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Energy & Fuels 1997, 11, 392-395
Statistical and Steric Effects on Pyrene Pyrolysis Product Distributions at High Temperature James A. Mulholland* Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0512
Jaideep Mukherjee and Adel F. Sarofim Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Received October 8, 1996. Revised Manuscript Received December 6, 1996X
Two sets of isomer products of pyrene pyrolysis at high temperatures are the six bipyrenes and their five cyclodehydrogenation products. Thermodynamic distributions of these isomer sets were computed using the AM1 semiempirical molecular model. Two properties of molecular structure, symmetry and steric hindrance associated with bonding between pyrene units, were found to govern these thermodynamic distributions. Distributions produced by pyrene pyrolysis, on the other hand, support a simple kinetic model of aryl addition and cyclodehydrogenation pathways in which reaction path degeneracy is a first-order effect and steric hindrance is of secondary importance.
Introduction The pyrolysis of pyrene between 1200 and 1500 K yields four major classes of products: (1) the six bipyrenes; (2) their five cyclodehydrogenation products; (3) pyrene fragmentation products, i.e. compounds which could not be formed without disruption of the pyrene aromatic rings; and (4) soot. Previously1 we presented pyrolysis product yields and put forth qualitative arguments based on product molecular topology to rationalize the distributions of isomers in the first two categories. In previous computational studies of the products of o-dichlorobenzene2 and anthracene3 pyrolysis, we found that biaryl product distributions appear to be controlled by statistical and steric factors associated with molecular structure. Here, we extend this work to the pyrene dimers and their condensation products.
Figure 1. Carbon atom numbering of pyrene molecule. Dashed lines denote axes of symmetry. Only three perimeter sites are unique. The three groups of degenerate sites are 1, 3, 6, and 8; 2 and 7; and 4, 5, 9, and 10.
Pyrene Pyrolysis Product Pathways Pyrene (C16H10) is a perifused polycyclic aromatic hydrocarbon that contains 10 perimeter carbon atoms with hydrogen bonds. Three of its perimeter sites are unique: the 1-, 2-, and 4-positions (Figure 1). Product pathways for pure pyrene pyrolysis are shown in Figure 2. In pyrolysis at high temperatures, three pyrenyl radicals (C16H9•) can be formed by C-H bond homolytic fission or by H-atom abstraction. The 2-pyrenyl radical is produced by H-atom loss from either of two sites; the 1- and 4-pyrenyl radicals are formed * Author to whom correspondence should be addressed [telephone (404) 894-1695; fax (404) 894-8266; e-mail james.mulholland@ce. gatech.edu]. X Abstract published in Advance ACS Abstracts, February 1, 1997. (1) Mukherjee, J.; Sarofim, A. F.; Longwell, J. P. Combust. Flame 1994, 96, 191. (2) Mulholland, J. A.; Sarofim, A. F.; Rutledge, G. C. J. Phys. Chem. 1993, 97, 6890. (3) Mulholland, J. A.; Mukherjee, J.; Wornat, M. J.; Sarofim, A. F.; Rutledge, G. C. Combust. Flame 1993, 94, 233.
S0887-0624(96)00172-7 CCC: $14.00
Figure 2. Pyrene pyrolysis pathways. Isomer designations for pyrenyl radicals, bipyrenes, and bipyrene cyclodehydrogenation products are given in parentheses. The number of degenerate reactions is given for each path (numbers not in parentheses).
via four degenerate pathways. Pyrenyl radicals add to pyrene to produce six resonance-stabilized bipyrenyl radicals (C32H19•), the structures of which are not shown in Figure 2. These aryl addition reactions, represented © 1997 American Chemical Society
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by eq 1, are exothermic due to the formation of a more stable radical.
