Measurement and Correlation of Densities and Dynamic Viscosities of

Article pubs.acs.org/IECR

Measurement and Correlation of Densities and Dynamic Viscosities of Perfluoropolyether Oils† Tara J. Fortin,* Arno Laesecke, and Jason A. Widegren National Institute of Standards and Technology, Material Measurement Laboratory, Applied Chemicals and Materials Division, 325 Broadway, Boulder, Colorado 80305-3328, United States S Supporting Information *

ABSTRACT: The densities and dynamic viscosities of five different polydisperse perfluoropolyethers (PFPE) were measured at atmospheric pressure over the combined temperature range 263.15−373.15 K. For one PFPE being considered as a high-temperature high-pressure viscosity standard reference material, measurements were made on two separate samples to examine the lot-to-lot variability in density and viscosity; significant variability was observed only for the viscosity data. Experimental data were correlated as a function of temperature. A simple quadratic equation was used for density, while three equations (DIPPR, VFT, and Waterman) were applied to the viscosity data. The DIPPR equation represented the viscosity data with deviations approximately an order of magnitude lower than the other two equations.

1. INTRODUCTION

shape, and charge distribution of the lubricant molecules on their interactions. Until recently, the explicit characterization of the viscosity− temperature relationship of industrially relevant fluids was largely unfeasible due to the time-consuming nature of making measurements with gravitational capillary viscometers immersed in large thermostated baths. In 1929, in an effort to minimize the experimental effort required, Dean and Davis introduced the viscosity index (VI) which characterizes the viscosity−temperature relationship based on the kinematic viscosities of a material at 313.15 and 373.15 K.3 The method is coded in ASTM Standard Practice D 2270.4 However, various shortcomings, inadequacies, and critiques of the VI have been reviewed and added to by Verdier et al.5 One should also note that the VI is focused on the kinematic viscosity, which is defined as ν = η/ρ. The temperature dependence of kinematic viscosity is less pronounced than that of the dynamic viscosity, η, because the latter is divided by the density, ρ, of the material which is also temperature dependent, although less so. Formulating the VI in terms of kinematic viscosity was a consequence of open gravitational capillary viscometers being the dominant type of viscometer, for which kinematic viscosity is the measurand. However, the dynamic viscosity is more important in science and engineering. To convert kinematic viscosity to dynamic viscosity, the density of a liquid has to be obtained from another data source. Because of this relationship, ideally viscosity and density should always be measured in

Perfluorinated compounds are predominantly hydrocarbons where the hydrogens have been substituted by fluorine atoms. These compounds are chemically stable and largely inert. The high electronegativity of fluorine is key to the understanding of these compounds’ unique material and thermophysical properties. Fluorine binds its electrons very tightly, resulting in strong C−F bonds and low electron cloud polarizabilities of perfluorinated compounds. Therefore, on the nanoscale the molecular interactions between perfluorinated compounds and other molecules are more repulsive than those of their hydrogenated counterparts. On the macroscale, this results in lower critical temperatures, lower surface tensions, greater hydrophobicities, and generally low miscibilites with other liquids. Morgado et al. discuss some of the applications that arise from these unique properties, including medical applications that take advantage of the biocompatibility of perfluorinated hydrocarbons.1 Perfluoropolyethers (PFPEs) have been in use since the 1960s as lubricant liquids and greases at high temperatures. The chemical formulation and physical properties of these polymers have been reviewed by Bell and Howell.2 As with many functional fluids, their properties have been characterized as needed for engineering purposes but not comprehensively. An important property of lubricants is their viscosity. However, the temperature dependence of the viscosity of liquids can be as important as the viscosity itself. For example, two lubricants may have the same viscosity at a given temperature, but how this value may change with temperature can be very different. Consequently, the temperature dependence of viscosity comprises additional information about the influence of size, © XXXX American Chemical Society

Received: May 19, 2016 Revised: June 28, 2016 Accepted: July 8, 2016

A

DOI: 10.1021/acs.iecr.6b01921 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research

Figure 1. The structure was obtained from quantum mechanical calculations with a semiempirical model using parameterization

parallel. Consequently, instruments combining densimeters and viscometers have been developed over the last two decades. For example, by taking advantage of the frictionless bearing resulting from the magnetic suspension coupling, single-sinker densimeters were expanded into rotating-cylinder viscometers to measure the combined density and viscosity of gases up to moderate pressures using a single pressure vessel outfitted with separate sensors.6−8 A second instrument utilized a vibrating wire technique to simultaneously measure density and viscosity of compressed liquids.9−11 Additional instruments have combined separate dedicated densimeters and viscometers in series to make measurements on a single sample. For example, Seibt et al.12 integrated a single-sinker densimeter into a vibrating-wire viscometer for highly accurate measurements of gases, while McBride-Wright et al.13 combined a vibrating-wire viscometer and a vibrating-tube densimeter for measurements of liquids to 100 MPa. Similarly, a novel rotating concentriccylinder viscometer was combined in series with a vibratingtube densimeter in the SVM 3000 (Anton Paar Inc.) for measurements at ambient pressure. (In order to describe materials and experimental procedures adequately, it is occasionally necessary to identify commercial products by manufacturers’ names or labels. In no instance does such identification imply endorsement by the National Institute of Standards and Technology nor does it imply that the particular product or equipment is necessarily the best available for the purpose.) This instrument was used in the present study for atmospheric pressure density and viscosity measurements of five PFPE lubricants over the combined temperature range 263.15−373.15 K. PFPEs are suitable standard reference materials because they are lipophobic as well as hydrophobic.14 These properties, in combination with their thermal stability, have resulted in the recent proposal of PFPEs as viscosity standard reference materials at elevated pressures and temperatures.15,16 Initial measurements of Baled et al.17,18 showed that GPL-102 has a viscosity at 533.15 K and a pressure of 241 MPa that is representative of oils under deepwater production conditions in the Gulf of Mexico. Therefore, a sample of GPL-102 is currently being characterized in several laboratories around the world.19 This same sample was included in the present measurements to provide additional reference data and to assess the lot-to-lot variability of density and viscosity. Finally, in an effort to facilitate their industrial use, the present experimental data have been correlated as a function of temperature, and the results are included herein. For viscosity in particular, a large number of such correlations have been developed in different fields of material science,20−24 but there is little guidance in the literature about their performance. Therefore, in this work we compare the results of three representative viscosity−temperature correlations. In contrast, experimental density data are correlated with a simple quadratic equation.

