(222ae) Estimation of Normal Boiling Point, Critical Properties, and Lennard-Jones Parameters for Polycyclic Aromatic Hydrocarbons and Fullerenes

SUMMARY

                 Group contribution methods for the estimation of normal boiling points and critical properties are reviewed in depth.  Several of these methods are used to predict the normal boiling point, critical temperature, and critical pressure for nearly 100 unsubstituted polycyclic aromatic hydrocarbons (PAH) and the fullerenes C₆₀ and C₇₀.  The methods vary greatly in their level of complexity, the sensitivity of their predictions to molecular structure, and their ability to predict realistic trends when extrapolated to large aromatic molecules.  Application of some of the methods to fullerenes and PAH containing both 5- and 6-membered rings (PAH5/6) presents unusual challenges in group assignments.  The predicted critical properties are not only of importance in themselves but also in deriving Lennard-Jones (LJ) parameters for use in calculating transport properties for these molecules.

BACKGROUND

                PAH are present in crude oil, including shale oil and its derivatives.  They can also be formed in the treatment of shale oil.  Properties related to the phase behavior of PAH are needed for design of processes involving the treatment of feedstocks with large aromatic content.  The vapor pressures of PAH are also pertinent to thermal remediation of contaminated soils.

                PAH and fullerenes can form under fuel-rich or incomplete combustion conditions.  Many PAH are known carcinogens.  They are also key intermediates in the formation of soot.  Fullerenes, spheroidal closed carbon cages, are a special class of polycyclic aromatic compounds; curved PAH5/6 are likely intermediates in their formation in flames [1].

                In detailed kinetic modeling of chemical processes in combustion, elementary-step mechanisms for the formation of PAH, fullerenes, and soot can contain O(10²) species and O(10³-10⁴) reactions, so there is a need for a computationally efficient way to calculate up to O(10⁴) binary diffusion coefficients, which subsequently are used to calculate multi-component diffusion coefficients.  LJ parameters are used as inputs for transport properties by modeling software packages like CHEMKIN [2,3].

                Correlations for LJ parameters are often based on the critical temperature (T_c) and critical pressure (P_c) [4,5], or these properties and the acentric factor (ω) [6].  There are correlations based on other properties such as liquid density and critical volume (V_c), but these properties are usually less available and less accurately estimated than T_c and P_c.  Many of the estimation methods for T_c require the normal boiling point (T_b), so estimations of T_balso need to be considered.

                Previous studies deriving LJ parameters for PAH [7,8] were limited by the estimation methods available then, and by lack of data for normal boiling points of most PAH.  Pope [7] compared predictions from the method of Joback and Reid [9-11] and of Forman and Thodos [12-14] for a series of the most peri-condensed (having the most tightly packed ring structure) benzenoid (containing only 6-membered rings) PAH.  This set of PAH, called the tau-upsilon (τυ) series, extends from benzene (C₆H₆ -- 1 aromatic ring, 78 amu) to circumcircumcoronene (C₉₆H₂₄ -- 37 aromatic rings, 1177 amu), and includes the first ten compounds in the one-isomer series of Dias [15].  The τυ series is representative of the PAH found under combustion conditions.  The method of Forman and Thodos [12-14] was chosen, since it does not rely upon T_b to estimate T_c.  Also, extrapolation of the Joback and Reid method to larger species yielded questionable values for θ=T_b/T_c.  Correlations for the LJ parameters were chosen which only require T_c and P_c, and not ω [5], since θ is a key input into equations for ω.  Wang and Frenklach [8] considered individual PAH up to coronene (C₂₄H₁₂ -- 7 aromatic rings, 300 amu).  They used experimental values for T_b and the method of Somayajulu [16] to find T_c and P_c; these values were used to obtain ω from the Lee-Kesler vapor-pressure relation [11,17].  The correlation of Tee, Gotoh, and Stewart [6] was used to derive the LJ parameters for the individual species.

APPROACH AND RESULTS

                Estimations of T_b, T_c, and P_c from group contribution methods are compared for three different series of PAH:  (1) acenes -- kata-condensed benzenoid PAH with 1 to 23 aromatic rings (C_2+4nH_4+2n); (2) the τυ series described above; (3) PAH5/6, starting with acenaphthalene (C₁₂H₈), which are proposed as intermediates in the formation of fullerenes C₆₀ and C₇₀ in flames [1], called the FFM (fullerene formation mechanism) series.  The majority of the PAH in the FFM series have the most condensed structures possible for PAH5/6 [18]; all of the structures obey the "isolated pentagon rule" [19].  All of the PAH considered have the maximum number of conjugated non-adjacent double bonds possible, with all the carbon atoms being sp² hybridized.  In that sense, all the carbon atoms are involved in an extended aromatic π-bond structure.

                The only estimation methods which are considered are those containing groups sufficient to predict properties for the PAH in all three series.  This does not mean that only the most complex methods, containing the largest sets of groups, are chosen.  For many of the methods considered only two groups are needed for all the PAH studied.  The more complex estimation methods are better at distinguishing between isomers having the same empirical formula, but their implementation is less straightforward, especially for the species in the FFM series.

                The estimation methods used include those of Forman and Thodos [12-14], Joback and Reid [9-11], Constantinou and Gani [20,21], Wilson and Jasperson [21], Marrero and Pardillo [21,22], Avaullée et al. [23,24], and Nannoolal, Rarey, and Ramjugernath [25,26].  Predicted values for T_b, T_c, and P_cvary greatly for the different methods, sometimes yielding nonsensical results.  The predictions are compared to the very limited data available (which include computational studies).  Given the sparse data for testing the estimations, the ability of the methods to predict plausible and consistent trends with respect to structure and size becomes a crucial factor in assessing their relative merits.  Results for the LJ parameters are given for the three series of PAH, and are correlated with molecular weight when feasible.

