Ind. Eng. Chem. Res. 1988,27, 1732-1736
1732
Greek Symbols bkl = Kronecker symbol 6i = solubility parameter A = difference between the two coexisting phases 4 = fraction in phase I K f = generalized K factors; see (15) bc = chemical potential of i eii = binary interaction coefficient ilk = family of species Superscripts I = first phase II = second phase F = feed y = phase (y = I, 11, F)
Literature Cited Baker, L. E.; Pierce, A. C.; Luks, K. D. “Gibbs Energy Analysis of Phase Equilibria“. Soc. Pet. Eng. J . 1982, 17,731-742. Beerbaum, S.; Bergmann, J.; Kehlen, H.; Ratzsch, M. T. “Spinodal Equation for Polydisperse Polymer Solutions”. Proc. R. SOC. London, Ser. A 1986, 63, A406. Hendriks, E. M. ‘Simplified Phase Equilibrium Equations for Multicomponent Systems”. Fluid Phase Equilib. 1987, 33, 207-221. Hendriks, E. M. “Perturbation Expansion for Phase Equilibrium Equations”. Koninklijke/Shell Laboratorium Amsterdam, unpublished data, 1988.
Jensen, B. H. ‘Densities, Viscosities and Phase Equilibria in Enhanced Oil Recovery”. Ph.D. Dissertation, Technical University of Denmark, Lyngby, Denmark, 1987. Jensen, B. H.; Fredeslund, A. ’Simplified Flash Procedure for Multicomponent Mixtures Containing Hydrocarbons and One Non-Hydrocarbon Using Two-Parameter Cubic Equation of State”. Ind. Eng. Chem. Res. 1987,26, 2129-2134. Kailath, T. Linear Systems; Prentice-Hall: Englewood Cliffs, NJ, 1980. Kehlen, R.; Raetzsch, M. T.;Bergman, J. ’Zur Stabilitiit komplexer Vielstaffsysteme”. Z. Chem. 1986,26, 1-6. Koningsveld, R. “On Liquid-Liquid Phase Relationships and Fractionation in Multicomponent Polymer Solutions”. Ph.D. Dissertation, University of Leiden, Leiden, The Netherlands, 1967. Michelsen, M. L. “The Isothermal Flash Problem. Part I. Stability”. Fluid Phase Equilib. 1982,9, 1-19. Michelsen, M. L. “SimplifiedFlash Calculations for Cubic Equations of State”. Ind. Eng. Chem. Process Des. Dev. 1986, 25, 184. Michelsen, M. L.; Heideman, R. A. “Calculation of Critical Points from Cubic Two-Constant Equations of State”. AIChE J. 1981, 27, 521. Schlijper, A. G . ’Flash Calculations for Polydisperse Fluids: A Variational Approach”. Fluid Phase Equilib. 1987,34,149-169. Van Dijk, M. A,; Hendriks, E. M. Koninklijhe/ShellLaboratorium, Amsterdam, unpublished data, 1988.
Receiued for review December 23, 1987 Revised manuscript received April 25, 1988 Accepted May 22, 1988
Correlating Vapor Pressures of Perfluorinated Saturated Hydrocarbons by a Group Contribution Method C. Michael Kelly* Department of Chemical Engineering, Villanova University, Villanova, Pennsylvania 19085
Paul M. Mathias and Frank K. Schweighardt Air Products and Chemicals, Inc., Allentown, Pennsylvania 18195
The normal boiling points and vapor pressure/ temperature relationship of a series of perfluorinated saturated hydrocarbons have been correlated by using a group contribution approach. The fundamental equation, derived from a physical model that describes any subject molecule as a set of coupled harmonic oscillators, contains only two adjustable parameters. Group contributions to these adjustable parameters were determined from an extensive published data base, by minimizing the least-squared errors between the model prediction and observed normal boiling points or vapor pressure data. The model successfully correlates boiling points within 2% of the absolute normal boiling point and vapor pressure under vacuum over a pressure range of approximately 10-1000 mmHg (0.2-20 kPa) for the compounds tested. Perfluorinated hydrocarbons have become a significant class of industrial chemicals whose scientific and commercial importance promises to increase greatly in the next several years. Their potential uses include augmenting in vivo oxygen transfer for medical applications and facilitating high-temperature heat transfer and specialty lubrication applications. In these and many other instances, the vapor pressure at the temperature of use is often a critical parameter when selecting the best candidate. When screening perfluorocarbon compounds for possible use in any given application, it is helpful to predict the vapor pressure (as well as related parameters such as normal boiling point and heat of vaporization) from the molecular structure. Lawson (1980) developed a group contribution approach based on an empirical equation originally proposed by Hildebrand and Scott (1950) that relates the latent heat of vaporization at 298 K to, the normal boiling point. Proceeding via the energy and entropy of vaporization, Lawson used an equation with the same form as that proposed by Hildebrand to develop a 0888-5885/88/2627-1732$01.50/0
