sign in sign up
<<
Home , Methylcyclopropane, Spiropentane

AUGUST 2005 HARSTAD 2977

Trend Analysis for Atmospheric Partitioning Using Continuous Thermodynamics

K. HARSTAD Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California

(Manuscript received 22 April 2004, in final form 31 January 2005)

ABSTRACT

The partitioning of atmospheric into vapor and condensed phases when the species count is large is considered using the formalism of continuous thermodynamics. The vapor saturation pressures and condensate species distribution are parameterized using the species normal boiling temperatures. Qualitative trends in activity coefficient values and phase equilibrium behavior that are relevant to the outer planets and Titan are discussed in terms of a much simplified perspective on these aspects of partitioning. The trends found are generally consistent with those from other published atmospheric model results.

1. Introduction with particular emphasis on extraterrestrial bodies Hydrocarbons (and possibly derivative, i.e., oxidized without oxidizing environments. These models are in species) are commonly present in small amounts in general, very complex, involving partly the kinetics of a planetary atmospheres (e.g., Earth, the outer planets, large number of chemical reactions as well as turbulent Titan), and may attain a relatively wide range of carbon diffusion of chemical species in the atmosphere (Do- number. Abiotic generation is possible by chemical in- brijevic et al. 2003; Lebonnois et al. 2001; Lee et al. 2000; Moses et al. 2000; Raulin and Bruston 1996). De- teraction of CO (or CO2) with H2 (Raulin and Bruston 1996; Zolotov and Shock 1999) and, more effectively, spite the relative complexity of the models in the cited references, a totally complete and precise description of photochemistry of CH4 (Dobrijevic et al. 2003; Lebon- nois et al. 2001; Lee et al. 2000; Moses et al. 2000; all of the relevant physical processes involved is cur- Raulin and Bruston 1996; Wong et al. 2003). On Earth, rently not readily available. To aid the understanding of significant biogenic and anthropogenic sources of or- this complex problem, present attention is focused ganic hydrocarbons exist. The hydrocarbons may be solely on one major aspect of the partitioning, which is present in both vapor and condensed (aerosol) forms. the thermodynamics of phase equilibrium. In particu- The vapor and condensed phases have separate, dis- lar, this aspect is important because, as discussed later, tinct distributions (e.g., sets of species mole fractions). the SOC saturation pressures are the prominent param- In Earth’s atmosphere, the presence of water droplets, eters in determining partitioning. Rather than trying to dust particles, and an oxidizing environment all serve to follow the exact detailed behavior of all of the many complicate in its essence the description of the semi- species, a simplified description of phase equilibrium volatile organic compounds (SOCs) also present. Re- with a limited number of model parameters will be in- views on the details are found in Jacobson et al. (2000) troduced in this study so as to tractably elucidate trends and also Seinfeld and Pankow (2003). Of interest are in partitioning. The mapping of simple condensed models for the partitioning (i.e., determining the distri- phase to vapor phase distributions is assumed deter- butions) of the vapor and condensed phases to be used mined by the equilibrium phase relations. Distribution in conjunction with remote sensing of atmospheric va- forms and parametric dependencies are discussed in por content for estimates of total amounts of the SOCs, section 3. The description focuses on pure hydrocar- bons; attention to oxidized hydrocarbons is given a lower priority. The model is thus most relevant to con- sideration of the outer planets and Titan, which is the Corresponding author address: Dr. Kenneth Harstad, Jet Pro- pulsion Laboratory, California Institute of Technology, M/S 125- focus here, but may still qualitatively apply to Earth. 109, 4800 Oak Grove Dr., Pasadena, CA 91109-8099. The dominant hydrocarbon (SOC) in the outer planets E-mail: [email protected] and Titan is (Raulin and Bruston 1996).

© 2005 American Meteorological Society

Unauthenticated | Downloaded 09/28/21 06:12 AM UTC

JAS3518 2978 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 62

The phase partition is commonly characterized (us- as a result, empirical curve fits to partition data of the ϭ ϩ age examples are found in Jang et al. 1997; Jacobson et form log(Kp,i) b m log(psat,i) are utilized (Jang et al. 2000; Liang et al. 1997; Pankow et al. 1994; Seinfeld al. 1997; Liang et al. 1997; Pankow et al. 1994; Storey et and Pankow 2003; Storey et al. 1995; Yamasaki et al. al. 1995), for b and m constant with values of m ϷϪ1. ␥ 1982) by what is known as the partition constant, Kp, Fitting to log( L,i Kp,i) may also be used instead of defined for any particular SOC as fitting to log(Kp,i) (Jang et al. 1997).