Figure 1. Molecular size, shape, and charge distribution of perfluoropolyether C32F66O10. See text for details.

method 3 (PM3).25 This is a very approximate approach to solving the Schrödinger equation, but it is sufficient for illustration purposes. The molecule is shown in terms of an electron density isosurface of 0.002 electrons·au−3 (with 1 atomic unit = 5.292 nm being the Bohr radius of hydrogen). This surface represents approximately 99% of a molecule. The electrostatic potential is color mapped onto the electron density surface. The color scale ranges from red (negative charge) to blue (positive charge). Due to their electronegativity, the fluorine atoms appear red. The charge distribution across the molecule is rather uniform and negative. This is the molecular basis for the stability of the PFPEs and for their hydro- and lipophobicity. Five samples of Krytox GPL oils were selected for the density and viscosity measurements presented in this work: GPL-101 (lot K1552), GPL-102 (lot K1608), GPL-104 (lot K0813), GPL-105 (lot L15777), and GPL-106 (lot K1848). Sample selection was guided by the frequency of their industrial use. Additionally, a second sample of GPL-102 (lot K2391) was measured to contribute to its characterization as a certified viscosity standard reference material (CVSRM) at hightemperature and high-pressure conditions. Given their hydrophobicity, PFPEs are not expected to contain much water. This was verified by performing a coulometric Karl Fischer titration on the sample of GPL-102 (lot K2391). Results indicated a water concentration below the detection limit of the apparatus (100 in all of the spectra. The resulting calculated average chain length (n) is shown in Table 1 for each of the six PFPE samples. The combined standard Table 1. Average Polymer Chain Length for Six PFPE Samples GPL-101 GPL-102 GPL-102 GPL-104 GPL-105 GPL-105 a b

(lot (lot (lot (lot (lot (lot

K1552) K1608) K2391) K0813) L15777) K1848)

na

uc(n)b

7.6 10.6 10.2 16.7 26.6 33.1

1.1 1.1 1.1 1.2 1.6 1.5

Average polymer chain length determined by 13C NMR spectroscopy. Combined standard uncertainty.

uncertainties (uc(n)) are based on an assessment of baseline drift and the agreement between spectral peak areas. Our results are consistent with the findings of Tapriyal et al.28 who report data, provided by DuPont, that correspond to average chain lengths from 6.3 for GPL-101 to 34.9 for GPL-106. C


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Industrial & Engineering Chemistry Research Table 2. Measured Densities for Six PFPE Samples at Ambient Pressurea GPL-101

GPL-102

GPL-102

(lot K1552)

(lot K1608)

(lot K2391)

(K)

ρ̅ (kg·m−3)

263.15 268.15 273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15

1907.72 1897.98 1888.24 1878.44 1868.68 1858.80 1848.98 1839.18 1829.36 1819.56 1809.72 1799.92 1790.02 1780.18 1770.30 1760.40 1750.46 1740.52 1730.56 1720.60 1710.56 1700.52 1690.48

T

t95b

U(ρ̅)c (kg·m−3)

U(ρ̅)c (%)

ρ̅ (kg·m−3)

t95b


U(ρ̅)c (%)

ρ̅ (kg·m−3)

t95b

(K)

ρ̅ (kg·m−3)


U(ρ̅)c (%)

263.15 268.15 273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15

1945.50 1936.35 1927.15 1917.90 1908.50 1899.00 1889.85 1880.85 1871.92 1863.05 1854.22 1845.42 1836.62 1827.78 1818.90 1810.03 1801.12 1792.25 1783.38 1774.50 1765.60 1756.70 1747.82

2.036 2.038 2.038 2.039 2.039 2.039 2.040 2.040 2.040 2.039 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.039 2.039 2.038 2.037

2.40 2.39 2.38 2.38 2.38 2.38 2.37 2.37 2.37 2.38 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.38 2.38 2.38 2.39

0.12 0.12 0.12 0.12 0.12 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.14 0.14

1931.35 1922.55 1913.70 1904.80 1895.82 1886.83 1877.90 1869.13 1860.53 1851.95 1843.45 1834.95 1826.45 1817.97 1809.48 1800.98 1792.48 1783.98 1775.50 1767.00

2.039 2.039 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.039

2.38 2.38 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.38

0.12 0.12 0.12 0.12 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13

1927.08 1918.36 1909.66 1900.98 1892.22 1883.42 1874.56 1865.82 1857.22 1848.74 1840.30 1831.90 1823.50 1815.16 1806.78 1798.46 1790.10 1781.70 1773.30

2.039 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.041 2.041 2.041 2.041 2.041 2.040 2.040

2.38 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37

0.12 0.12 0.12 0.12 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13

T

t95b


2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.041 2.041 2.041 2.040 2.040 2.040 2.041 2.041 2.040 2.040 2.040 2.040 2.040 GPL-104

2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37

U(ρ̅)c (%)

ρ̅ (kg·m−3)

0.12 0.12 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.14 0.14 0.14 0.14 0.14 0.14 0.14

1924.38 1914.56 1905.00 1895.58 1886.20 1876.86 1867.48 1858.14 1848.76 1839.36 1830.00 1820.58 1811.20 1801.82 1792.40 1782.92 1773.52 1764.04 1754.56 1745.08 1735.58 1726.08 1716.60