C16H10 + C16H9• f C32H19•
(1)
Subsequent formation of the six bipyrenes (C32H18), the structures of which are shown in Figure 2, is achieved by loss of H atom at the site of radical addition (eq 1). The six bipyrene isomers, designated 1,1′, 1,2′, 1,4′, 2,2′, 2,4′, and 4,4′, have reaction path degeneracies as follows. The 2,2′ isomer is formed from only the 2-pyrenyl radical via two degenerate pathways, resulting in an overall reaction path degeneracy of four. The 1,1′-, 1,2′-, 2,4′-, and 4,4′-bipyrene isomers each have overall reaction path degeneracies of 16. The 1,4′ isomer has an overall reaction path degeneracy of 32. Cyclodehydrogenation of the bipyrenes is observed to occur by five- and six-membered ring closure. Five condensation products (C32H16), the structures of which are shown in Figure 2, are found. The two isomers formed by six-membered ring closure (labeled C1 and C2) each have overall reaction path degeneracies of 32, whereas the three isomers formed by five-membered ring closure (labeled C3, C4, and C5) each have overall reaction path degeneracies of 64. Thus, the statistical yields of bipyrene isomers and their condensation products have the following orders:
1,4′ > 1,1′ ) 1,2′ ) 2,4′ ) 4,4′ > 2,2′
(2)
C3 ) C4 ) C5 > C1 ) C2
(3)
In addition to these statistical factors, which are inversely related to molecular symmetry,4 steric effects associated with features of molecular structure may be important determinants of the relative rates of formation of bipyrene isomers and their condensation products. Steric Hindrance Effects The bipyrenes have pairs of three-, four-, or five-sided concave regions in each of their two planar configurations; these are described as bay, cove, or fjord regions, respectively, following the nomenclature of Dias.5 Repulsion between H atoms in a bay, cove, or fjord region causes the aromatic ring systems to twist out of plane, reducing conjugation between ring systems. Of the three geometries, the bay region has the least steric repulsion and the fjord region has the greatest steric repulsion. In both of its planar configurations, 2,2′bipyrene has two bay regions; the 1,2′ and 2,4′ isomers have bay and cove regions in each of their planar configurations. The 1,1′-, 1,4′-, and 4,4′-bipyrene isomers have two distinct planar configurations: one with two cove regions and one with bay and fjord regions. The bipyrene cyclodehydrogenation products also have regions of steric hindrance where the two pyrene systems fused. The two products formed by sixmembered ring closure, C1 and C2, each have two bay regions. Two of the three products formed by fivemembered ring closure, the C3 and C4 isomers, each (4) Bishop, D. M.; Laidler, K. J. J. Chem. Phys. 1965, 42, 1688. (5) Dias, J. Chem. Inf. Comput. Sci. 1990, 30, 61.
have one bay region and one cove region. The third fivemembered ring closure product, C5, has two cove regions. Thus, the bipyrenes and their condensation products can be ranked as follows, from isomers with least to most steric hindrance:
2,2′ > 1,2′ ) 2,4′ > 1,1′ ) 1,4′ ) 4,4′
(4)
C1 ) C2 > C3 > C4 ) C5
(5)
These stability orders are very different from the statistical rankings given by eqs 2 and 3. Both statistical and steric factors affect thermodynamic isomer distributions. Thermodynamic distributions were computed to assess these effects and to provide a reference point for discussion of pyrene pyrolysis product distributions. Computational Methods Due to the large number of atoms involved, a semiempirical rather than ab initio molecular orbital model was used to compute thermodynamic distributions of the bipyrenes (50 atoms) and their condensation products (48 atoms). Three semiempirical parametrizations, each based on the neglect of diatomic differential overlap approximation, have been used extensively: MNDO, AM1, and PM3.6 We used biphenyl conformational data from experimental measurements to test the predictive capability of each method because differences in the conformational energies of biaryl isomers may govern their distribution. Biphenyl vapor phase twist angle has been measured to be 42°,7 and energy barriers to rotation through 0° (planar) and 90° have been measured to be 2 and 1 kcal/mol, respectively.8 Ab initio calculations yield a biphenyl twist angle of 42° and rotational energy barriers of 3.76 and 2.26 kcal/mol.9 The three semiempirical methods yield very different values for biphenyl twist angle. MNDO gives 90° as the optimum twist angle, which is not surprising since aromatic resonance is not included in the MNDO parameterization. At the other extreme, PM3 yields a biphenyl twist angle of 0°. The AM1 result is 41°, which is almost identical to the measured value. Moreover, AM1 energy barriers to rotation through 0° and 90° are 2.1 and 1.1 kcal/mol, respectively. Thus, the AM1 results for rotational energy barriers are closer to the experimental values than even the ab initio results. On the basis of these results, we elected to use AM110 to predict thermodynamic distributions of the bipyrenes as well as their condensation products. The ratio of equilibrium concentrations of two isomers A and B is given by
[A]/[B] ) exp[-(∆GAB)/(RT)]
(6)
The total free energy is factored into enthalpic and entropic terms. The entropic term is partitioned into a statistical (or symmetry) factor (SF), a hindered internal rotation factor (Qir), and a residual electronic and (6) Stewart, J. J. P. J. Comput.-Aided Mol. Des. 1990, 4, 1. (7) Bastiansen, O. Acta Chem. Scand. 1949, 3, 408. (8) Carreira, L. A.; Towns, T. G. J. Mol. Struct. 1977, 41, 1. (9) McKinney, J. D.; Gottschalk, K. E.; Pedersen, L. J. Mol. Struct. 1983, 104, 445. (10) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J. Am. Chem. Soc. 1985, 107, 3902.