K ϭ C ր͑C ␷ C ͒, ͑1͒ p SOC, p SOC, TSP 2. Hydrocarbon saturation pressure where C denotes mass concentrations with subscripts p To capture trends in the behavior of partitioning in a ␷ for particle (condensed) phase, for vapor phase, and meaningful way, a relatively simple description of the TSP for total suspended particulates (i.e., SOCs plus functional dependence of psat,i on temperature T and nonvolatiles and other species). The parameter Kp is species i properties is desirable. In particular, for a SOC temperature dependent. The condensed phase may be regime of tens or even possibly hundreds of species, the obtained either by vapor absorption (formation of liq- dependence on species properties should be as simple uid droplets from nucleation or liquid layers on par- as possible. Parameters that are commonly used to ticles of immiscible material) or by vapor adsorption form an equation of state model for a particular species (formation of monolayers on particles) (Jacobson et al. include the molar weight, critical properties, acentric 2000; Liang et al. 1997; Pankow et al. 1994; Storey et al. factor (for shape effects), and also possibly a reduced 1995). In either case, for a given species denoted by i, (dimensionless) dipole moment. It may be noted that Kp,i is inversely proportional to the pure liquid satura- the acentric factor is not really a completely indepen- tion pressure psat,i. High molar weight, relatively non- dent parameter since there is a rough linear correlation volatile, liquid species may be subcooled in condensed of this parameter with carbon number and also with the phase solutions (Jacobson et al. 2000; Jang et al. 1997; square of the normal boiling temperature Tb,i (the satu- Liang et al. 1997; Storey et al. 1995) making estimates ϭ ϭ ration temperature when psat,i patm 1013.25 mb). of the value of psat,i difficult (Seinfeld and Pankow (There is a distinct difference in the proportionalities 2003). In many circumstances, absorption may domi- between aromatics and nonaromatics.) Thus for a mix- nate the condensed phase (Jacobson et al. 2000; Jang et ture of many species, the mean effect of the acentric al. 1997). For this absorption limit, the standard ther- factor tends to correlate with other parameters, such as modynamic relation for bulk phase equilibrium of spe- mean Tb. Also, it will be demonstrated later that for a cies i is given by mixture, the mean molar weight is highly correlated to ϭ ␥ ͑ ͒ ͑ ͒ the mean boiling temperature. For the current applica- p␷,i XL,i L,i psat,i T , 2 tion, where interest is only for pressures of about one ϭ where p␷,i X␷,i p␷ is the partial vapor pressure, X bar or less, a natural choice for a correlation parameter denotes mole fraction, p␷ is the total vapor pressure, is T . An attempt to find a generic saturation curve ␥ b,i and L,i is the liquid activity coefficient. Equations (1) valid for any pure hydrocarbon based solely on this one and (2) combine to give as a limit parameter was made. There is a considerable amount ϭ ր͑ ␥ ͒ ͑ ͒ of data on p at the National Institute of Standards Kp,i fSOCRuT mSOC L,i psat,i , 3 sat,i and Technology (NIST) Chemistry WebBook (avail- where fSOC is the mass fraction of all SOCs relative to able online at http://webbook.nist.gov/chemistry/) in TSP, Ru is the universal gas constant, and mSOC is the the form of data fits over given temperature intervals to mean SOC molar weight. Equivalent expressions of the Antoine form of saturation curve. This empirical slightly different form appear in Jacobson et al. 2000, data is for low temperature ranges for the lighter, more Jang et al. 1997, and also Seinfeld and Pankow 2003. It volatile species (e.g., mostly 100 to 300 K) and higher ␥ is obvious that L,i and psat,i are important quantities in ranges for heavy, less volatile species (300 K or greater, determining the partitioning for absorption. It should some above 400 K). Using this data source, the follow- ␥ be noted that the value of L,i is frequently of order ing approximate fit for psat(T;Tb) in millibars for tem- unity (Seinfeld and Pankow 2003), while psat,i is peratures in kelvins has been generated here: strongly temperature dependent, varying over many or- ͑ ͒ ϭ Ϫ ր͑ ͒ ϩ Ϫ ͑ ր ͒ ͑ ͒ ␥ ln psat As AsTb bsT cs 1.67 T Tb , 4 ders of magnitude. [Values of L,i of order (10) are ϭ 0.12 possible for high molar weight, subcooled liquid species As 10.365T b , such as , see Abildskov et al. (2001).] In gen- ϭ ϩ Ϫ0.15 bs 1 1.453Tb , eral, it may be stated that psat,i is the prominent param- ϭ Ϫ ϫ Ϫ4 eter for partitioning by absorption and/or adsorption; cs 0.963 5.3 10 Tb.

Unauthenticated | Downloaded 09/28/21 06:12 AM UTC AUGUST 2005 HARSTAD 2979

Let R denote the ratio of the above fit to the data as bon numbers about 17 or greater) as shown in Tables 1 given by the Antoine expressions. Table 1 gives the and 3 are likely due to a steric effect whose behavior is ͗ ͘ Յ Յ mean values R over a range pmin psat pmax, the apparently peculiar and exceptionally strong. Since minimum and maximum values Rmin, Rmax, and also the these species are unlikely to occur in measurable ϭ ͗ ͗ ͘Ϫ 2͘ 1/2 relative standard deviation, Rdev [ (R/ R 1) ] amounts in atmospheres, if at all, this exception to the for 77 hydrocarbons. The error in the fit is Յ5% for validity of fit Eq. (4) is ignored in this study. 38% of the hydrocarbons, Յ 10% for 68% count, and Overall, it may be stated that except possibly for a Յ Յ 3 20% for 78% count. The fit is very good for psat 10 few species of very low volatility (namely subcooled mbar except for -based and very low volatility very high molar weight ), Eq. (4) adequately Ն Ն (Tb 600 K) species. Most of the data is for psat characterizes the saturation behavior of hydrocarbons O(1 mb), except for some n-alkanes. over a very wide pressure range up to about 103 mbar. Since the empirical data is limited (e.g., to tempera- Thus trends in the behavior of partitioning may be di- tures above melting points), the generic nature of rectly related to the single parameter Tb. The apparent Eq. (4) has yet to be established. As a step in the at- near agreement, or extension, of fit Eq. (4) to oxidized tempt to do this, although the fit is optimized solely hydrocarbons leads to possible consideration of Earth’s for hydrocarbons, it was further tested against satura- atmosphere to the trend analysis; this is not carried out tion pressures for a group of 22 oxidized hydrocarbons here.

(CmHnOk). The results are given in Table 2; the fit is Յ also reasonably good for this group with an error 10% 3. Hydrocarbon activity coefficients for seven of the species. Worst agreement is for the Ն alcohols and for species with Tb 400 K. It may be Although the effect of psat,i is expected to dominate ␥ noted that several species listed in Table 2 (acetalde- the behavior of partitioning, an examination of L,i val- hyde, acetone, methyl acetate, vinyl acetate, methyl ues to determine their effect is also appropriate, see Eq. propenate) have dipole moments as large as the alcohols, (3). Species solution models (e.g., UNIFAC) for liquids yet behave relatively well with respect to fit Eq. (4), that usually give good estimates of activity coefficients unlike the alcohols. This indicates potential difficulty in are available (Prausnitz et al. 1986). These models re- using a dipole moment parameter in a fit equation. quire data on semiempirical species parameters and The next step is to compare results from estimates of also binary interaction parameters. However, these vapor pressures for low temperature, subcooled liquids conventional solution theories do not always give ad- to extrapolations from Eq. (4). Such estimates are made equate activity values because of possible difficulties in either as the result of the use of thermodynamic mod- estimating the combinatorial terms used in the models els, or alternately, as adjustment of measured sublima- (Abildskov et al. 2001; Jang et al. 1997; Kato et al. tion pressures using fusion temperature and entropy 2002). Note there is no unique UNIFAC model for the (e.g., Mader and Pankow 2003; Prausnitz et al. 1986). combinatorial terms (Abildskov et al. 2001). As an ex- Note that subcooled liquid vapor pressure values are ample, difficulties in the modeling of values of sub- somewhat uncertain and frequently only agree to cooled liquid infinite dilution coefficients of O(10) for within a factor of 2 to 3 (Jang et al. 1997; Mader and anthracene in n-alkanes and in mixed binary Pankow 2003). Subcooled liquid saturation pressure solvents are noted in Abildskov et al. (2001). The con- values for low volatility hydrocarbons at 285 K Յ T Յ ventional solution theories may lose their usual capa- 309 K given by Jang et al. (1997), Liang et al. (1997), bility for good accuracy when needed most: for sub- Mader and Pankow (2003), Pankow et al. (1994), and cooled species where there are large deviations of hy- Storey et al. (1995) were used for the results presented drocarbon activity coefficients from unity. Since in Table 3 with pressures as low as O(10Ϫ6 mb). The fit melting temperatures increase with increasing molar Eq. (4) overestimates vapor pressures for high molar weights, subcooled liquid species (i.e., whose melting weight subcooled n-alkanes, with carbon number 17 or points exceed T) are limited to the heaviest species, greater, by 1 to 2 orders of magnitude; the other species which are expected to have relatively very low concen- pressures are captured to within a factor of 2 or less trations. For a mixture with a large number of compo- error (factor of 3 for the three oxidized species). Aside nents, the possible lack of sufficient known parameter from the heavy alkanes, the fit Eq. (4) extrapolates to data combined with a lack of direct experimental cor- the values from the references to within the expected relative data makes activity coefficient estimates sub- accuracy. (Note that the references cited direct their ject to nonnegligible uncertainties. attention to conditions in Earth’s atmosphere.) The What is needed is to address the effect of a large ␥ overestimates for long-chain alkanes (especially for car- number of species on L,i values, some of which may be

Unauthenticated | Downloaded 09/28/21 06:12 AM UTC 2980 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 62

TABLE 1. Values of R, the ratio of the hydrocarbon saturation pressure curve fit to data from NIST; T (K) and p (mb).