(lot K0813)

t95b


2.038 2.039 2.039 2.040 2.039 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 GPL-105

2.38 2.38 2.38 2.37 2.38 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37

U(ρ̅)c (%)

ρ̅ (kg·m−3)

0.12 0.12 0.12 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.14 0.14 0.14 0.14 0.14

1922.70 1912.95 1903.40 1893.95 1884.52 1875.12 1865.72 1856.30 1846.90 1837.50 1828.05 1818.62 1809.20 1799.72 1790.27 1780.80 1771.30 1761.83 1752.30 1742.80 1733.25 1723.70 1714.12

(lot L15777)

t95b


2.039 2.039 2.039 2.039 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.040 2.041 2.040 2.040 2.041 2.041 2.041 2.041 2.041 2.040 2.040 2.040 GPL-106

2.38 2.38 2.38 2.38 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37

U(ρ̅)c (%) 0.12 0.12 0.12 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.14 0.14 0.14 0.14 0.14

(lot K1848)

Ambient pressure during measurements was ∼83 kPa. bCoverage factor from the t-distribution for each corresponding degrees of freedom and a 95% level of confidence. cU(ρ̅) is expanded uncertainty at the 95% confidence level for density.

a

ature to 373.15 K in 5 K increments. Although the reported viscosity range of the instrument extends to 20 000 mPa·s, we encountered problems with some of the samples when trying to

measure viscosity at 263.15 K, despite being below the reported upper viscosity limit. As a result, the minimum temperature measured varied from 263.15 K for GPL-101, GPL-102, and D


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Industrial & Engineering Chemistry Research GPL-104, to 278.15 K for GPL-105, and 283.15 K for GPL106. At least five separate scans were performed for each of the samples with a fresh aliquot of sample injected into the instrument prior to each scan. In between PFPE samples, the measurement cells were thoroughly cleaned and dried to avoid cross-contamination. This was of particular concern since our past experience has shown that the removal of perfluorinated compounds from glass or metal surfaces can be difficult due to their wetting properties.30 If GPL-102, or any other PFPE, is to be used as a commercially available CVSRM, the identification of suitable solvent(s) is of critical importance. After experimenting with several solvents, DuPont Vertrel XF (1,1,1,2,3,4,4,5,5,5decafluoropentane, CAS No. 138495-42-8) was selected for use in this work. As an additional precaution against potential cross-contamination, the first measurement scan for each new PFPE sample was excluded during subsequent analyses.

3. RESULTS 3.1. Density. Density measurement results for the six PFPE samples are presented in Table 2. Tabulated densities are averages (ρ̅) of four to six separate temperature scans. Associated expanded uncertainty estimates (U(ρ̅)) are also included. These are calculated according to the expression U (ρ ̅ ) = t 95(dfρ ) ·u(ρ ̅ )

Figure 3. Density measurements as a function of temperature at ambient pressure.

(1)

where t95(dfρ) is the coverage factor taken from the tdistribution for dfρ degrees of freedom and 95% confidence level and u(ρ̅) is the combined standard uncertainty for the density measurements. The corresponding value of t95(dfρ) can be determined with appropriate software or via interpolation of the values in Table G.2 of the Guide to the Expression of Uncertainty in Measurement.31 The corresponding values of t95(dfρ) are included in Table 2 for clarity. Resulting expanded uncertainties range from 2.37 to 2.40 kg·m−3 and correspond to relative expanded uncertainties that range from an overall minimum of 0.12% to an overall maximum of 0.14%. Additional details regarding the density uncertainty analysis employed in this work are given in section S2 of the Supporting Information. The density results reported in Table 2 are plotted as a function of temperature in Figure 3. It is clear from this figure that the density increases with increasing polymer chain length. GPL-101 is the least dense with values that range from 1907.72 kg·m−3 at 263.15 K to 1690.48 kg·m−3 at 373.15 K. GPL-106 is the densest with values ranging from 1927.08 kg·m−3 at 283.15 K to 1773.30 kg·m−3 at 373.15 K. This corresponds to a difference in density between these two samples of 3.0% at 283.15 K and 4.7% at 373.15 K. In contrast to the large differences observed between GPL-101 and GPL-106, GPL-105 and GPL-106 exhibit densities that are much more similar varying by 0.2% at 283.15 K to 0.4% at 373.15 K. Also worth noting in Figure 3 is that the two lots of GPL-102 exhibit very similar densities. This is more clearly shown in the top half of Figure 4, where the lot-to-lot density deviations are plotted as a function of temperature. Observed deviations range from 0.08% at 263.15 K to 0.14% at 373.15 K and are within estimated expanded uncertainties (Table 2). The relative order of these two lots, with lot K1608 exhibiting slightly higher densities than lot K2391, is consistent with the higher average polymer chain length of lot K1608 (10.6) relative to that of lot K2391 (10.2) (Table 1).

Figure 4. Density deviations for GPL-102. Lot-to-lot deviations for the two samples measured in this work are shown in the top graph. Deviations of literature data from measurement results reported in this work for GPL-102 (lot K2391) are shown in the bottom graph. Data from both Harris32 and Comuñas et al.33 are for lot K2391, while the data from Bamgbade et al.34 are for lot K1537.