model that predicts vapor pressures at any temperature. To obtain the necessary group contributions to the energy of vaporization, Lawson fit published boiling point data for 19 fluorochemical compounds to his empirical equation. This empirical approach (using Lawson’s best fit group contributions) predicts normal boiling points moderately well for linear and branched chain fluorocarbons, as well as simple ring structures, but becomes less accurate when applied to fused ring structures with perfluoroalkyl substituents. Presumably, this could be improved by determining the group contributions via a least-squares fit to a larger data base, incorporating several representatives of this type of compound. Nevertheless, the resulting method wodd still depend on the form of Hildebrand’s original empirical equation (relating latent heat at 298 K to the normal boiling point), for which there is no fundamental theoretical justification. An alternative approach is to develop group contributions to such parameters as the excess Gibbs free energy 0 1988 American Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 9, 1988 1733 and the residual UNIFAC group activity coefficients, as was done for light hydrocarbon compounds by Jensen et al. (1981). We feel it is preferable to start with an equation that relates the vapor pressure directly to the temperature, especially if its parameters can be ascribed to a physical model. Abrams et al. (1974) followed this approach, using a vapor pressure equation based on a kinetic theory of a polyatomic liquid proposed by Moelwyn-Hughes (1961). The AMP model (after Abrams, Massaldi, and Prausnitz) includes three parameters with physical interpretations: the van der Waals volume of the molecule, the number of loosely coupled harmonic oscillators in a single molecule, and a characteristic energy that must be overcome for a molecule to escape from the liquid. The molecular volume is determined independently by an unrelated group contribution method (Bondi, 1968); thus the AMP method requires fitting of only two adjustable parameters. Abrams et al. (1974) determined the best fit for their two parameters for a wide range of compounds and demonstrated that their model extrapolates vapor pressures more accurately than a simple Antoine-type equation over a wide range of temperatures. However, the appropriate values of the AMP parameters must be determined independently for each compound of interest. This requires experimental measurement of vapor pressure as a function of temperature for each compound considered and prevents the method from being used predictively. Macknick and Prausnitz (1979) used the AMP model as the basis to develop a group contribution method that can be used predictively for hydrocarbon compounds. Later, Edwards and Prausnitz (1981) extended this model to include nitrogen and sulfur heteroatoms. The present paper follows the AMP approach to develop a similar group contribution method for perfluorinated hydrocarbons. Nonlinear least-squares regression yields best fit values for group contributions to the two adjustable parameters of the AMP equation. The data base for this regression analysis includes normal boiling point or vapor pressureltemperature data for a wide variety of perfluorinated hydrocarbon compounds. The method presented here is expected to predict boiling points and vapor pressureltemperature relationships for perfluorochemicals similar to those in the data base, with acceptable accuracy for screening evaluations.