͗ ͘ Name Formula Tb pmin pmax R Rmin Rmax Rdev ϫ 2 ϫ 4 Methane CH4 111.0 1.24 10 4.25 10 0.823 0.542 1.005 0.185 ϫ 2 ϫ 2 Methane CH4 111.0 2.46 10 8.39 10 0.984 0.972 1.022 0.015 ϫ 2 ϫ 2 Methane CH4 111.0 1.57 10 7.42 10 1.002 0.991 1.007 0.005 ϫ 2 ϫ 3 C2H4 169.4 2.73 10 2.69 10 0.998 0.975 1.018 0.013 ϫ Ϫ2 ϫ C2H6 184.6 1.82 10 4.41 10 1.009 0.978 1.052 0.020 ϫ ϫ 3 Ethane C2H6 184.6 2.55 10 2.08 10 0.993 0.970 1.006 0.013 ϫ 3 ϫ 3 Acetylene C2H2 189.1 1.31 10 2.54 10 0.935 0.911 0.960 0.016 ϫ 3 ϫ 4 Acetylene C2H2 189.1 1.87 10 4.28 10 1.206 0.770 1.796 0.255 ϫ ϫ 3 C3H6 225.6 2.16 10 1.04 10 1.003 0.986 1.027 0.014 ϫ ϫ 3 C3H8 231.0 1.54 10 1.01 10 0.995 0.949 1.040 0.030 ϫ 3 ϫ 4 Propane C3H8 231.0 1.04 10 1.47 10 1.022 0.999 1.033 0.010 ϫ 2 1,2- C3H4 240.0 1.27 8.24 10 1.023 0.955 1.304 0.096 ϫ ϫ 2 C3H6 240.8 3.46 10 8.84 10 0.989 0.962 1.017 0.018 ϫ 3 ϫ 4 Methylacetylene C3H4 250.0 1.02 10 4.72 10 0.895 0.767 1.037 0.087 ϫ ϫ 3 Isobutene C4H8 266.7 9.07 10 1.31 10 0.979 0.930 1.043 0.036 ϫ ϫ 3 1- C4H8 266.8 2.47 10 1.07 10 0.940 0.752 1.084 0.108 ϫ ϫ 3 1,3- C4H6 268.6 1.99 10 1.11 10 1.011 0.978 1.057 0.026 ϫ ϫ 2 Trans-butene C4H8 274.2 2.03 10 8.81 10 0.986 0.937 1.042 0.034 ϫ ϫ 3 Cis-butene C4H8 276.8 1.73 10 1.99 10 1.033 1.004 1.078 0.024 ϫ 3 C4H8 278.0 1.32 1.02 10 1.018 0.974 1.164 0.047 ϫ 2 Vinylacetylene C4H4 278.0 1.35 9.94 10 1.192 1.077 1.556 0.113 ϫ ϫ 2 C4H6 280.0 1.17 10 9.85 10 0.794 0.696 0.891 0.076 ϫ 2 Ethylacetylene C4H6 283.0 5.00 9.12 10 1.026 0.986 1.131 0.041 ϫ 2 Diacetylene C4H2 284.0 1.24 9.95 10 1.398 0.987 3.274 0.436 ϫ ϫ 2 C4H8 284.0 2.45 10 8.65 10 1.061 1.002 1.120 0.035 ϫ 2 1,2-butadiene C4H6 290.0 1.33 8.09 10 1.019 0.963 1.122 0.049 ϫ 2 ϫ 3 Isopropylethylene C5H10 293.0 4.86 10 2.68 10 1.078 1.023 1.127 0.029 ϫ ϫ 1,4-pentadiene C5H8 299.0 1.06 10 3.40 10 0.973 0.972 0.974 0.001 ϫ 2 1,4-pentadiene C5H8 299.0 2.06 6.27 10 0.987 0.956 1.041 0.029 ϫ 2 ϫ 3 1- C5H10 303.0 5.37 10 1.04 10 1.050 1.032 1.068 0.010 ϫ 2 ϫ 3 Isopentene C5H10 304.3 3.07 10 2.49 10 1.059 1.010 1.104 0.027 ϫ Isoprene C5H8 307.0 8.73 3.37 10 0.942 0.937 0.950 0.004 ϫ 2 ϫ 2 Isoprene C5H8 307.0 5.40 10 9.76 10 1.051 1.034 1.069 0.010 ϫ 2 ϫ 3 Cis-pentene C5H10 309.8 2.53 10 2.46 10 1.068 1.019 1.113 0.027 ϫ 2 ϫ 3 Trimethylethylene C5H10 312.0 2.48 10 2.72 10 1.048 0.993 1.097 0.030 ϫ 2 ϫ 3 C5H8 312.0 2.53 10 2.46 10 1.063 1.022 1.101 0.023 ϫ 3-methyl-1, 2-butadiene C5H8 314.0 4.14 3.50 10 1.009 1.000 1.026 0.008 ϫ 2 ϫ 3 3-methyl-1, 2-butadiene C5H8 314.0 2.02 10 1.20 10 1.043 1.018 1.068 0.015 ϫ 2 1,3-pentadiene C5H8 315.4 1.29 8.19 10 1.001 0.968 1.055 0.028 ϫ Trans-1,3-pentadiene C5H8 315.0 4.13 3.43 10 0.965 0.963 0.970 0.002 ϫ Cis-1,3-pentadiene C5H8 317.0 3.46 3.00 10 1.006 0.999 1.026 0.008 ϫ 2,3-pentadiene C5H8 321.4 2.43 3.17 10 1.070 1.039 1.119 0.022 ϫ 2 C5H10 322.4 8.38 2.68 10 0.931 0.877 0.989 0.037 ϫ 2 ϫ 2 Cyclopentane C5H10 322.4 3.04 10 9.48 10 1.030 0.998 1.061 0.019 ϫ ϫ 2 1,5-hexadiene C6H10 333.0 9.50 10 9.02 10 0.965 0.894 1.046 0.048 ϫ ϫ 2 Diisopropenyl C6H10 342.0 6.07 10 9.92 10 0.996 0.933 1.054 0.037 ϫ Ϫ2 ϫ C6H14 342.0 1.11 10 2.55 10 1.061 0.978 1.365 0.094 ϫ 2 ϫ 3 Hexane C6H14 342.0 1.16 10 1.02 10 1.011 0.961 1.063 0.031 ϫ 2 ϫ 3 C6H12 354.0 1.03 10 1.02 10 0.992 0.923 1.064 0.044 ϫ 2 ϫ 2 Cyclohexane C6H12 354.0 1.61 10 7.21 10 0.990 0.943 1.038 0.029 ϫ 2 ϫ 4 Cyclohexane C6H12 354.0 3.62 10 2.56 10 1.159 0.984 1.230 0.066 ϫ ϫ 3 C7H16 371.5 6.36 10 1.03 10 1.012 0.962 1.072 0.034 ϫ 2 C7H8 384.0 8.91 1.22 10 0.912 0.893 0.945 0.018 ϫ ϫ 2 Toluene C7H8 384.0 6.19 10 9.40 10 0.985 0.921 1.056 0.043 ϫ ϫ 2 1- C8H16 395.0 6.36 10 9.24 10 0.984 0.933 1.045 0.035 ϫ Ϫ2 ϫ C8H18 399.0 2.32 10 1.61 10 1.168 1.047 1.360 0.079 ϫ ϫ 3 Octane C8H18 399.0 7.65 10 1.02 10 1.008 0.964 1.063 0.031 ϫ ϫ 2 Propylcyclopentane C8H16 404.0 6.39 10 9.07 10 0.981 0.907 1.062 0.049 ϫ 3 P- C8H10 411.5 5.65 2.68 10 0.992 0.877 1.142 0.089 ϫ ϫ 3 1- C9H18 419.0 6.44 10 1.01 10 1.044 1.004 1.099 0.029