The bottom half of Figure 4 shows the results of comparisons with available literature data for GPL-102 plotted as percent deviation as a function of temperature. Harris32 reports density measurements at atmospheric pressure (0.1 MPa) from 273.15 to 363.15 K for GPL-102 (lot K2391). Comuñas et al.33 report density measurements for GPL-102 (lot K2391) from two separate instruments over a combined temperature range of 278.15−398.15 K and for pressures up to 120 MPa; data at atmospheric pressure (0.1 MPa) are included in Figure 4. Bamgbade et al.34 report density measurements at elevated pressures to 275 MPa and temperatures between 298.05 and 533.05 K for a different lot of GPL-102 (K1537); atmospheric pressure values for the comparisons shown in E


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Industrial & Engineering Chemistry Research Table 3. Measured Dynamic Viscosities for Six PFPE Samples at Ambient Pressurea GPL-101

GPL-102

GPL-102

(lot K1552)

(lot K1608)

(lot K2391)

(K)

η̅ (mPa·s)

263.15 268.15 273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15

142.6 102.0 75.17 56.77 43.82 34.50 27.63 22.49 18.55 15.50 13.10 11.19 9.637 8.374 7.331 6.461 5.730 5.111 4.583 4.130 3.737 3.396 3.096

T

t95b

U(η)̅ c (mPa·s)

U(η)̅ c (%)

η̅ (mPa·s)

t95b

(K)

η̅ (mPa·s)

263.15 268.15 273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15

3450.9 2138.8 1376.9 917.7 631.4 446.7 323.7 240.2 182.0 140.4 110.2 87.90 71.08 58.23 48.27 40.44 34.22 29.22 25.15 21.80 19.03 16.72 14.79

1.990 1.991 1.995 1.993 1.992 1.992 1.991 1.990 1.990 1.991 1.991 1.992 1.993 1.994 1.994 1.995 1.995 1.995 1.995 1.997 1.999 2.002 2.006

65.3 35.7 21.2 9.8 6.3 4.2 3.0 2.1 1.6 1.2 0.9 0.70 0.55 0.44 0.37 0.31 0.26 0.23 0.20 0.18 0.16 0.15 0.14

1.9 1.7 1.5 1.1 0.99 0.95 0.91 0.88 0.86 0.83 0.81 0.79 0.78 0.76 0.76 0.76 0.76 0.77 0.79 0.82 0.85 0.89 0.93

3289.8 2155.0 1460.3 1018.2 728.2 533.2 398.6 303.7 235.5 185.5 148.3 120.1 98.46 81.62 68.36 57.80 49.29 42.37 36.69 31.99

1.993 1.994 1.997 1.992 1.992 1.992 1.992 1.992 1.992 1.993 1.994 1.995 1.997 1.998 1.999 1.999 1.999 1.999 1.998 1.999

T

t95b

U(η)̅ c (mPa·s)

1.991 1.6 1.989 1.0 1.990 0.68 1.991 0.48 1.993 0.36 1.994 0.27 1.994 0.21 1.995 0.17 1.997 0.14 1.998 0.11 2.000 0.09 2.001 0.08 2.003 0.067 2.005 0.057 2.007 0.049 2.008 0.043 2.008 0.038 2.009 0.034 2.008 0.031 2.007 0.028 2.006 0.026 2.004 0.024 2.003 0.022 GPL-104

U(η)̅ c (%)

η̅ (mPa·s)

1.1 0.98 0.90 0.85 0.81 0.79 0.77 0.75 0.74 0.72 0.71 0.70 0.69 0.68 0.67 0.67 0.67 0.67 0.67 0.68 0.68 0.70 0.71

496.2 334.5 232.9 166.8 122.6 92.26 70.87 55.50 44.20 35.75 29.31 24.34 20.44 17.34 14.85 12.83 11.17 9.789 8.638 7.668 6.845 6.138 5.530

(lot K0813)

t95b

(%)

η̅ (mPa·s)

1.3 1.1 1.0 0.93 0.88 0.85 0.83 0.81 0.79 0.77 0.75 0.73 0.72 0.71 0.70 0.70 0.70 0.70 0.71 0.72 0.73 0.75 0.78

432.3 293.2 205.3 147.8 109.2 82.53 63.68 50.06 40.02 32.48 26.72 22.25 18.74 15.94 13.68 11.84 10.33 9.069 8.016 7.126 6.368 5.717 5.156

U(η)̅ c (mPa·s)

U(η)̅ c

t95b

(%)

η̅ (mPa·s)

U(η)̅ c (mPa·s)

U(η)̅ c (%)

58.1 34.2 21.6 10.1 6.8 4.8 3.4 2.5 1.9 1.5 1.2 0.9 0.73 0.59 0.49 0.41 0.36 0.31 0.27 0.25

1.8 1.6 1.5 0.99 0.93 0.89 0.86 0.84 0.82 0.80 0.78 0.76 0.74 0.73 0.72 0.72 0.72 0.73 0.75 0.77

3901.8 2598.1 1785.3 1261.2 912.4 674.6 508.7 390.6 304.9 241.5 194.0 157.8 129.8 107.9 90.63 76.79 65.61 56.50 49.01

1.994 1.994 1.997 2.001 1.991 1.991 1.992 1.992 1.992 1.993 1.994 1.996 1.997 1.998 1.999 1.999 1.998 1.998 1.999

70.0 41.4 26.5 17.8 8.5 6.0 4.4 3.3 2.5 1.9 1.5 1.2 1.0 0.8 0.65 0.55 0.48 0.42 0.38

1.8 1.6 1.5 1.4 0.93 0.89 0.86 0.83 0.81 0.79 0.77 0.75 0.74 0.73 0.72 0.72 0.73 0.75 0.77

U(η)̅ c (mPa·s)

1.993 6.3 1.991 3.7 1.991 2.3 1.991 1.5 1.991 1.1 1.991 0.79 1.992 0.59 1.992 0.45 1.993 0.35 1.994 0.27 1.995 0.22 1.997 0.18 1.999 0.15 2.000 0.12 2.001 0.10 2.002 0.09 2.002 0.08 2.002 0.068 2.001 0.061 2.000 0.055 2.000 0.050 2.000 0.046 2.000 0.043 GPL-105

U(η)̅ c

(lot L15777)

t95b

U(η)̅ c (mPa·s)

1.993 5.4 1.991 3.2 1.991 2.0 1.992 1.4 1.992 1.0 1.992 0.69 1.992 0.52 1.993 0.40 1.994 0.31 1.995 0.25 1.996 0.20 1.998 0.16 2.000 0.13 2.001 0.11 2.003 0.10 2.003 0.08 2.004 0.07 2.003 0.063 2.002 0.056 2.001 0.051 2.001 0.046 2.000 0.043 1.999 0.040 GPL-106

U(η)̅ c (%) 1.2 1.1 0.98 0.92 0.87 0.84 0.82 0.79 0.78 0.76 0.74 0.73 0.71 0.70 0.69 0.69 0.69 0.69 0.70 0.71 0.72 0.74 0.77

(lot K1848)

Ambient pressure during measurements was ∼83 kPa. bCoverage factor from the t-distribution for each corresponding degrees of freedom and a 95% level of confidence. cU(η̅) is expanded uncertainty at the 95% confidence level for dynamic viscosity.

a

Figure 4 were calculated from the reported equation and associated parameters. The data of Harris32 deviate from −0.07% to −0.03% relative to the values reported in Table 2.

