(257u) Estimation of Diffusion Coefficients of Polycyclic Aromatic Hydrocarbons (PAH) and Fullerenes

Diffusion coefficients for unsubstituted polycyclic aromatic hydrocarbons (PAH) and fullerenes are estimated, using the results of previous work on application of group contribution methods to estimate corresponding-states properties (critical properties, the acentric factor), normal boiling points, and Lennard-Jones parameters [1-4, see also references cited therein].

Values are obtained for these species under conditions pertinent to their formation in processes such as pyrolysis, combustion, gasification of carbon-containing substances (e.g., coal, biomass), thermal treatment of contaminated soils, and processing of heavy hydrocarbon feedstocks such as shale oils. Binary diffusion coefficients are calculated for these large species with common gases found either in industrial processes or laboratory experiments (e.g., Ar, N₂, H₂O). The current results have a much more sound basis than the previous studies of Pope [5] and Wang and Frenklach [6].

Often in these high-temperature systems, diffusion velocities can be significant compared to convective velocities; therefore, molecular diffusion cannot be neglected, even for such large molecules as considered here.  For detailed kinetic modeling of systems in which the molecular-weight growth chemistry producing PAH and fullerenes occurs, quite large elementary-step reaction models are required.  These reaction sets routinely contain O(10²-10³) chemical species and O(10³-10⁴) reactions, so there is a need for a computationally efficient way to calculate up to O(10⁴-10⁶) binary diffusion coefficients, often at many spatial points in the reacting system; these binary diffusion coefficients are subsequently used to calculate multi-component diffusion coefficients. There is a need for reliable and quick computational methods for calculating these values, especially since there are very few data for these large molecules.

There is a considerable amount of combinatorial complexity in this study, due to (a) several available estimation methods for the underlying properties, especially the critical temperature (T_c), critical pressure (P_c), and normal boiling point (T_b); (b) multiple interpretations for group assignments within some of these methods, especially for the species containing five-membered rings; (c) different correlations for the Lennard-Jones parameters as functions of T_c, P_c, and sometimes the acentric factor (ω); (d) calculating the diffusion coefficients via the Chapman-Enskog equation or other estimation methods; and (e) the dozens of species considered in the study.

These molecules are grouped into four homologous (or nearly so) series of increasing size but with varying structures:

(1) linear acenes: kata-condensed benzenoid PAH with 1 to 23 aromatic rings (C_2+4nH_4+2n). The first four compounds beyond benzene in this series are naphthalene, anthracene, tetracene, and pentacene.

(2) zig-zag acenes: kata-condensed benzenoid PAH with 1 to 23 aromatic rings (C_2+4nH_4+2n). The first four compounds beyond benzene in this series are naphthalene, phenanthrene, chrysene, and picene.

(3) peri-condensed PAH: benzenoid PAH which have tightly packed ring structures (like chicken wire), extending from benzene to circumcircumcoronene (C₉₆H₂₄-- 37 aromatic rings, 1177 amu), including the first ten compounds in the one-isomer series of Dias [7]. This series of PAH is representative of those found under combustion, pyrolysis, and gasification conditions.

(4) the fullerene formation mechanism (FFM) series: PAH containing both 5- and 6- membered rings (PAH5/6), starting with acenaphthalene (C₁₂H₈) and extending to the fullerene C₆₀, which have been previously proposed as intermediates in the formation of C₆₀in flames [8]. The majority of the PAH in the FFM series have the most condensed structures possible for PAH5/6 [9]; all of the structures obey the "isolated pentagon rule" [10].

Assessments are made as to which of the many approaches yield the most realistic and well-behaved values for the estimated diffusion coefficients, including which most favorably compare with the very sparse data available. Trends with respect to molecular structure and size are explored in depth.

Especial attention is paid to the assignment of groups for the five-membered-ring-containing species. A key factor in group assignment is the extent to which the bonds in the five-membered rings are associated with the delocalized π-bond structure.  A preliminary ring-additivity method, containing groups comparable to those described for benzenoid PAH by Gutman and Cyvin [11], some of which are used as third-order groups by Marrero and Gani [12], is described for both five- and six-membered rings.

References

[1] Pope, C.J. "Estimation of Normal Boiling Point, Critical Properties, and Lennard-Jones ---Parameters for Polycyclic Aromatic Hydrocarbons and Fullerenes", poster presented at the American Institute of Chemical Engineers Annual Meeting, November 2013, San Francisco, CA.

[2] Pope, C.J. "Revisiting Approaches to Obtaining Transport Properties of PAH and Fullerenes", poster presented at the Thirty-Fifth Symposium (International) on Combustion, August 2014, San Francisco, CA.

[3] Pope, C.J. "Estimation of the Acentric Factor for Polycyclic Aromatic Hydrocarbons (PAH) and Fullerenes", poster presented at the American Institute of Chemical Engineers Annual Meeting, November 2014, Atlanta, GA.

[4] Pope, C.J. "Application of the Marrero and Pardillo Property Estimation Method to Unsubstituted Polycyclic Aromatic Hydrocarbons (PAH) and Fullerenes", poster presented at the American Institute of Chemical Engineers Annual Meeting, November 2014, Atlanta, GA.

[5] 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.

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

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

[8] 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.

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

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

[11] Gutman, I.; Cyvin, S.J. (1989) "Introduction to the Theory of Benzenoid Hydrocarbons", Springer-Verlag, New York.

[12] Marrero, J.; Gani, R. (2001) "Group-contribution based estimation of pure component properties", Fluid Phase Equil., 183–184:183–208.