Unauthenticated | Downloaded 09/28/21 06:12 AM UTC AUGUST 2005 HARSTAD 2981

TABLE 1. (Continued)

͗ ͘ Name Formula Tb pmin pmax R Rmin Rmax Rdev ϫ 2 ϫ 3 C8H16 422.0 2.00 10 2.42 10 1.116 0.997 1.232 0.065 ϫ Ϫ3 C9H20 424.0 5.34 10 5.95 1.342 1.260 1.650 0.081 ϫ ϫ 3 Nonane C9H20 424.0 6.55 10 1.01 10 1.014 0.979 1.066 0.027 ϫ ϫ 3 C9H12 425.6 6.30 10 1.03 10 0.986 0.916 1.067 0.047 ϫ ϫ 2 Propylcyclohexane C9H18 429.0 6.44 10 9.13 10 0.989 0.903 1.083 0.056 ϫ ϫ 2 N-propylbenzene C9H12 432.4 6.70 10 9.04 10 0.980 0.913 1.056 0.045 ϫ ϫ 2 Camphene C10H16 434.0 1.32 10 8.68 10 1.040 1.012 1.063 0.016 ϫ ϫ 3 1, 3, 5-trimethylbenzene C9H12 438.0 6.51 10 1.02 10 1.003 0.952 1.063 0.034 ϫ ϫ 3 1- C10H20 440.0 6.38 10 1.05 10 1.139 1.117 1.180 0.018 ϫ 2 Beta-myrcene C10H16 445.0 1.37 8.28 10 0.945 0.845 1.052 0.070 ϫ ϫ 3 Butylbenzene C10H14 456.5 6.30 10 1.03 10 0.986 0.921 1.064 0.045 ϫ ϫ 3 Trans- C10H18 460.5 5.41 10 1.03 10 0.919 0.782 1.064 0.094 ϫ ϫ 3 Cis-decalin C10H18 469.0 5.52 10 1.02 10 0.926 0.799 1.062 0.087 ϫ ϫ 2 P-diisopropylbenzene C12H18 483.5 3.72 10 5.53 10 1.828 1.709 1.971 0.044 ϫ ϫ 3 Dodecane C12H26 489.5 6.49 10 1.03 10 1.024 1.008 1.060 0.016 ϫ ϫ 2 C10H8 490.0 1.03 10 3.83 10 0.897 0.811 0.998 0.064 ϫ ϫ 2 Naphthalene C10H8 490.0 7.17 10 9.31 10 0.985 0.903 1.082 0.056 ϫ ϫ 2 1, 2, 4-triethylbenzene C12H18 494.0 4.66 10 9.98 10 0.927 0.845 0.999 0.051 ϫ ϫ 2 1-methylnaphthalene C11H10 518.0 5.67 10 9.09 10 0.942 0.851 1.042 0.062 ϫ Ϫ1 ϫ 1, 8-dimethylnaphthalene C12H12 540.0 3.39 10 1.79 10 1.199 1.160 1.298 0.035 ϫ 2, 3-dimethylnaphthalene C12H12 541.0 4.54 1.84 10 0.883 0.879 0.892 0.004 ϫ ϫ 3 N-pentadecane C15H32 543.8 5.56 10 1.02 10 1.035 1.024 1.056 0.009 ϫ ϫ 3 1-hexadecene C16H32 558.0 6.87 10 1.01 10 1.034 1.024 1.050 0.008 ϫ ϫ 3 Hexadecane C16H34 560.0 6.89 10 1.01 10 1.036 1.027 1.058 0.008 ϫ ϫ 3 C13H10 570.0 2.37 10 1.01 10 0.935 0.775 1.051 0.090 ϫ ϫ 2 N-decylcyclohexane C16H32 571.0 6.95 10 9.98 10 0.991 0.964 1.040 0.025 ϫ ϫ 2 Heptadecane C17H36 575.0 1.51 10 7.50 10 1.062 1.027 1.167 0.040 ϫ ϫ 3 Octadecane C18H38 589.5 1.50 10 1.01 10 1.063 1.039 1.149 0.029 ϫ Ϫ1 C14H10 610.0 3.01 10 4.18 0.714 0.710 0.726 0.007 ϫ ϫ 3 Phenanthrene C14H10 610.0 3.65 10 1.04 10 0.920 0.751 1.073 0.107 ϫ 2 Heneicosane C21H44 630.0 1.34 8.30 10 1.102 0.922 1.318 0.111 ϫ 2 Fluoranthene C16H10 660.0 6.37 9.73 10 0.722 0.598 1.007 0.171 ϫ 2 Tetracosane C24H50 665.0 1.32 8.22 10 1.230 0.933 1.720 0.188 ϫ 2 Pyrene C16H10 668.0 3.47 8.55 10 0.870 0.758 1.226 0.137