where V , is the van der Waals volume of the molecule, S is interpreted as the number of loosely coupled harmonic oscillators in a single molecule, and E, is related to the energy barrier to be overcome by a molecule as it leaves the liquid state into the vapor. For noninteger values of S, the expression ( S - l)!indicates the gamma function, I'(S). Note that the argument used for the gamma function in most computer libraries is S, even though the traditional notation of eq 2 denotes ( S - l)!. In this dimensional form of eq 1, the set of units chosen for the other parameters establishes the numerical value of a , which is essentially a universal proportionality constant, independent of the identity of the compound. The numerical value of a depends on the dimensions chosen for the fundamental constants R , V,, T , P, and E,. In the present study, T was expressed in kelvins, P in atmospheres, V , in cubic centimeterslmole, and E,/R in kelvins. The gas law constant was R = 82.06 (cm3.atm/ (mol-K). This set of dimensions yields a numerical value of a = 0.0966. Bondi (1968) indicates a method to calculate molecular volume (V,) independently from the knowledge of the compound's structure. The two remaining parameters, S and E,, although they have physical interpretations, cannot be determined independently. They can, however, be treated as adjustable parameters, to be determined by a nonlinear least-squares fit of eq 1 to vapor pressure or boiling point data. Thus, eq 2 is a two-parameter semiempirical equation. Bondi (1968) relates the molecular volume to group contributions by
Methods The basic equation has the form of an empirical equation proposed by Miller (1964): lnP, = A + B / T + Cln T + D T + E T 2 (1) In its original form, the five constants A, B, C, D, and E were treated as adjustable parameters, without physical significance. Abrams et al. (1974) demonstrated that the five constants of Miller's equation can be expressed in terms of three parameters which can be assigned a physical interpretation. As later revised by Macknick et al. (1977), the five constants of eq 1 become A = In (R/V,,,) + ( S - 1/2) In (E,/R) In [(S- l)!]+ In a (2) B = -E,/R (3) C = 3/2 - S (4)
where niis the number of groups of type i in the molecule, and Siand EOiare the group contribution parameters of that group. The best values of Si and EOiwere obtained by minimizing the summation of the squared error between model predictions and experimental vapor pressure data, using a computerized direct-search optimization technique. The groups selected to describe generalized perfluorocarbon molecules are shown in Table I, along with Bondi's group contributions to the molecular volume. The model does not distinguish between isomers of the same compound (e.g., different substituent-group positions on a ring structure.) Table IV demonstrates computation of parameters V,, S, and E, for representative molecules, using these groups. The data base comprises published vapor pressures up to 1atm for 13 compounds, as well as normal boiling points of 13 additional substances for which complete vapor pressure data are lacking. Published normal boiling poins were used when available. However, boiling points of a few compounds were taken from vendor data sheets. Tables I1 and I11 identify the sources of all values included in the data base.
v, = CniV,i i
(7)
where Vmi,the group contribution to the molecular volume, can be calculated directly from van der Waals radii of the atoms in the group. Following Macknick and Prausnitz (1979), we propose that the parameters S and E, be described by equivalent linear group contribution relations:
s = cnisi i E, = CniEoi i
(9)
1734 Ind. Eng. Chem. Res., Vol. 27, No. 9, 1988 TEMPERATURE, "C 200
50
100
150
-50
0
10.0
1.0
5s n 'TI
m n cn cn C m n x
'TI
m
1.1
-Computed by Group Contribution Method 0 Experimental (from Data Base)
2.0
3.0
4.0
INVERSE TEMPERATURE I/T, OK-' X 103
Figure 1. Vapor pressures of selected perfluorinated hydrocarbons at temperatures below the normal boiling point. Table I. Constituent Groups and Best Fit Group Contributions name -CF3 (terminal) -CF2- (chain) -CF- (branch point) -C- (quaternary C in perfluoro compd) 6-membered ring (saturated HC precursor) 5-membered ring (saturated HC precursor) fusion of two rings (per fusion)
cm3/mol E,/R, K Si 21.33 1491.9 3.4104 15.33 802.2 0.7632 9.33 68.2 -2.0267 3.33
-310.9
-3.9573
-1.69
1121.4
4.9731
-1.80
1096.9
4.7807
0.00
-579.2
-1.2055
Results Table I presents the resulting best fit values for the group contributions Si and Eoi. The best fit group contributions Si are negative for three of the groups. This result is at first somewhat unsettling, because of the physical significance of the summation S = CSi as the number of loosely coupled oscillators in the molecule. However, it should be noted that these groups can only occur in conjunction with other groups, such as chain CF2 or terminal CF3. In such molecules, the total number of coupled oscillators is always positive, in spite of the negative contributions of certain individual groups to the summation. Groups whose Si contributions are negative are present only in a condensed molecule (as compared to an unbranched perfluorinated alkane) which might be expected to have less oscillatory freedom (again, by comparison to a linear molecule.) This is reflected in a reduction of the summation of S, compared to a linear molecule with the same number of carbon atoms.