While these deviations are not within Harris’s reported uncertainties of 0.02%,32 they are well within the uncertainties reported in this work. The data of Comuñas et al.33 deviate F


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Industrial & Engineering Chemistry Research from −0.08% to −0.02%. Again, these deviations exceed the authors’ reported uncertainties of 0.03−0.04%33 but are within the uncertainties reported here. Finally, deviations for the data of Bamgbade et al.34 range from a minimum of −0.6% to a maximum of +1.0%; these values are within the authors’ reported uncertainties of 0.7% for all but the warmest temperatures (>358.15 K).34 Similar deviations are observed when comparing the data of Bamgbade et al.34 to the results for GPL-102 (lot K1608) reported in this work (not plotted); those values range from −0.7% to +0.8%. 3.2. Dynamic Viscosity. Averaged dynamic viscosity measurement results (η)̅ are presented in Table 3, along with their associated expanded uncertainties (U(η̅)). Reported uncertainties are calculated using an expression analogous to the aforementioned one for density (eq 1), and corresponding values of t95(dfη) are included in Table 3. Expanded uncertainties for dynamic viscosity range from an overall minimum of 0.022 mPa·s to an overall maximum of 70.0 mPa·s. In terms of relative expanded uncertainties, estimates range from an overall minimum of 0.67% to an overall maximum of 1.9%. Additional details regarding the dynamic viscosity uncertainty analysis employed in this work are given in section S3 of the Supporting Information. Dynamic viscosity results are also plotted as a function of temperature in Figure 5. As was observed with density (Figure

Table 1. This is more clearly shown in the top half of Figure 6 where the lot-to-lot dynamic viscosity deviations are plotted as

Figure 6. Dynamic viscosity deviations for GPL-102. Lot-to-lot deviations for the two samples measured in this work are shown in the top graph. Deviations of literature data from measurement results reported in this work for GPL-102 (lot K2391) are shown in the bottom graph. Data from Harris,32 Bair,35 and Mylona et al.36 are all for lot K2391, while the data from Baled et al.17,18 are for lot K1537.

a function of temperature. Observed deviations range from 7.2% at 373.15 K to 14.8% at 263.15 K and far exceed estimated expanded uncertainties (Table 3). This is consistent with the >10% lot-to-lot variability observed by Bair for viscosity measurements of two separate lots of GPL-102 (K2391 and K1537).35 The bottom half of Figure 6 shows the results of comparisons with available literature data for GPL-102 plotted as percent deviation as a function of temperature. Harris32 reports viscosity measurements at pressures to 203 MPa and from 273.15 to 368.15 K for GPL-102 (lot K2391); comparisons to atmospheric pressure (0.1 MPa) data are shown in Figure 6. Baled et al.17,18 report viscosity measurements at pressures to 243 MPa and temperatures between 311 and 533 K for a different lot of GPL-102 (K1537); atmospheric pressure values for the comparisons shown in Figure 6 were calculated from reported correlations. Bair35 reports viscosity measurements at atmospheric pressure (0.1 MPa) and at 313.15 and 343.15 K for GPL-102 (lot K2391). Finally, Mylona et al.36 report viscosity measurements for GPL-102 (lot K2391) from two separate instruments over a combined temperature range of 282.961−363.637 K and for pressures up to 20 MPa; Figure 6 shows data reported at atmospheric pressure (0.1 MPa). The data of Harris32 show deviations ranging from −5.4% to +0.6% relative to the values reported in Table 3. These deviations are within the author’s reported uncertainties of 2% for temperatures ≤313.15 K but mostly exceed reported uncertainties at higher temperatures. Deviations for the data of Baled et al.17,18 range from +3.6% to +9.2%, exceeding reported experimental uncertainties of 2.4% and largely exceeding the reported mean absolute percent deviation for the correlation of 3.9%. However, when considered in light of the previously discussed lot-to-lot variations observed in this work and by

Figure 5. Dynamic viscosity measurements as a function of temperature at ambient pressure.

3), dynamic viscosity increases with increasing polymer chain length. GPL-101 exhibits the lowest viscosities with values that range from 3.096 mPa·s at 373.15 K to 142.6 mPa·s at 263.15 K. GPL-106 exhibits the highest viscosities with values ranging from 49.01 mPa·s at 373.15 K to 3901.8 mPa·s at 283.15 K. This corresponds to a difference in dynamic viscosity between these two samples of 98.9% at 283.15 K and 93.7% at 373.15 K. Again, as was observed with the density results (Figure 3), GPL-105 and GPL-106 exhibit viscosities that are more similar than other pairings varying by 34.7% at 373.15 K to 44.8% at 283.15 K. In contrast to their small differences in density, the two lots of GPL-102 exhibit viscosities that are substantially different but still consistent in their relative order (Figure 5) with their different average polymer chain lengths shown in G


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Table 4. Coefficients (αi) and Associated Standard Uncertainties (u(αi)) from the Fit of Eq 2 to Experimental Density Data for Six PFPE Samples