for subcooled liquid species. Moreover, this is to be Peng–Robinson kij may be taken null except for inter- done in the context of a simple parameterization pro- actions of methane with other hydrocarbons (Anasta- cedure, namely using Tb,i. Given the complexity and siades et al. 1994). Using the limited kij values from uncertain reliability of conventional solution theories, it Anastasiades et al. (1994) along with parameter Tb, was decided to make some estimates based on fugacity used for the psat correlation, results in the rough ap- ␾ Ϸ ϫ Ϫ5 coefficients, i, calculated using the cubic Peng– proximation (1 refers to methane) k1j 8.3 10 Tb,j. Robinson equation of state (Anastasiades et al. 1994; Once the kij are provided, the input to the Peng– Prausnitz et al. 1986). Note that the development of this Robinson equation is completed by specifying the liq- state equation was targeted at hydrocarbons and it is uid species distribution. For the distribution of species, considered useful and accepted for petroleum engineer- the concept of continuous thermodynamics (Cotterman ing applications (Anastasiades et al. 1994). It has the et al. 1985) is applied: that is, the discrete distribution is advantage of relative simplicity and also consistency replaced by a continuous probability distribution func- Ն with only a few, mostly well known, parameters. Well tion (PDF) in parameter Tb, given by P(Tb), for Tb known are the species critical properties; also required Tmin. The aggregate mole fraction of species with Tmin Յ Յ are acentric factors and binary interaction parameters, Tb Tu is given by kij (see Prausnitz et al. 1986). Although this is a model Tu ͑ ͒ ϭ ͵ ͑ ͒ ͑ ͒ equation that only approximately mimics actual hydro- S Tu P Tb dTb. 5 carbon behavior, it is expected to provide useful trends. Tmin ␥ ϭ ␾ ␾0 → → ϱ The needed relation is L,i i / i where superscript 0 Note that S 1asTu . A PDF is expected useful ϭ denotes the pure (Xi 1) limit. For hydrocarbons, the for a mixture with a large number of components whose

Unauthenticated | Downloaded 09/28/21 06:12 AM UTC 2982 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 62

TABLE 2. Values of R, the ratio of the saturation pressure curve fit to data on oxidized hydrocarbons from NIST; T (K) and p (mb).

͗ ͘ Name Formula Tb pmin pmax R Rmin Rmax Rdev ϫ 2 ϫ 3 Acetaldehyde C2H4O 293.9 4.41 10 1.55 10 1.044 1.039 1.047 0.003 ϫ 2 ϫ 3 Acetaldehyde C2H4O 293.9 9.95 10 9.33 10 1.052 1.041 1.072 0.010 ϫ 2 ϫ 2 Dimethyl formal C3H8O2 315.0 1.73 10 7.75 10 1.079 1.077 1.086 0.002 ϫ ϫ 2 Acetone C3H6O 329.3 4.29 10 9.99 10 1.073 1.070 1.080 0.002 ϫ 2 ϫ 4 Acetone C3H6O 329.3 9.99 10 4.26 10 1.006 0.897 1.070 0.054 ϫ ϫ 2 Methyl acetate C3H6O2 330.0 9.24 10 8.87 10 1.108 1.071 1.164 0.025 ϫ ϫ 3 Methanol CH4O 337.8 9.79 10 1.83 10 1.200 0.972 1.499 0.132 ϫ 3 ϫ 4 Methanol CH4O 337.8 1.79 10 4.77 10 0.739 0.546 0.981 0.177 ϫ 3 ϫ 4 Methanol CH4O 337.8 1.68 10 6.51 10 0.746 0.527 1.044 0.207 ϫ 2 ϫ 2 Vinyl acetate C4H6O2 345.7 1.32 10 9.84 10 1.092 1.074 1.118 0.012 ϫ ϫ 3 Dioxolane C3H6O2 348.0 6.18 10 1.07 10 1.095 1.076 1.126 0.015 ϫ ϫ 2 Ethanol C2H6O 351.5 1.57 10 9.95 10 1.558 1.069 2.329 0.239 ϫ ϫ 3 Ethanol C2H6O 351.5 5.80 10 1.76 10 1.308 0.965 1.814 0.193 ϫ 3 ϫ 4 Ethanol C2H6O 351.5 1.59 10 5.06 10 0.753 0.558 1.037 0.188 ϫ 2 Methyl propenate C4H6O2 354.0 1.40 9.95 10 1.072 1.042 1.203 0.041 ϫ Cyclobutanone C4H6O 372.0 2.63 4.99 10 1.029 1.006 1.055 0.014 ϫ 2 Ethyl propenoate C5H8O2 373.0 1.36 9.92 10 1.104 1.052 1.316 0.067 ϫ ϫ 2 2-methoxyethanol C3H8O2 397.6 7.03 10 8.73 10 1.162 1.070 1.268 0.051 ϫ ϫ 2 Propanoic acid C3H6O2 414.0 7.51 10 6.63 10 1.216 1.112 1.350 0.059 ϫ 2 Methacrylic acid C4H6O2 435.7 1.39 9.92 10 1.596 1.040 2.649 0.291 ϫ 3 Pyruvic acid C3H4O3 438.2 1.38 1.00 10 1.355 1.072 1.854 0.167 ϫ ϫ 3 Trans-crotonic acid C4H5O2 458.0 1.32 10 1.01 10 1.468 1.072 2.042 0.196 ϫ ϫ 2 2-isoproplyphenol C9H12O 487.0 1.33 10 8.56 10 1.281 1.084 1.515 0.102 ϫ 2 ϫ 3 3,5-dimethylphenol C8H10O 494.0 1.08 10 1.04 10 1.139 1.082 1.233 0.040 ϫ 2 Levulinic acid C5H8O3 518.7 1.32 7.92 10 2.727 1.145 6.071 0.522 ϫ 2 Succinic anhydride C4H4O3 534.2 1.45 7.82 10 1.218 1.069 1.848 0.176 ϫ 3 Glutaric anhydride C5H6O3 560.15 1.33 1.00 10 1.140 1.055 1.196 0.038 ϫ 3 9,10-anthraquinone C14H8O2 653.2 1.07 1.02 10 1.396 0.929 4.005 0.562 actual (discrete) distribution is reasonably smooth, es- K. Note that the minimum hydrocarbon critical tem- pecially when a complete species list is not available. perature is 191 K (for methane), so that psat,i is well Continuous thermodynamics PDFs have been used suc- defined for all components. The range for T covers cessfully for mixtures with a large number of species, values pertinent to atmospheres of the outer planets whose detailed composition may be impractical or im- and Titan for total pressures Ն10Ϫ3 mbar (Lee et al. ␥ Ն possible to characterize fully, to describe phase equilib- 2000). The resulting Peng–Robinson L,i 1.0, and for Յ rium problems such as petroleum flash calculations and Tb,i 500 K, typical values are no more than about 2.0, natural gas dew points (Cotterman et al. 1985; Rätzsch being very weakly dependent on T or species distribu- Ͼ et al. 1988). The mole fraction, Xi, of a species with tion parameters. However, for Tb,i 500 K, large val- ϭ ␥ boiling temperature Tb,i may be expressed as Xi ues of L,i of Order(10) or greater are obtained having ϩ Ϫ Ϫ Ϯ ϭ 1/2 ͗ ͘ S(T b,i) S(T b,i) where T b,i (Tb,i Tb,iϮ1) . Following strong variation with changes in T and/or Tb . (The ͗ ͘ common usage in petroleum applications (Cotterman largest values are for the smallest T and Tb .) The ␥ et al. 1985) the activity estimates were made using the Peng–Robinson large L,i values are limited to the very ⌫ -PDF large Tb,i values, regardless of the state of subcooling, ͑ ͒ ϭ ͑ Ϫ ͒aϪ1 which is a useful result. For the absorption limit, Eq. P Tb Tb Tmin (3), a pressure-average mean is defined by ␥ ϵ͗␥ ͓Ϫ͑ Ϫ ͒ր ͔ր͓͑ ͒a ⌫͑ ͔͒ ͑ ͒ L,ave L exp Tb Tmin Td Td a , 6 ͘ ͗ ͘ Յ ␥ Յ psat / psat ; it has values in the range 1.3 L,ave 1.7. ⌫ ϭ ͗ ͘ϭ ␴ where (a) is the gamma function and the distribution Results from the case T 125 K, Tb 300 K, and Tb ϭ ␥ ϭ parameters a and Td are related to the mean and vari- 70 K are presented in Fig. 1. For this case, L,ave ͗ ͘ϭ ϩ ␴ 2 ϭ͗ 2͘Ϫ͗ ͘2 ance by Tb Tmin aTd and ( Tb) (Tb) Tb 1.57 with a standard deviation of 0.064. ϭ 2 ϭ ͗ ͘Ϫ ␴ 2 ϭ a(Td) , so that a [( Tb Tmin)/ Tb] and Td Other available information on hydrocarbon activity ␴ 2 ͗ ͘Ϫ ( Tb) /( Tb Tmin). Calculations were performed for a coefficients includes subcooled liquid infinite dilution Յ Յ ϭ series of 60 test cases with 60 K T 170 K, Tmin values of Order(10) for anthracene and pyrene in al- Յ ͗ ͘ Յ ␴ ϭ 100 K, 250 K Tb 400 K, and Tb 50, 70, or 97 kanes and/or cycloparaffins as mentioned previously