Table 11. Vapor Pressure Data Base Used for Regression Analysis perfluoro compd (hydrocarbon no. of precursor) data pts sourcea n-butane 5 Simons and Mausteller (1952) 2-methylbutane 8 Crowder et al. (1967) n-pentane 8 Barber and Cady (1956) cyclopentane 7 Barber and Cady (1956) 2-methylpentane 9 Stiles and Cady (1952) 3-methylpentane 10 Crowder et al. (1967) n-hexane 8 Stiles and Cady (1952) 4 cyclohexane Crowder et al. (1967) 2,3-dimethylbutane 9 Crowder et al. (1967) methylcyclohexane 9 Fowler et al. (1947) n-heptane 10 Fowler et al. (1947) decalin 7 McBee and Bechtol (1947) perhydroISC 5 phenanthrene "ISC = Vendor data for PP-11 fluorocarbon (ISC Chemicals, Inc.); otherwise, literature reference cited here.
Table I11 compares model-predicted normal boiling points to the data base used in the regression analysis. Figure 1compares model predictions to several compounds in the data base for which the temperature dependence of the vapor pressure is known. (Identical data points have been removed for clarity.) With few exceptions, the model-predicted boiling points are within f 2 "C of the observed normal boiling points, which range from -2 to 240 "C. For the full data base, the average (arithmetic mean) difference between model predictions and measured normal boiling points is less than 0.5 70 of the experimental boiling point (expressed in absolute temperatures). The data base comprises linear and branched saturated perfluorocarbons of various lengths, as well as cyclic (single-
Ind. Eng. Chem. Res., Vol. 27, No. 9, 1988 1735 Table 111. Published and Predicted Boiling Points (Data Base) bp, OC perfluoro compd predicted diff. 1 n-butane -0.02 2.13 30.19 1.13 2 n-pentane 3 n-hexane 57.31 0.46 4 n-heptane 81.85 -0.50 104.20 0.65 5 n-octane 124.68 -0.67 6 n-nonane 143.53 -0.72 7 n-decane 8 n-undecane 160.98 0.13 9 n-dodecane 177.18 -0.87 192.28 -2.27 10 n-tridecane 232.12 -6.93 11 n-hexadecane 12 2-methylbutane 31.17 1.13 13 2-methylpentane 58.46 0.80 14 3-methylpentane 58.46 0.09 1.59 15 3-methylhexane 83.14 59.65 -0.13 16 2,3-dimethylbutane 2.46 17 3,7-dimethyloctane 146.61 82.10 0.05 18 2,2,3-trimethylbutane 103.97 -0.08 19 2,2,4-trimethylpentane 20 cyclopentane 22.57 0.07 47.92 -4.78 21 cyclohexane 22 methylcyclohexane 74.76 -1.38 23 n-butylcyclohexane 138.97 -5.88 24 diisopropylcyclohexane 178.70 -2.25 139.10 -1.75 25 decalin 160.45 0.60 26 methyldecalin 1.87 27 perhydrophenanthrene 216.92
obsd -2.15 29.06 56.85 82.35 103.55 125.35 144.25 160.85 178.05 194.55 239.05 30.04 57.66 58.37 81.55 59.78 144.15 82.05 104.05 22.50 52.70 76.14 144.85 180.95 140.85 159.85 215.05
sourcea** Simons and Mausteller (1952) Barber and Cady (1956) Stiles and Cady (1952) Fowler et al. (1947) Moore and Clark (1985) Moore and Clark (1985) Terranova (1979) Terranova (1979) PCR Terranova (1979) PCR Crowder et al. (1967) Stiles and Cady (1952) Crowder et al. (1967) PCR Crowder et al. (1967) Terranova (1979) Terranova (1979) Terranova (1979) Barber and Cady (1956) Crowder et al. (1967) Fowler et al. (1947) McBee and Bechtol (1947) Moore et al. (1985) McBee and Bechtol (1947) Wesseler et al. (1977) ISC
OISC = vendor data for PP-11 fluorocarbon (ISC Chemicals, Inc., Avonmouth, Bristol, UK). bPCR = vendor data for commercial products of Peninsula Chemical Research, Division of SCM, Gainesville, FL. Otherwise, literature reference cited.