α1 (kg·m−3) u(α1) (kg·m−3) α2 (kg·m−3·K−1) u(α2) (kg·m−3·K−1) α3 (kg·m−3·K−2) u(α3 (kg·m−3·K−2) min dev. (%) max dev. (%) AAD (%)

GPL-101 (lot K1552)

GPL-102 (lot K1608)

GPL-102 (lot K2391)

GPL-104 (lot K0813)

GPL-105 (lot L15777)

GPL-106 (lot K1848)

2402.03 1.34 −1.8117 0.0085 −2.543 × 10−04 1.334 × 10−05 −0.006 0.004 0.003

2411.67 3.12 −1.8323 0.0197 −8.063 × 10−05 3.098 × 10−05 −0.010 0.024 0.005

2410.51 2.54 −1.8295 0.0161 −9.750 × 10−05 2.522 × 10−05 −0.008 0.019 0.004

2462.65 6.81 −2.0897 0.0431 4.695 × 10−04 6.767 × 10−05 −0.029 0.018 0.014

2484.53 6.26 −2.1836 0.0387 7.007 × 10−04 5.935 × 10−05 −0.017 0.013 0.008

2488.14 5.57 −2.1882 0.0341 7.318 × 10−04 5.196 × 10−05 −0.012 0.010 0.007

others,35 these large deviations are not surprising. Additionally, it should be noted that the situation improves when the data of Baled et al.17,18 are compared with the results for GPL-102 (lot K1608) reported in this work (not plotted); those values range from −4.2% to −0.4%. Deviations for the data of Bair35 are equal to +3.1% at 313.15 K and −1.7% at 343.15 K and are within the author’s reported uncertainties of approximately 3%. Finally, the data of Mylona et al.36 deviate from −4.7% to +0.5%, largely exceeding the authors’ reported uncertainties of 2−3%.

4. CORRELATIONS To facilitate their use, the experimental data reported herein were correlated as a function of temperature. In this work, we utilized the orthogonal distance regression (ODR) fitting algorithms implemented in the NIST-developed ODRPACK software package.37−39 In ordinary least-squares (OLS) fitting, the independent variables are assumed to have no measurement errors associated with them. However, this may not be a valid assumption for some measurement processes. ODR is one method for handling this so-called “errors in variables” problem.40 During fitting of the experimental data reported in Tables 2 and 3, we input uncertainties in density and dynamic viscosity as well as temperature. Although the temperature uncertainties were significantly smaller than those for either density or dynamic viscosity, we found that in all cases the use of ODR resulted in slightly better fits than OLS in terms of both the resultant deviations and the coefficient errors. 4.1. Density. While compressed liquid densities are commonly correlated using the Tait equation,41 atmospheric pressure data can be modeled using a simple polynomial provided the temperature range is far away from the critical point. The atmospheric density data reported in Table 2 were correlated using a quadratic equation ρ = α1 + α2T + α3T 2

Figure 7. Relative deviations for the correlation of the experimental density data with eq 2.

4.2. Dynamic Viscosity. In contrast to density, multiple equations have been proposed in the literature for the correlation of experimental viscosity data22 but there is virtually no guidance as to which is most applicable and when. In this work, we compared the performance of three different correlation equations. The first, designated DIPPR, is equation 101 in the Design Institute for Physical Properties (DIPPR) 801 Database42 ⎡ ⎤ β η = η0 exp⎢β1 + 2 + β3 ln(Tr ) + β4 Trβ5⎥ Tr ⎣ ⎦

(2)

The resulting coefficients and their associated uncertainties for each of the six PFPE samples are listed in Table 4. Figure 7 shows the relative deviations between experimental and calculated densities plotted as a function of temperature. The deviations for all six samples are well within reported uncertainties. GPL-101 exhibits the lowest deviations, ranging from −0.006% to +0.004%, with an average absolute deviation (AAD) of 0.003%. The highest deviations are observed for GPL-104, ranging from −0.029% to +0.018%, with an AAD of 0.014%. The AADs for the remaining samples are 0.005%, 0.004%, 0.008%, and 0.007% for GPL-102 (lot K1608), GPL102 (K2391), GPL-105, and GPL-106, respectively.

(3)

where Tr = T/273.15 K and η0 is a dimensioning factor of 1 mPa·s. Equation 3 is also one of the equations utilized by NIST’s ThermoData Engine (TDE) software to model saturated liquid viscosity of pure fluids as a function of temperature.43 With the exception of the final term, eq 3 follows the same functional form as the work of Baum,44 who adopted a vapor pressure formula based on similarities in the temperature dependence of vapor pressures and liquid viscosities. The second correlation equation utilized in this work is the Vogel−Fulcher−Tammann (VFT) equation45−47 H


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Table 5. Coefficients (βi) and Associated Standard Uncertainties (u(βi)) from the Fit of Eq 3 to Experimental Dynamic Viscosity Data for Six PFPE Samples

β1 u(β1) β2 u(β2) β3 u(β3) β4 u(β4) β5 u(β5) min. dev. (%) max. dev. (%) AAD (%)

GPL-101

GPL-102

GPL-102

GPL-104

GPL-105

GPL-106

(lot K1552)

(lot K1608)

(lot K2391)

(lot K0813)

(lot L15777)

(lot K1848)

2.8515 0.4940 −1.0692 0.5807 −4.8112 0.3174 2.5376 0.0868 −4.8301 0.0618 −0.028 0.019 0.009

16.2266 1.2935 −17.6836 1.6986 −12.4598 0.7565 6.9072 0.4055 −3.5040 0.0694 −0.028 0.030 0.010

17.9824 1.7464 −19.8513 2.3073 −13.6379 1.0170 7.1929 0.5612 −3.4610 0.0908 −0.034 0.032 0.015

22.7653 3.4123 −26.4928 4.7661 −15.4879 1.9170 10.9555 1.3545 −3.1095 0.1246 −0.053 0.053 0.019