Unauthenticated | Downloaded 09/28/21 06:12 AM UTC AUGUST 2005 HARSTAD 2983

TABLE 3. Values of R, the ratio of saturation pressure curve fit to some psat values for low volatility compounds (see text for references); T (K) and p (mb).

Name Formula Tb pmin pmax Rave Rmin Rmax ϫ Ϫ3 ϫ Ϫ2 Fluorene C13H10 570.0 1.15 10 2.10 10 0.95 0.61 1.42 ϫ Ϫ4 ϫ Ϫ3 Phenanthrene C14H10 610.0 1.73 10 3.16 10 0.78 0.52 1.11 ϫ Ϫ4 ϫ Ϫ3 Anthracene C14H10 613.0 1.62 10 2.95 10 0.70 0.47 1.00 ϫ Ϫ5 ϫ Ϫ4 Fluoranthene C16H10 660.0 1.44 10 2.40 10 0.71 0.47 0.86 ϫ Ϫ6 ϫ Ϫ4 Pyrene C16H10 668.0 9.10 10 1.60 10 0.72 0.45 0.88 ϫ Ϫ6 ϫ Ϫ6 a Benzo[a]fluorene C17H12 686.0 7.85 10 7.85 10 0.96 —— ϫ Ϫ7 ϫ Ϫ6 b Benz[a]anthracene C18H12 711.0 4.07 10 1.60 10 1.6 1.5 1.77 ϫ Ϫ6 ϫ Ϫ6 b C18H12 721.0 4.03 10 6.09 10 0.52 0.39 0.66 Alkanes: ϫ Ϫ4 ϫ Ϫ3 Heptadecane C17H36 575.0 5.0 10 1.55 10 6.25 5.3 6.94 ϫ Ϫ5 ϫ Ϫ4 Nonadecane C19H40 603.0 4.90 10 1.15 10 16.0 12.8 17.7 ϫ Ϫ5 ϫ Ϫ5 Eicosane C20H42 617.0 1.10 10 3.70 10 21.0 12.0 26.0 ϫ Ϫ6 ϫ Ϫ5 Heneicosane C21H44 630.0 4.90 10 1.80 10 35.0 29.0 41.6 ϫ Ϫ7 ϫ Ϫ6 Docosane C22H46 642.0 6.50 10 6.00 10 57.0 51.5 70.0 ϫ Ϫ7 ϫ Ϫ7 c Tetracosane C24H50 665.0 4.0 10 6.60 10 197.0 189.0 205.0 Oxidized hydrocarbons: ϭ ϭ ϭ ϭ Name Formula Tb P (T 285) R (T 285) P (T 295) R (T 295) ϫ Ϫ2 ϫ Ϫ2 2-isopropylphenal C9H12O 487.0 3.76 10 3.15 9.44 10 2.70 ϫ Ϫ2 ϫ Ϫ2 3,5-dimethylphenol C8H10O 494.0 2.11 10 3.95 5.43 10 3.35 ϫ Ϫ6 ϫ Ϫ5 9,10-anthraquinone C14H8O2 653.2 5.82 10 3.10 2.11 10 2.59 a 1 point only. b 3 points only. c 2 points only.

(Abildskov et al. 2001) and also known values for low solution theory in continuous thermodynamics form ϭ molar weight, lower Tb n-alkanes in higher molar yield at T 623 K values between 0.5 to 1.0 (Rätzsch et weight, higher Tb n-alkanes in the range between 0.64 al. 1988). The information indicates that activity coef- and 1.08 for 280 K Յ T Յ 373 K, with lower values at ficient values below unity tend to occur for T Ն 300 K. ␥ Ն higher T (Kato et al. 2002). Also, estimates of pseudo- Also, the presence of L,i Order(10) apparently does binary activity coefficients in mixtures divided into aro- not depend on any particular distribution form, but is matic and nonaromatic submixtures using conventional limited to the heaviest, low volatility species with low concentrations. To summarize the results, except for hydrocarbons Ͼ that are less volatile (Tb 500 K), indications are that ␥ values of L,i are not far from unity, that is, the con- densate mixture is close to being ideal if the amount of Ͼ species with Tb 500 K is negligible. In this situation, ␥ ␥ ϭ based on the Peng–Robinson L,ave values, using L 1.5 for estimates of the mean behavior of SOC parti- tioning is a reasonable assumption. The inapplicability (overestimations) of Eq. (4) for

very long-chain alkanes with Tb of about 550 K, or greater, may produce errors that countervail possible ␥ Ն low values in L,i estimates. Note that for Tb 500 K Յ Ϫ6 and T 200 K, psat is less than or about equal to 10 mbar, and its ratio to the methane saturation pressure is 10Ϫ10 or less. Thus any errors from using Eq. (4) as a generic saturation pressure estimate or from large de- ϭ partures from mixture near-ideality is for far-tail spe- FIG. 1. Liquid activity coefficient vs Tb for the case T 125 K, ͗ ͘ϭ ␴ ϭ ⅙ cies whose capabilities of being detected are low. Re- Tb 300 K, and Tb 70 K. The “ ” symbols refer to the left linear scale, and the “ϫ” symbols refer to the right logarithmic scale. lated to this, the distinction between high molar weight,