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Table 1. AM1 Thermodynamic Data for Bipyrenes isomer
steric regions
ψopt (deg)
∆H°f (kcal/mol)
SF/SF2,2′
Qir/Qir;2,2′
H - H2,2′a (kcal/mol)
S′ - S′2,2'a (cal mol-1 K-1)
2,2′ 1,2′ 2,4′ 1,1′ 1,4′ 4,4′
bay,bay/bay,bay bay,cove/bay,cove bay,cove/bay,cove cove,cove/bay,fjord cove,cove/bay,fjord cove,cove/bay,fjord
43 59 60 66 70 75
138.7 140.3 140.6 141.6 142.0 142.2
1 4 4 4 8 4
1 0.81 0.83 0.64 0.65 0.52
0 1.7 2.0 3.0 3.3 3.5
0 -0.4 -0.4 0.1 -0.7 0.5
a
Enthalpy and entropy differences evaluated over the temperature range of 1200-1500 K.
vibrational term (S′). Equation 6 is rewritten as follows:
[A]/[B] ) (SFA/SFB)(Qir,A/Qir,B) × exp[-(∆HAB)/(RT)] exp(∆S′AB/R) (7) The statistical factor, or the reaction path degeneracy, has already been discussed. Enthalpies and entropies are calculated using MOPAC 6.0 on an IBM RS/6000. First, the bipyrene isomer geometry is optimized over all possible bond lengths, bond angles, and dihedral angles (3N - 6 coordinates in all, where N is the number of atoms); this requires about 10 min of cpu time. The subsequent thermodynamic calculation requires about 120 min to complete. Enthalpy and entropy are calculated with numerical precisions of 0.1 kcal/mol and 0.5 cal mol-1 K-1, respectively. The internal rotation partition function is calculated for a free internal rotor and then corrected for hindrance as described elsewhere.2,3 Results and Discussion Computed thermodynamic distributions of bipyrenes and their condensation products are presented and compared to distributions from pyrene pyrolysis experiments. Bipyrenes. Results of AM1 calculations for the bipyrenes are shown in Table 1. Molecular topology, described by bay, cove, and fjord regions, controls the optimum twist angle, designated ψopt, and thermodynamic properties of bipyrene isomers. As expected, the isomer with only bay regions, 2,2′-bipyrene, is the most planar (ψopt ) 43°), has the least hindered internal rotation, and has the lowest heat of formation (∆H°f). The 1,2′ and 2,4′ isomers, each containing bay and cove regions, have twist angles of 60°, internal rotation factors that are 80% of that of 2,2′-bipyrene, and heats of formation that are 2 kcal/mol less than that of 2,2′bipyrene. The 1,1′, 1,4′, and 4,4′ isomers have twist angles of approximately 70°, internal rotation factors that are 60% of that of 2,2′-bipyrene, and heats of formation that are 3 kcal/mol less than that of 2,2′bipyrene. Due to the similar nature of the bond structure and UV spectra of the bipyrenes, differences in the residual entropic term (S′) are very small. The dependences of bipyrene enthalpy and entropy differences on temperature are negligible over the temperature range of interest. Bipyrene distributions from pyrene pyrolysis are shown in Figure 3, as are statistical (dashed lines) and thermodynamic (lower graph) distributions. Total bipyrene yields ranged from 1 to 7% of pyrene mass feed. At the lower temperatures studied (1213-1303 K), the pyrene pyrolysis distribution of bipyrenes is approximately a statistical distribution. At the highest temperature studied (1483 K), pyrolysis yields a bipyrene
Figure 3. Bipyrene isomer fractions (mass) from pyrene pyrolysis (3, 1,1′; 4, 1,2′; 0, 1,4′; b, 2,2′; ], 2,4′; O, 4,4′), statistical considerations (dashed lines), and AM1 thermodynamic calculations (lower graph).
