AUGUST 2005 HARSTAD 2977 Trend Analysis for Atmospheric Hydrocarbon 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 hydrocarbons 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 methane (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 anthracene, 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.