Unauthenticated | Downloaded 09/28/21 06:12 AM UTC 2984 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 62

FIG. 2. Total hydrocarbon vapor pressure vs T for ͗ ͘ given values of Tb of the liquid distribution. Distri- bution std dev is (a) 50, (b) 70, and (c) 97 K.

low volatility hydrocarbons and nonvolatile elemental from measurements and/or models is somewhat lim- carbon (i.e., the appropriate composition of the far tail ited, the use of qualitative trends based on a simplified of the distribution) is not well defined (Seinfeld and parameterization of partitioning may be considered as

Pankow 2003). Values of Kp,i for individual less volatile useful reference states in understanding a generally species may be difficult to obtain with accuracy; such complex situation. In particular, the ⌫-PDF is chosen as species should be treated separately. the model PDF for determining qualitative behavior ␥ and Peng–Robinson L,i values are used. 4. Trends in mean SOC behavior Shown in Figs. 2a–c are plots of the total SOC vapor ͗ ͘ pressure, p␷, in mb, versus T (in K) for certain Tb and ␴ ϭ As mentioned in the introduction, emphasis is here Tb 50, 70, and 97 K, respectively. For the outer placed on trends resulting from the important vapor- planets and Titan, the ratio of p␷ to total atmospheric condensate phase equilibrium, rather than a detailed pressure p is about 10Ϫ3 to 10Ϫ2 (Raulin and Bruston examination of the complex physicochemical behavior 1996). Also since Lee et al. (2000) give p Յ O(103 mb), Յ of planetary atmospheres. The parameterization of psat then typically p␷ O(10 mb), so that Fig. 2 suggests ͗ ͘ on Tb given by Eq. (4) along with describing condensate that relatively large values of Tb are appropriate in species distribution by a continuous thermodynamics describing the aerosols in atmospheres of the outer

PDF, P(Tb), enables such an analysis based on the val- planets and Titan. This is consistent with the assump- ues of atmospheric temperature T and condensate pa- tion of a species count that is not small. The cases stud- ͗ ͘ ␴ ͗ ͘ϭ ␴ ϭ rameters Tb and Tb (for given Tmin). Since informa- ied when Tb 250 K and Tb 97 K are for total tion on atmospheres of the outer planets and Titan pressures of O(104 mb), outside the range of interest.

Unauthenticated | Downloaded 09/28/21 06:12 AM UTC AUGUST 2005 HARSTAD 2985

FIG. 3. Vapor distribution mean boiling temperature ͗ ͘ vs T for given values of Tb and standard deviation of (a) 50, (b) 70, and (c) 97 K.

Note that successful calculations over the entire range T Յ 90 K for the lower atmospheres (total pressure p Ն of T were not always possible (see all figures) due to 10 mb) with higher temperatures (T Ն 125 K) at higher convergence difficulties. regions (p Յ 1 mb). Define a relative mixing ratio as The phase equilibrium relation, Eq. (2), combined the ratio of a species mixing ratio to that of the most

with Eq. (4) for psat(T;Tb) and Eq. (6) for P(Tb) enables abundant species, methane. (The largest relative mixing ͗ ͘ the calculation of the vapor PDF with mean Tb␷ and ratio is for the species ethane.) The results of Wong et ␴ standard deviation Tb␷. Similar to the plots of p␷ in Fig. al. (2003), Lee et al. (2000), and Moses et al. (2000) ͗ ͘ Յ Ϫ3 Ն 2, plots of Tb␷ for the vapor phase distribution are show relative mixing ratios 10 for p 10 mb (i.e., ␴ ϭ Յ presented in Figs. 3a–c; again for Tb 50, 70, and 97 T 90 K) and also show largest values for p values very ϭ Ϫ3 Ն K, respectively. For methane, Tb 111 K and the triple roughly O(10 mb), or T 150 K. That is, significant point is 91 K, so that atmospheres that are dominated vapor species content is for T relatively high and vapor Յ ␴ Յ Ϫ5 by methane vapor with T 90 K and larger Tb (e.g., pressure tending low, for example, p␷ 10 mb. Com- ͗ ͘ Fig. 3c) do not have well-defined condensed phase dis- parison with the trend results thus disfavor the low Tb , ␴ tributions. Not surprisingly, methane dominance is as- high Tb (flat and wide) liquid phase distributions that sociated with a bias of the condensed phase toward the correspond to nearly pure methane in the vapor phase. most volatile, which is quantified in Fig. 3. Examination of the variation of the vapor PDF tail Ն ͗ ͘ϩ ␴ The trends shown in Figs. 2 and 3 may be compared (defined by Tb Tb␷ 2 Tb␷) showed that, for a Ϫ to some general results from published atmospheric parameter T*, it is proportional to exp( Tb/T*). Fig- ͗ ͘ models relating to the outer planets and Titan. Atmo- ures 4a–c feature plots of T* versus T for various Tb ␴ spheric profiles (Lee et al. 2000; Moses et al. 2000) have and the Tb values. It is seen that T* depends mostly on

Unauthenticated | Downloaded 09/28/21 06:12 AM UTC 2986 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 62

FIG. 4. Vapor distribution tail decay parameter T* ͗ ͘ vs T for given values of Tb and std dev of (a) 50, (b) 70, and (c) 97 K.

Յ ͗ ͘ T and is of O(10 K). Cold atmospheres (T 100 K) of T. This figure indicates a high correlation of mSOC ͗ ͘ tend to be methane dominated (Fig. 3) and also tend and Tb . A fit to the curves shown in Fig. 5 gives ͗ ͘ϭ ϩ ␴ ϭ ϫ Ϫ3͗ ͘1.875 to be sharp (Fig. 4); that is, the tail drop-off is weaker mSOC am bm Tb, where am 1.4 10 Tb Ն ϭ ϫ Ϫ4͗ ͘ with warmer (T 150 K) atmospheres. The magnitude and bm 0.157 – 2.53 10 Tb . The near equivalence ͗ ͘ ͗ ͘ for T* is not inconsistent with the approximate varia- of mSOC and Tb as correlation parameters mirrors tion with Tb of the log of the atmospheric mixing ratio results in petroleum applications where both boiling Ն of species with Tb 200 K for some detailed model temperature and molar weight are successfully used as results or data for Jupiter (Wong et al. 2003) and Titan parameters in continuous thermodynamics PDFs relat- (Coustenis et al. 2003; Raulin and Bruston 1996). Note ing to a particular hydrocarbon class (e.g., , aro- that Dobrijevic et al. (2003) have determined that the matic). Ն uncertainties in the mixing ratios for Tb 200 K O may exceed a factor of 2 [up to factors of (10)], 5. Summary which means that vapor distributions for the models are not well determined in their entirety. This translates It has been shown that the important thermodynamic to some uncertainties also in liquid phase distribu- phase equilibrium effects on atmospheric hydrocarbon tions. vapor/condensate partitioning may be simplified by a Figure 5 presents the mean condensate molar weight parameterization using the species normal boiling tem- ͗ ͘ Ϫ1 ͗ ͘ used in Eq. (3), mSOC ,ingmol , versus Tb for the peratures that is applied to both vapor saturation pres- ␴ ͗ ͘ three values of Tb. The value of mSOC is independent sure and continuous thermodynamics PDFs for liquid