isomer distribution that is approaching one consistent with steric hindrance considerations (eq 4). The pyrolysis results do not compare well with the thermodynamic distribution at any temperature. These results support a simple kinetic model of bipyrene formation during pyrene pyrolysis in which reaction path degeneracy is a first-order effect and steric hindrance is a second-order effect. Further supporting the importance of statistical factors in this system is a consideration of condensation product pathways that deplete bipyrenes; these are shown in Figure 2. The total yield of cyclodehydrogenation products increased from 5% at high temperatures. 2,2′-Bipyrene does not undergo cyclodehydrogenation since four-membered ring closure is not observed; its yield increases at high temperature. The 1,2′ and 2,4′ isomers undergo cyclodehydrogenation in two ways, whereas the 1,1′, 1,4′, and 4,4′ isomers each have three condensation routes. As condensation product yields increase with increasing temperature, bipyrene distribution changes from one proportional to the number of formation pathways to one inversely related to the number of bipyrene depleting reactions. The finding that statistical factors control the distribution of bipyrenes may be due to low activation energies for aryl addition (eq 1). These reactions are
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Energy & Fuels, Vol. 11, No. 2, 1997 395
Table 2. AM1 Thermodynamic Data for Bipyrene Cyclodehydrogenation Products fivemembered isomer rings C1 C2 C3 C4 C5
0 0 1 1 1
steric regions bay,bay bay,bay bay,cove bay,cove cove,cove
S′ - S′C1a ∆H°f SF/ H - HC1a (cal mol-1 (kcal/mol) SFC1 (kcal/mol) K-1) 143.0 143.2 162.9 162.9 167.2
1 1 2 2 2
0 0.2 20.3 20.3 24.6
0 -2.9 -5.1 -5.2 -4.1
a Enthalpy and entropy differences evaluated over the temperature range of 1200-1500 K.
exothermic, and geometries that result in bipyrene steric hindrance are not fully formed in the transition state. The second-order effect of steric hindrance is unlike the first-order effect observed in previous studies of o-dichlorobenzene2 and anthracene3 pyrolysis. In those biaryl products, however, species with much higher steric hindrance were formed. In the case of o-dichlorobenzene pyrolysis, formation of ortho-substituted polychlorinated biphenyls with large steric hindrance was suppressed. In the case of anthracene pyrolysis, formation of the 9,9′-bianthryl, with two fjord regions in both planar conformations, was suppressed. In the pyrene system, high steric hindrances due to chlorine substitution and fjord regions are not present. Bipyrene Cyclodehydrogenation Products. AM1 thermodynamic properties for five bipyrene condensation products, the structures of which are shown in Figure 2, are listed in Table 2. Product isomers C1 and C2 contain only six-membered rings and are 20 kcal/ mol more stable than isomers C3, C4, and C5, each of which contain an internal five-membered ring. This difference in stabilities is largely due to the lack of electron delocalization across the five-membered ring. The AM1 method was based on its ability to predict biaryl conformational energy differences due to twist angle, not on considerations of the degree of conjugation in fused aromatic systems; thus, five-membered ring effects may not be computed accurately by AM1. A comparison of semiempirical methods for pyrene, containing only six-membered rings, and fluoranthene, containing an internal five-membered ring, demonstrates that PM3 and AM1 yield almost identical results for this five-membered ring effect. Regarding steric hindrance effects on the thermodynamic distribution of isomers, AM1 predicts a 4 kcal/mol higher heat of formation for the isomer with two cove regions (C5) than for the isomers with one bay and one cove region (C3 and C4). Entropy differences are not negligible for these cyclodehydrogenation product isomers. Measured bipyrene condensation product distributions from pyrene pyrolysis are shown in Figure 4 with statistical (dashed lines) and thermodynamic (lower graph) distributions. The experimental data and thermodynamic results differ by several orders of magnitude
Figure 4. Isomer fractions (mass) of bipyrene cyclodehydrogenation products from pyrene pyrolysis (O, C1; 4, C2; 0, C3; ], C4; 3, C5), statistical considerations (dashed lines), and AM1 thermodynamic calculations (lower graph).
for the set of products with internal five-membered rings (C3, C4, and C5), clearly supporting a kinetically controlled process. As in the case of bipyrene formation, the distributions of these fused aromatic isomer products appear to be most influenced by statistical effects. Above 1400 K, steric and other thermodynamic effects appear to become more important, as evidenced by the increasing fractions of the C1 and C2 isomers and by the low yield of the C5 isomer (two cove regions) relative to the yields of the C3 and C4 isomers (each with bay and cove regions). Conclusion Statistical factors and steric effects associated with features of molecular structure play major roles in determining the thermodynamic distributions of the six bipyrenes and their five cyclodehydrogenation products. The distributions of these two isomer sets produced by pyrene pyrolysis, however, appear to be most influenced by statistical factors, supporting a simple kinetic model of their formation. Acknowledgment. We gratefully acknowledge the support of the National Institute of Environmental Health Sciences and the National Science Foundation. EF960172A