−3.2497 1.0798 7.8729 1.2959 0.0831 0.6755 3.9316 0.2165 −4.6338 0.1000 −0.086 0.070 0.017

−13.4844 1.5184 20.4001 1.7313 6.6937 1.0002 2.2694 0.2121 −5.9448 0.2507 −0.063 0.059 0.016


β6 u(β6) β7 u(β7) β8 u(β8) min. dev. (%) max. dev. (%) AAD (%)

GPL-101

GPL-102

GPL-102

GPL-104

GPL-105

GPL-106

(lot K1552)

(lot K1608)

(lot K2391)

(lot K0813)

(lot L15777)

(lot K1848)

3.1183 0.0220 0.5568 0.0020 −2.7157 0.0190 −0.711 0.631 0.265

3.4199 0.0082 0.5759 0.0006 −2.6146 0.0075 −0.308 0.204 0.114

3.3856 0.0096 0.5744 0.0008 −2.6319 0.0087 −0.411 0.190 0.130

4.0643 0.0215 0.5818 0.0014 −2.4927 0.0199 −1.174 0.444 0.285

4.3835 0.0143 0.5932 0.0009 −2.2074 0.0121 −0.491 0.198 0.127

4.5488 0.0113 0.5937 0.0007 −1.9984 0.0094 −0.246 0.138 0.083


β9 u(β9) β10 u(β10) β11 u(β11) min. dev. (%) max. dev. (%) AAD (%)

GPL-101

GPL-102

GPL-102

GPL-104

GPL-105

GPL-106

(lot K1552)

(lot K1608)

(lot K2391)

(lot K0813)

(lot L15777)

(lot K1848)

−1.8268 0.0464 1.3031 0.0458 1.5514 0.0279 −1.251 1.746 0.565

−1.5079 0.0316 1.2716 0.0280 1.6997 0.0177 −1.204 1.012 0.410

−1.5488 0.0348 1.2726 0.0312 1.6866 0.0196 −1.270 1.126 0.449

−1.1180 0.0194 1.4488 0.0166 1.7509 0.0092 −0.924 0.618 0.257

−0.8876 0.0207 1.6933 0.0200 1.7172 0.0099 −0.349 0.765 0.175

−0.6838 0.0220 1.8117 0.0220 1.6926 0.0102 −0.252 0.736 0.165

⎡ β ⎤ 6 η = η0 exp⎢ + β8⎥ ⎢⎣ Tr − β7 ⎥⎦

with Tr and η0 as defined above (eq 3). It was included here because recent studies found the performance of this correlation to be superior to the VFT correlation.49−51 Following the rediscovery of Waterton’s correlation by Mauro et al.,49 the correlation is referred to as the “Mauro−Yue− Ellison−Gupta−Allen (MYEGA) model of liquid viscosity” in subsequent publications of Mauro and coauthors. The correlation coefficients and their associated uncertainties are shown in Tables 5, 6, and 7 for eqs 3, 4, and 5, respectively. Figure 8 shows the relative deviations between experimental and calculated viscosities plotted as a function of temperature. Deviations for the DIPPR correlation (eq 3) are shown in Figure 8A, those of the VFT correlation (eq 4) in Figure 8B, and those of the Waterton correlation (eq 5) in Figure 8C. For

(4)

with Tr and η0 as defined above (eq 3). In the literature, eq 4 is perhaps the most commonly utilized expression to describe the temperature dependence of liquid viscosity. It was originally developed to describe the viscosity behavior of glass-forming liquids. The third correlation equation was proposed by Waterton48 as follows ⎡ ⎡ β ⎤⎤ β η = η0 exp⎢β9 + 10 exp⎢ 11 ⎥⎥ ⎢⎣ Tr ⎣ Tr ⎦⎥⎦

(5) I


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Figure 8. Relative deviations for the correlation of the experimental dynamic viscosity data with eqs 3 (A), 4 (B), and 5 (C). For ease of comparison, the highlighted areas in graphs B and C represent the y-axis range of graph A.

(GPL-101) for the Waterton correlation (Figure 8C). In contrast, AAD ranges from 0.009% (GPL-101) to 0.019% (GPL-104) for the DIPPR correlation (Figure 8A). The superiority of the DIPPR equation can be attributed to its more flexible functional form; it can represent curves containing inflection points, while both the VFT and Waterton equations are strictly convex functions.

all six samples, all three equations represent most of the data within their reported uncertainties. The only exceptions occur for samples GPL-101, GPL-102 (K1608), and GPL-102 (K2391) with the Waterton equation at low temperatures (Figure 8C). The most important conclusion to draw from Figure 8 is that the DIPPR equation represents the experimental data of all six PFPE samples with significantly smaller deviations than either the VFT or the Waterton equation. Whereas the deviations of the VFT correlation (Figure 8B) and particularly of the Waterton correlation (Figure 8C) both show clear trends with temperature, the deviations of the DIPPR correlation (Figure 8A) scatter more randomly. Furthermore, the deviations of the DIPPR correlation are approximately an order of magnitude lower than those of the other two correlations. AAD ranges from 0.083% (GPL-106) to 0.285% (GPL-104) for the VFT correlation (Figure 8B) and from 0.165% (GPL-106) to 0.565%

5. CONCLUSIONS The results of density and dynamic viscosity measurements for several samples of PFPE lubricant oils have been presented in this work. The samples measured included five separate Krytox GPL oils (GPL-101 (lot K1552), GPL-102 (lot K1608), GPL104 (lot K0813), GPL-105 (lot L15777), and GPL-106 (lot K1848)) and a second sample of GPL-102 (lot K2391) currently being characterized as a potential high-temperature high-pressure (HTHP) certified viscosity standard. Ambient J


