(231aa) Estimation of the Acentric Factor for Polycyclic Aromatic Hydrocarbons (PAH) and Fullerenes

The acentric factor (ω) is estimated from three different vapor-pressure correlations using values of θ=T_b/T_c and P_c estimated by four different group-contribution (GC) methods for dozens of PAH (plus the fullerene C₆₀), grouped in four broad classes.  The acentric factor is also directly estimated via two group-contribution methods.  There is little agreement among the results from the various methods chosen for estimating ω.  Even within the same authors' method, the directly-estimated values for ω differ dramatically from those obtained from vapor-pressure correlations using values of θ=T_b/T_c and P_c.  Expected patterns in the trends for ω which might be expected for different structures of PAH are rarely seen.  On the whole, the reliability of the results is highly suspect.

DISCUSSION AND RESULTS

The acentric factor was defined by Pitzer et al. [1] for use in three-parameter equations of state.  It also is used in correlations for other properties, such as Lennard-Jones parameters [2], which can be used to derive transport properties (viscosities, binary diffusion coefficients). 

Values of the acentric factor are estimated for dozens of unsubstituted polycyclic aromatic hydrocarbons (PAH) and fullerenes.  Values for ω are derived from three different vapor pressure correlations (Edminster [3,4], Lee-Kesler [5-7], Ambrose-Walton [8-10]), using θ=T_b/T_c and P_c estimated by four different group-contribution (GC) methods (Avaullée et al. [11,12], Constantinou and Gani [13,14], Marrero and Gani [10,15], Nannoolal et al. [16,17]).  Two of these methods, those of Avaullée et al. and Constantinou and Gani, also directly estimate ω from group contributions.

Four series of unsubstituted PAH are considered in the present work:

(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 [18].  This series of PAH is representative of those found under combustion 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 C₆₀ in flames [19]. The majority of the PAH in the FFM series have the most condensed structures possible for PAH5/6 [20]; all of the structures obey the "isolated pentagon rule" [21].

The results for ω were largely insensitive to the choice of vapor-pressure correlation used.  Vapor-pressure-derived values for ω varied greatly with the estimation method used.  Also, for both the Avaullée et al. and the Constantinou and Gani methods, the directly estimated ω values not only differed dramatically between the two methods but also disagreed strongly with those derived from those derived from θ and P_c from the same method.

With the exception of the values of ω directly estimated by the Avaullée et al. method, the results showed strong sensitivity to the type of molecular structure.  (Only the Avaullée et al. and Marrero and Gani methods could distinguish between the linear and zig-zag acenes.)  However, the general trends for ω with respect to molecular structure often differed from what could be expected based on the intended purpose of the acentric factor of providing a measure of the deviation from sphericity of the molecule.  Broadly interpreted, the more compact the PAH structure, the lower the value of ω one might expect.  So the broad trends should be that ω(linear acenes) > ω(zig-zag acenes) > ω(peri-condensed PAH) > ω(FFM).  This trend was not often observed in the results.

For the Avaullée et al. method, the group-contribution-derived acentric factors showed only slight sensitivity to molecular structure.  They were also higher than those from the vapor-pressure correlations, except for the species with four or fewer rings, when the two ω values for each PAH approximately agreed with each other.  For PAH up to 550 amu, the trend with structure was ω(acenes) > ω(peri-condensed PAH) > ω(FFM); above 550 amu, it was ω(peri-condensed PAH) > ω(acenes) > ω(FFM).

A truly remarkable set of results came from the Constantinou and Gani method.  All of the group-contribution-derived acentric factors were higher than those from the vapor-pressure correlations.  The only times the differently-derived ω values were close to agreement with each other were for (a) the PAH with 1 to 5 rings, and (b) C₆₀.  The group-contribution ω values showed the following trend with structure:  ω(acenes) > ω(peri-condensed PAH) > ω(FFM).  However, the vapor-pressure-derived ω values exhibited the opposite trend.

Clearly, further work in this area is indicated.  PAH are present in many hydrocarbon fuels and their products, such as petroleum coke.  They are also products of combustion in themselves as well as precursors to soot particle formation.  Many of them are mutagenic or carcinogenic.  Therefore, more information on their properties would be of value.

REFERENCES

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