolf, L. A. Temperature and Pressure Dependence of the Viscosity of the Ionic Liquids 1-Octyl-3methylimidazolium Hexafluorophosphate and 1-Octyl-3-methylimidazolium Tetrafluoroborate. J. Chem. Eng. Data 2006, 51, 1161−1167. (20) Kanakubo, M.; Harris, K. R. Density of 1-Butyl-3-methylimidazolium Bis(trifluoromethanesulfonyl)amide and 1-Hexyl-3-methylimidazolium Bis(trifluoromethanesulfonyl)amide over an Extended Pressure Range up to 250 MPa. J. Chem. Eng. Data, DOI: 10.1021/ je501118w. (21) Comuñas, M. J. P. University of Santiago de Compostela, Spain, unpublished data; private communication. ́ (22) Fandiño, O. Propiedades Termofisicas de Lubricantes Tipo Éster. Densidad y Solubilidad del CO2. Ph.D. Thesis, University of Santiago de Compostela, Spain, 2009. (23) Malhotra, R.; Price, W. E.; Woolf, L. A.; Easteal, A. J. Thermodynamic and Transport Properties of 1,2-dichloroethane. Int. J. Thermophys. 1990, 11, 835−861. (24) Harris, K. R. Temperature and Pressure Dependence of the Viscosity of Toluene. J. Chem. Eng. Data 2000, 45, 893−897. (25) Harris, K. R.; Woolf, L. A.; Kanakubo, M. Temperature and Pressure Dependence of the Viscosity of the Ionic Liquid 1-butyl-3methylimidazolium Hexafluorophosphate. J. Chem. Eng. Data 2005, 50, 1777−1782. (26) Angell, C. A. Formation of Glasses from Liquids and Biopolymers. Science 1995, 267, 1924−1935. (27) Harris, K. R. Temperature and Pressure Dependence of the Viscosities of 2-EthylhexylBenzoate, Bis(2-ethylhexyl) Phthalate, 2,6,10,15,19,23-Hexamethyltetracosane (Squalane), and Diisodecyl Phthalate. J. Chem. Eng. Data 2009, 54, 2729−2738. (28) Bair, S. The Temperature and Pressure Dependence of Viscosity and Volume for Two Reference Liquids. Lubrication Sci., 2015, in press. (29) Roland, C. M.; Bair, S.; Cassalini, R. Thermodynamic Scaling of the Viscosity of van der Waals, H-bonded, and Ionic Liquids. J. Chem. Phys. 2006, 125, 124508. (30) Comuñas, M. J. P.; Paredes, X.; Gaciño, F. M.; Fernández, J.; Bazile, J. P.; Boned, C.; Daridon, G.; Galliero, J. L.; Pauly, J.; Harris, K. R. Viscosity Measurements for Squalane at High Pressures to 350 MPa from T = (293.15 to 373.15) K. J. Chem. Thermodynamics 2014, 69, 201−208. (31) Fernández, J.; López, E. R.; Density Scaling Approach. In Experimental Thermodynamics. Vol. IX. Advances in Transport Properties of Fluids. Assael, M. J., Goodwin, A. R. H., Vesovic, V., Wakeham, W. A., Eds.; Royal Society of Chemistry: London, 2014; Chapter 9.3. (32) López, E. R.; Pensado, A. S.; Fernández, J.; Harris, K. R. On the Density Scaling of pVT Data and Transport Properties for Molecular and Ionic Liquids. J. Chem. Phys. 2012, 136, 214502. (33) Fragiadakis, D.; Roland, C. M. On the Density Scaling of Liquid Dynamics. J. Chem. Phys. 2011, 134, 044504. (34) Schrøder, T. B.; Pedersen, U. R.; Bailey, N. P.; Toxvaerd, S.; Dyre, J. C. Hidden scale invariance in molecular van der Waals liquids: A simulation study. Phys. Rev. E 2009, 80, 041502. (35) Dyre, J. C. Hidden Scale Invariance in Condensed Matter. J. Phys. Chem. B 2014, 118, 10007−10024. (36) Dymond, J. H. The Interpretation of Transport Coefficients on the Basis of the Van der Waals Model: I Dense Fluids. Physica 1974, 75, 100−114. (37) Tyrrell, H. J. V.; Harris, K. R. Diffusion in Liquids; Butterworths: London, 1984; Chapter 9.3. (38) Harris, K. R. The Selfdiffusion Coefficient and Viscosity of the Hard Sphere Fluid Revisited: A Comparison with Experimental Data for Xenon, Methane, Ethene and Trichloromethane. Mol. Phys. 1992, 77, 1153−1167. (39) Assael, M. J.; Dymond, J. H.; Papadaki, M.; Patterson, P. M. Correlation and Prediction of Dense Fluid Transport Coefficients. I. nAlkanes. Int. J. Thermophys. 1992, 13, 269−281.

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Temperature and Pressure Dependence of the Viscosities of Krytox

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