Unauthenticated | Downloaded 09/28/21 06:12 AM UTC AUGUST 2005 HARSTAD 2987

Parisot, 2003: Effect of chemical kinetic uncertainties on pho- tochemical modeling results: Application to Saturn’s atmo- sphere. Astron. Astrophys., 398, 335–344. Jacobson, M. C., H.-C. Hansson, K. J. Noone, and R. J. Charlson, 2000: Organic atmospheric aerosols: Review and state of sci- ence. Rev. Geophys., 38, 267–294. Jang, M., R. M. Kamens, K. B. Leach, and M. R. Strommen, 1997: A thermodynamic approach using group contribution meth- ods to model the partitioning of semivolatile organic com- pounds on atmospheric particulate matter. Environ. Sci. Technol., 31, 2805–2811. Kato, S., D. Hoshino, H. Noritomi, and K. Nagahama, 2002: In- finite dilution activity coefficients of n-alkane solutes, to , in n-alkane solvents, heptane to hexatriacontane. Fluid Phase Equil., 194, 641–652. Lebonnois, S., D. Toublanc, F. Hourdin, and P. Rannou, 2001: Seasonal variations of Titan’s atmospheric composition. Icarus, 152, 384–406. Lee, A. Y. T., Y. L. Yung, and J. Moses, 2000: Photochemical

modeling of CH3 abundances in the outer solar system. J. ͗ ͘ Geophys. Res., 105, 20 207–20 225. FIG. 5. Liquid mean molar weight vs Tb for given values of the std dev. Liang, C., J. F. Pankow, J. R. Odum, and J. H. Seinfeld, 1997: Gas/particle partitioning of semivolatile organic compounds to model inorganic, organic, and ambient smog aerosols. En- phase composition. Trends in the overall behavior of viron. Sci. Technol., 31, 3086–3092. Mader, B. T., and J. F. Pankow, 2003: Vapor pressures of the partitioning have been developed, including aspects of polychlorinated dibenzodioxins (PCDDs) and the polychlo- atmospheres with methane as the dominant hydrocar- rinated dibenzofurans (PCDFs). Atmos. Environ., 37, 3103– bon (outer planets and Titan). The simplified approach 3114. serves to aid the qualitative understanding of the par- Moses, J. I., B. Bezard, E. Lellouch, G. R. Gladstone, H. Feucht- titioning problem, which has many complexities. gruber, and M. Allen, 2000: Photochemistry of Saturn’s at- mosphere. I. Hydrocarbon chemistry and comparison with ISO observations. Icarus, 143, 244–298. Acknowledgments. This research was carried out at Pankow, J. F., L. M. Isabelle, D. A. Buchnolz, W. Luo, and B. D. the Jet Propulsion Laboratory, California Institute of Reeves, 1994: Gas/particle partitioning of polycyclic aromatic Technology, under a contract with the National Aero- hydrocarbons and alkanes to environmental tobacco smoke. nautics and Space Administration and funded through Environ. Sci. Technol., 28, 363–365. the internal Research and Technology Development Prausnitz, J. M., R. N. Lichtenthaler, and E. G. deAzevedo, 1986: Molecular Thermodynamics of Phase Equilibrium. 2d ed. program. The author wishes to express appreciation to Prentice-Hall, 600 pp. Dr. Josette Bellan of JPL for her helpful comments Raulin, F., and P. Bruston, 1996: Photochemical growing of com- during preparation of this paper. plex organics in planetary atmospheres. Adv. Space Res., 18, 41–49. Rätzsch, M. T., H. Kehlen, and J. Schumann, 1988: Flash calcula- REFERENCES tion for a crude oil by continuous thermodynamics. Chem. Abildskov, J., R. Gani, P. Rasmussen, and J. P. O’Connell, 2001: Eng. Comm., 71, 113–125. Analysis of infinite dilution activity coefficients of solutes in Seinfeld, J. H., and J. F. Pankow, 2003: Organic atmospheric par- hydrocarbons from UNIFAC. Fluid Phase Equil., 181, 163– ticulate material. Annu. Rev. Phys. Chem., 54, 121–140. 186. Storey, J. M. E., W. Luo, L. M. Isabelle, and J. F. Pankow, 1995: Anastasiades, K., S. Stamataki, and D. Tassios, 1994: Prediction/ Gas/solid partitioning of semivolatile organic compounds to correlation of vapor-liquid equilibrium in synthetic gas and model atmospheric solid surfaces as a function of relative oil systems. Fluid Phase Equil., 93, 23–54. humidity. I. Clean quartz. Environ. Sci. Technol., 29, 2420– Cotterman, R. L., R. Bender, and J. M. Prausnitz, 1985: Phase 2428. equilibria for mixtures containing very many components: Wong, A.-S., Y. L. Yung, and A. J. Friedson, 2003: and Development and application of continuous thermodynamics haze formation in the polar atmosphere of Jupiter. Geophys. for chemical process design. Ind. Eng. Chem. Process Des. Res. Lett., 30, 1447, doi:10.1029/2002GL01661. Dev., 24, 194–203. Yamasaki, H., K. Kuwata, and H. Miyamoto, 1982: Effects of Coustenis, A., A. Salama, B. Schulz, S. Ott, E. Lellouch, T. En- ambient temperature on aspects of airborne polycyclic aro- crenaz, D. Gautier, and H. Feuchtgruber, 2003: Titan’s atmo- matic hydrocarbons. Environ. Sci. Technol., 16, 189–194. sphere from ISO mid-infrared spectroscopy. Icarus, 161, 383– Zolotov, M., and E. Shock, 1999: Abiotic synthesis of polycyclic 403. aromatic hydrocarbons on Mars. J. Geophys. Res., 104, Dobrijevic, M., J. L. Ollivier, F. Billebaud, J. Brillet, and J. P. 14 033–14 049.

Unauthenticated | Downloaded 09/28/21 06:12 AM UTC