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(5) Verdier, S.; Coutinho, J. A. P.; Silva, A. M. S.; Alkilde, O. F.; Hansen, J. A. A Critical Approach to Viscosity Index. Fuel 2009, 88, 2199−2206. (6) Docter, A.; Lösch, H. W.; Wagner, W. A New Apparatus for Combined Measurements of the Viscosity and Density of Fluids for Temperatures from 233 to 523 K at Pressures up to 30 MPa. Int. J. Thermophys. 1999, 20, 485−505. (7) Evers, C.; Lösch, H. W.; Wagner, W. An Absolute ViscometerDensimeter and Measurements of the Viscosity of Nitrogen, Methane, Helium, Neon, Argon, and Krypton over a Wide Range of Density and Temperature. Int. J. Thermophys. 2002, 23, 1411−1439. (8) Schäfer, M. Improvements to Two Viscometers Based on a Magnetic Suspension Coupling and Measurements on Carbon Dioxide. Dr.-Ing. Thesis, Department of Mechanical Engineering, Ruhr-Universität Bochum, 2015. (9) Caudwell, D. R.; Trusler, J. P. M.; Vesovic, V.; Wakeham, W. A. The Viscosity and Density of n-Dodecane and n-Octadecane at Pressures up to 200 MPa and Temperatures up to 473 K. Int. J. Thermophys. 2004, 25, 1339−1352. (10) Wakeham, W. A.; Fitt, A. D.; Ronaldson, K. A.; Goodwin, A. R. H. A Review of Vibrating Objects for the Measurement of Density and Viscosity in Oilfields Including Devices Fabricated by the Method of MEMS. High Temp.-High Press. 2008, 37, 137−151. (11) Pádua, A. A. H. Vibrating-Wire Viscometer. In Experimental Thermodynamics Vol. IX: Advances in Transport Properties of Fluids; Assael, M. J., Goodwin, A. R. H., Vesovic, V., Wakeham, W. A., Eds.; The Royal Society of Chemistry: Cambridge, UK, 2014; pp 96−102. (12) Seibt, D.; Herrmann, S.; Vogel, E.; Bich, E.; Hassel, E. Simultaneous Measurements on Helium and Nitrogen with a Newly Designed Viscometer-Densimeter over a Wide Range of Temperature and Pressure. J. Chem. Eng. Data 2009, 54, 2626−2637. (13) McBride-Wright, M.; Maitland, G. C.; Trusler, J. P. M. Viscosity and Density of Aqueous Solutions of Carbon Dioxide at Temperatures from (274 to 449) K and at Pressures up to 100 MPa. J. Chem. Eng. Data 2015, 60, 171−180. (14) Zarzar, L. D.; Sresht, V.; Sletten, E. M.; Kalow, J. A.; Blankschtein, D.; Swager, T. M. Dynamically Reconfigurable Complex Emulsions via Tunable Interfacial Tensions. Nature 2015, 518, 520− 524. (15) Minutes of the 9th IATP Meeting, Boulder, CO, June 20, 2009. http://transp.eng.auth.gr/index.php/iatp/2009 (accessed Feb. 10, 2016). (16) Executive Summary for the HPHT Viscosity Standards Workshop, Cambridge, MA, Jan. 22, 2010. http://www.slb.com/ services/characterization/reservoir/core_pvt_lab/fluid_lab_services/ hpht_pvt_studies/hpht_viscosity_standards.aspx (accessed Feb. 10, 2016). (17) 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. (18) 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. Erratum to: Exploratory Characterization of a Perfluoropolyether Oil as a Possible Viscosity Standard at Deepwater Production Conditions of 533 K and 241 MPa. Int. J. Thermophys. 2015, 36, 807−808. (19) International Standard for Viscosity at Temperatures up to 473 K and Pressures Below 200 MPa. Project 2012−051−1-100. http:// www.iupac.org/nc/home/projects/project-db/project-details.html?tx_ wfqbe_pi1%5Bproject_nr%5D=2012-051-1-100 (accessed Feb. 10, 2016). (20) Madge, E. W. The Variation of the Viscosity of Liquid with Temperature. J. Phys. Chem. 1929, 34, 1599−1606. (21) Cornelissen, J.; Waterman, H. I. The Viscosity Temperature Relationship of Liquids. Chem. Eng. Sci. 1955, 4, 238−246.

pressure density and dynamic viscosity data and their associated expanded uncertainties were reported over the combined temperature range of 263.15−373.15 K. Experimental results for the two separate samples of GPL-102 were compared to one another and to available literature data. Lot-to-lot deviations for density were well within reported experimental uncertainties in this work. Additionally, comparisons with literature data showed agreement predominantly within reported uncertainties. In contrast, lot-to-lot deviations for viscosity far exceeded estimated expanded uncertainties in this work but were consistent with lot-to-lot variability reported by others. Comparisons with literature data showed similar discrepancies with deviations that predominantly exceeded reported uncertainties. Finally, results for correlations of both density and viscosity as a function of temperature were reported. Density was correlated with a simple quadratic equation resulting in AAD ranging from 0.003% to 0.014%. Viscosity was correlated with three separate equations. The best representation was achieved with the DIPPR equation with AAD ranging from 0.009% to 0.019%. Kinematic viscosities can be calculated at reported experimental temperatures from the measured densities and dynamic viscosities or at intermediate temperatures from their respective correlations.

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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.iecr.6b01921. Experimental details for 13C NMR sample purity analysis and details of uncertainty calculations for density and viscosity measurements (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Phone: 303-497-3522. Fax: 303-497-6682. E-mail: tfortin@ boulder.nist.gov. Notes

The authors declare no competing financial interest. † Contribution of the National Institute of Standards and Technology. Not subject to Copyright © in the U.S.A.

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ACKNOWLEDGMENTS We gratefully acknowledge E.I. du Pont de Nemours and Co. for providing five of the six PFPE samples. Additionally, we would like to thank the U.S. Department of Energy’s National Energy Technology Laboratory and Prof. Robert Enick of the University of Pittsburgh for providing a sample of the proposed HTHP viscosity standard Krytox GPL 102 (lot K2391).

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REFERENCES

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