REFERENCES

[1]  Pope, C.J.; Marr, J.A.; Howard, J.B. (1993)  "Chemistry of Fullerenes C₆₀ and C₇₀ Formation in Flames", J.Phys.Chem., 97:11001-11013.

[2]  Kee, R.J.; Rupley, F.M.; Miller, J.A.  (1989)  "CHEMKIN-II:  A Fortran Chemical Kinetics Package for the Analysis of Gas-Phase Chemical Kinetics", Rep. SAND89-8009, Sandia National Laboratories, Livermore, CA.

[3]  CHEMKIN is currently licensed by Reaction Design, San Diego, California [http://www.reactiondesign.com/products/chemkin/].

[4]  Hirschfelder, J.O.; Curtiss, C.F.; Bird, R.B.  (1964)  "Molecular Theory of Gases and Liquids", Wiley, New York.

[5]  Bird, R.B.; Stewart, W.E.; Lightfoot, E.N.  (1960)  "Transport Phenomena", Wiley, New York.

[6]  Tee, L.S.; Gotoh, S.; Stewart, W.E.  (1966)  "Molecular Parameters for Normal Fluids:  The Lennard-Jones 12-6 Potential",  Ind.Eng.Chem.Fundam., 5:356-363.

[7]  Pope, C.J.  (1988)  "Fluxes and Net Reaction Rates of High Molecular Weight Material in a Near-Sooting Benzene-Oxygen Flame", S.M. Thesis, Massachusetts Institute of Technology.

[8]  Wang, H.; Frenklach, M.  (1994)  "Transport Properties of Polycyclic Aromatic Hydrocarbons for Flame Modeling",  Combust.Flame, 96:163-170.

[9]  Joback, K.G.  (1984)  "A unified approach to physical property estimation using multivariate statistical techniques", S.M. Thesis, Massachusetts Institute of Technology.

[10]  Joback, K.G.; Reid, R.C.  (1987) "Estimation of Pure-Component Properties from Group-Contributions",  Chem.Eng.Comm., 57:233-243.

[11]  Reid, R.C.; Prausnitz, J.M.; Poling, B.E.  (1987)  "The Properties of Gases and Liquids", Fourth Edition, McGraw-Hill, New York.

[12]  Thodos, G.  (1957) "Critical Constants of the Aromatic Hydrocarbons", AIChE J., 3:428-431.

[13]  Forman, J.C.; Thodos, G.  "Critical Temperatures and Pressures of Hydrocarbons", (1958)  AIChE J., 4:356-361.

[14]  Reid, R.C.; Sherwood, T.K.  (1966)  "The Properties of Gases and Liquids", Second Edition, McGraw-Hill, New York.

[15]  Dias, J.R.  (1984)  "Isomer enumeration of nonradical strictly peri-condensed polycyclic aromatic hydrocarbons", Can.J.Chem., 62:2914-2922.

[16]  Somayajulu, G.R.  (1989) "Estimation Procedures for Critical Constants"  J.Chem.Eng.Data, 34:106-120.

[17]  Lee, B.I.; Kesler, M.G.  (1975)  "A generalized thermodynamic correlation based on three-parameter corresponding states", AIChE J., 21:510-527.

[18]  Smalley, R.E. (1992) "Self-Assembly of the Fullerenes", Acc.Chem.Res., 25:98-105.

[19]  Schmalz, T.G.; Seitz, W.A.; Klein, D.J.; Hite, G.E.  (1988)  "Elemental Carbon Cages",  J.Am.Chem.Soc., 110:1113-1127.

[20]  Constantinou, L.; Gani, R.  (1994)  "New Group Contribution Method for Estimating Properties of Pure Compounds", AIChE J. 40:1697–1710.

[21]  Poling, B.E.; Prausnitz, J.M.; O'Connell, J.P.  (2001)  "The Properties of Gases and Liquids", Fifth Edition,  McGraw-Hill, New York.

[22]  Marrero-Marejon, J., and E. Pardillo-Fontdevila  (1999) "Estimation of Pure Compound Properties Using Group-Interaction Contributions", AIChE J., 45:615-621.

[23]  Avaullée, L.; Neau, E.; Zaborowski, G.  (1997)  "A Group Contribution Method for the Estimation of the Normal Boiling Point of Heavy Hydrocarbons", Entropie, 202/203:36-40.

[24]  Avaullée, L.; Trassy, L; Neau, E.; Jaubert, J.N.  (1997) "Thermodynamic modeling for petroleum fluids I. Equation of state and group contribution for the estimation of thermodynamic parameters of heavy hydrocarbons", Fluid Phase Equil., 139:155-170.

[25]  Nannoolal, Y.; Rarey, J.; Ramjugernath, D.; Cordes, W. (2004)  "Estimation of pure component properties:  Part 1. Estimation of the normal boiling point of non-electrolyte organic compounds via group contributions and group interactions"  Fluid Phase Equil., 226:45-63.

[26]  Nannoolal, Y.; Rarey, J.; Ramjugernath, D.  (2007) "Estimation of pure component properties:  Part 2. Estimation of critical property data by group contribution",  Fluid Phase Equil., 252:1–27.