Table IV. SamDle Determination of AMP Parameters from GrouD Contributions group no. V,, cms/mol S A. Perfluoroisopropyldecalin, C13F23 2 2(21.33) = 42.66 2(3.4104) = 6.82 CF3 CF2 7 7(15.33) = 107.31 7(0.7632) = 5.34 CF 4 4(9.33) = 37.32 4(-2.0267) = -8.11 2 2(-1.69) = -3.38 2(4.9731) = 9.95 6-membered ring 1 l(0) = 0 1(-1.2055) = -1.21 ring fusion C = 183.91 = 12.79 CF2 CF 6-membered ring ring fusion
B. Perfluoroperhydrophenanthrene, C1Pz4 lO(15.33) = 153.3 lO(0.7632) = 7.63 4(-2.0267) = -8.11 4(9.33) = 37.32 3(4.9731) = 14.92 3(-1.69) = -5.07 2(0) = 0 2(-1.2055) = -2.411 I3 = 185.55 = 12.03
10 4 3 2
Eo/R, K 2(1491.9) = 2984 7(802.2) = 5615 4(68.2) = 272.8 2(1121.4) = 2243 1(-579.2) = 9 = 10536 lO(802.2) = 8022 4(68.2) = 273 3(1121.4) = 3364 2(-579.2) = -1158 = 10501
x
Computation of Constants for Perfluoroisopropyldecalin, C13F23
+
+ + +
= In (RIV,) (S - 1/2) In (Eo/R) - In [(S- l)!] In 01 = In (82.06/183.9) (12.79 - 0.5) In (10536) - In [r(12.79)] In (0.0966) = In (0.4462) (12.29) In (10536) - In (2.823 X los) In (0.0966) = -0.807 113.84 - 19.458 - 2.337 = 91.238 B = -Eo/R = -10 356 C = 3/2 - S = 1.5 - 12.79 -11.29 D = (S - l)/(Eo/R) = 11.79/10536 = 0.001 119 E = (S - 3)(S - 1)/(2(E0/R)2)= (9.79)(11.79)/(2(10536)*) = 5.189 X lo-' at T = 470 K (=196.85 "C) l n P , = A B/T C l n T DT ET2
A A A A
+
+
+
+
+
+
+
In P, = 91.24 + (-10356)/470 + (-11.29) In (470) + 0.001119(470) In P, = 91.24 - 22.42 - 6..46 + 0.526 + 0.115 = -0.00316 P, = exp(4.00316) = 0.997 atm = 758 mmHg
and multiple-ring) and fused-ring compounds, both with various substituents. (Ring compounds are derived from saturated hydrocarbons and are therefore not aromatic in nature.) The model fits the various classes of compounds equally well. The model was also applied to 11 proprietary fluorocarbons of similar types prepared by Air Products and Chemicals, Inc. These compounds were synthesized from pure hydrocarbon precursors, isolated by distillation, and shown by GCMS to contain greater than 95% isomers of the expected fluorocarbons. Boiling points were measured
+ 5.189 X 10-'(470)*
at atmospheric pressure and are estimated to be within 5 "C of the pure-component normal boiling point. (Their boiling points ranged from approximately 150 to 250 "C.) The predicted boiling points of these compounds differed by no more than 5 "C from the observed boiling points for 10 out of 11 compounds tested. The arithmetic mean of the difference was 0.67% of the normal boiling point (expressed in absolute temperatures) for these 10 compounds. Extrapolation to temperatures below the normal boiling point introduces a greater percentage error, but the pre-
1736
Ind. Eng. Chem. Res., Vol. 27, No. 9, 1988
dicted vapor pressures are reasonable (Figure 1). The original data base consisted mostly of normal boiling point data, although some low-pressure data were included. Presumably, incorporating more low-pressure data would lead to slightly different group contributions that would better express the temperature dependency of the vapor pressure.
Conclusions The two-parameter semiempirical AMP model extends readily to a group contribution method for correlating boiling point and vapor pressure data for a homologous series of compounds. When applied to perfluorinated analogues of saturated hydrocarbons, the method successfully correlates boiling points of compounds whose molecular weights range from 238 to 624. The arithmetic mean deviation between model-predicted and experimental boiling points (expressed as absolute temperatures) is less than 0.5%. All but 3 (out of 26) compounds in the data base were within 2.5 “C. Macknick et al. (1977) present a group contribution method for the equivalent saturated hydrocarbons. The reader is cautioned that these cannot be combined directly with the group contributions determined here for fluorocarbons, in hopes of predicting vapor pressures of (for example) a molecule with mixed CH2 and CF2 groups. Attempts to do so for a few partially fluorinated compounds produced erratic predictions of boiling points, usually with high percentage errors. The dipole moments of such molecules would be expected to introduce another intermolecular interaction beyond those assumed for the simple model of liquid behavior on which this method is based. However, it is hoped that the approach taken here will be a useful starting point when developing vapor pressure correlations for this type of compound. Literature Cited Abrams, D. S.; Massaldi, H. A.; Prausnitz, J. M. “Vapor Pressures of Liquids as a Function of Temperature. Two-Parameter Equation Based on Kinetic Theory of Fluids.” Ind. Eng. Chem. Fundam. 1974,13, 259-262. Barber, E. J.; Cady, G. H. “Vapor Pressures of Perfluoropentanes”. J . Phys. Chem. 1956, 60(4), 504-505.
Bondi, A. Physical Properties of Molecular Crystals, Liquids and Glasses; Wiley: New York, 1968; Chapters 8 and 14. Crowder, G. A.; Taylor, Z. L.; Reed, T. M.; Young, J. A. “Vapor Pressures and Triple Point Temperatures for Several Pure Fluorocarbons”. J . Chem. Eng. Datu 1967, 12(4), 481-485. Edwards, D. R.; Prausnitz, J. M. “Estimation of Vapor Pressures of Heavy Liquid Hydrocarbons Containing Nitrogen or Sulfur by a Group-Contribution Method”. Znd. Eng. Chem. Fundam. 1981, 20, 280-283. Fowler, R. D.; Hamilton, J. M.; Kasper, J. S.; Weber, C. E.; Burford, W. B.; Anderson, H. C. “Physical and Chemical Properties of Pure Fluorocarbons”. Znd. Eng. Chem. 1947,39(3), 375-378. Hildebrand, J. H.; Scott, R. L. The Solubility of Non-electrolytes, 3rd ed.; Reinhold: New York, 1950. Jensen, T.; Fredenslund, A.; Rasumasen, P. ”Pure-Component Vapor Pressures Using UNIFAC Group Contribution”. Znd. Eng. Chem. Fundam. 1981,20, 239-246. Lawson, D. D. “Methods of Calculating Engineering Parameters for Gas Separations”. Appl. Energy 1980,6, 241-255. Macknick, A. B.; Prausnitz, J. M. “Vapor Pressures of Heavy Liquid Hydrocarbons by a Group-Contribution Method”. Ind. Eng. Chem. Fundam. 1979,18, 348-351. Macknick, A. B.; Winnick, J.; Prausnitz, J. M. “Vapor Pressures of Liquids as a Function of Temperature. Two-Parameter Equation Based on Kinetic Theory of Fluids”. Znd. Eng. Chem. Fundam. 1977, 16, 392. McBee, E. T.; Bechtol, L. D. “Preparation of Fused-Ring Fluorocarbons”. Ind. Eng. Chem. 1947, 39(3), 380-384. Miller, D. G. “Derivation of Two Equations for the Estimation of Vapor Pressures”. J . Phys. Chem. 1964, 68, 1399-1408. Moelwyn-Hughes, E. A. Physical Chemistry, 2nd ed.; Pergammon: Oxford, 1961. Moore, R. E.; Clark, L. C. “Chemistry of Fluorocarbons in Biomedical Use”. Znternational Anesthesiologic Clinics;Tremper, K. K., Ed.; Little, Brown and Co.: Boston, 1985; Vol. 23, No. 1. Simons, J. H.; Mausteller, J. W. “The Properties of n-Butforane and Its Mixtures with n-Butane”. J . Chem. Phys. 1952, 20(10), 1516-1519. Stiles, V.; Cady, G. H. “Physical Properties of Perfluoro-n-hexane and Perfluoro-2-methylpentane”. J. Am. Chem. SOC.1952, 74(15), 3771-3773. Terranova, T. F. “Synthesis of Fluorocarbon Hydrocarbon Compounds, A Thermodynamic Scheme for Predicting Their Physical Properties, and an Estimation of the Basicity of Diazene”. M.S. (Chemistry) Thesis, University of Southern California, 1979. Wesseler, E. P.; Iltis, R.; Clark, L. C. “The Solubility of Oxygen in Highly Fluorinated Liquids”. J. Fluorine Chem. 1977,9,137-146. Receiued f o r review December 21, 1987 Accepted April 8, 1988
