J. Phys. Chem. 1993,97,6890-6896
6890
Semiempirical Molecular Orbital Estimation of the Relative Stability of Polychlorinated Biphenyl Isomers Produced by o-Dichlorobenzene Pyrolysis J, A. Mulbolland,’ A. F. Sarofim, and G. C. Rutledge Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Receiued: October 2, I992
The pyrolysis of pure o-dichlorobenzene at temperatures between 1100 and 1400 K produced a small set of triand tetrachlorobiphenyls whose relative yields appear to be related to steric factors associated with the presence of o-chlorine atoms. To evaluate the hypothesis that product stability governs the distribution of PCB isomers produced in this system, biphenyl and all 209 polychlorinated biphenyl (PCB) congeners were modeled using the semiempirical molecular orbital method AM1 (Austin model 1). Relative enthalpies and entropies of PCB isomers were calculated, from which a small set of parameters that can be used for estimation by the method of group additivity was derived. These calculations suggest that PCBs produced by o-dichlorobenzene pyrolysis below 1400 K are thermodynamically distributed.
Introduction During pyrolysis of unsubstituted arenes at temperatures below which ring rupture and fragmentation occur, carbon growth takes place by the addition of aryl radicals.14 First formed are a set of biaryl isomers comprised of fuel molecule dimers. The pyrolysis of pure o-dichlorobenzene (CaH4C12) at temperatures between 1100 and 1400 K produced a small set of tri- and tetrachlorobiphenyl^.^ Possible pathwaysof polychlorinated biphenyl (PCB) formation are illustrated in Figure 1. Initiation occurs by C-H or C-Cl bond fission to form one of three radicals: l-chloro2-phenyl (C6H4Cl0),1,2-dichlor0-4-phenyl (C6H3C12*)~,or 1,2dichloro-3-phenyl(C6H3C12’)~. Subsequent formation of these aryl radicals occurs via fast H-atom and C1-atom abstraction reactions. Additions of these aryls to the parent o-dichlorobenzene molecule, or dimerizations of the aryl radicals, result in the formation of six PCBs: 2,2’-dichlorobiphenyl (C12H&12), 2’,3,4and 2,2’,3-trichlorobiphenyls(C12H7C13),and 3,3’,4,4’-, 2,3,3’,4’-, and 2,2’,3,3’-tetrachlorobiphenyls(C12H6C4). Measured yields of five of these six PCBs are shown in Figure 2; 2,2’-dichlorobiphenyl was not detected in any of the product tars. In the tar from pyrolysis at 1100 K, the five PCBs detected account for 93%of the total tar yield. As pyrolysis temperature was increased to 1375 K, yields of other PCBs increased; their formation can be explained by the substitution of H atoms for C1 atoms in the five initial PCB products. At 1460 K, a wide distribution of fused aromatic compounds, with only trace amounts of PCBs, was produced. This distribution appears to have resulted from the addition of acyclic carbon fragments, such as acetylene. These nonoxidative pyrolysis results are consistent with the oxidative pyrolysis results of Van Dell and Mahle.6 They found tri- and tetrachlorobiphenyls to be the major products of incompletecombustion generated in fuel-rich, o-dichlorobenzene flames. Moreover, they found 2’,3,4-trichlorobiphenyl and 3,3‘,4,4‘- and 2,3,3’,4’-tetrachlorobiphenyls to be the most abundant isomers in the product samples, as was the case in the nonoxidative pyrolysis experimentsjust described (Figure 2). The similar isomer distributions suggest that PCB formation pathways may be the same in the two systems. A striking feature of the data shown in Figure 2 is that PCB yields are ordered with respect to the number of o-chlorineatoms they contain. That is, thePCB withnoo-chlorineatoms (3,3’,4,4’) To whom correspondence should be addressed at: School of Civil C Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0355.
I
T @-
CI
(2’,3,4)
&CI
&&
CI
&&
L
(3,3‘,4,4‘) (2,3,3’,4’)
c&c~ CI
(2,2’,3)
CI
CI
ci
CI
Pathways of PCB formation during o-dichlorobenzenepyrolysis at temperatures ranging from 1100 to 1375 K. Thick lines represent pathways to PCBs found in greatest abundance. Only the 2,2’dichlorobiphenyl was not found; its formation pathway is indicated by a dashed line. Figure 1.
+ W Z
g
20
W
a W
6
10
I
0 1100
1200
1300 TEMPERATURE (K)
1400
1500
F m e 2. Yieldsof major PCB products fromo-dichlorobenzenepyrolysis. Solid lines represent yields of three tetrachlorobiphenylisomers; dashed lines represent yields of two trichlorobiphenyl isomers.
was produced in twice the abundance of the two PCB congeners with one o-chlorine atom (2,3,3‘,4‘ and 2’,3,4) and in about 10 times theabundanceof the two PCBcongenerswith twoo-chlorine atoms (2,2’,3,3’ and 2,2’,3). The presence of o-chlorine atoms in PCBs is destabilizing due to steric effects. Thus, the
0022-365419312097-6890$04.00/0 0 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 26, I993 6891
PCBs Modeled by AM1 experimental results suggest that biaryl formation of this type is governed by product stability. Product stability would be controlling if the governing reactions were reversible and equilibrated. After initiation, the levels of H atoms and C1 atoms achieve a partially equilibrated state via reactions such as
H'
+ HC1+
H2 + C1'
(1) These radicals participate in rapid H-atom and C1-atom abstraction reactions from o-dichlorobenzenemolecules, yielding a distribution of three chlorinated phenyl radicals (i = A, B):
+ C&C12 + C&C1' + HCl H' 4- C6H4C12 (c6H3c12*)i+ H2 c1' + C6H4C12 (c6H$l;), + HCl H'
(24 (2b)
(2c) The formation of six PCB products (j= A, B; k = A, B, C) can occur by the addition of these aryl radicals to the parent o-dichlorobenzenemolecules via the following reversiblereactions: C6H4C1'
+ C,H,C12
+
(C12H7C13), H'
+
(C6H3C12*), C6H4C12+ (C12H&14)k H' (c6H3c1;)i
+ C6H4C12
(C12H7Cl3),
c1'
(3a)
(3C)
(3d)
Alternatively,aryl-aryl recombinationreactions can produce the six PCBs: C&Cl' C,H,Cl'
+ C,jH&l' * C&&C12
+ (c6H3c1;)i
F? (C12H7C13),
(4a) (4b)
*
(4c) (c6H3c12'), + (c6H3c1;)j (c12H&14)k In either case, a thermodynamic distribution of each set of PCB isomers would be produced if the chlorinated phenyl radical isomers were equilibrated by reactions 2 and if the PCB formation reactions (3 and/or 4) were under thermodynamic control. Equilibration would result in relative yields of PCB isomers (A and B) given by differences in their total free energies (AGAB).
Kq = [AI / [BI = expWGAB/RT)
(5) The total free energy difference between isomers A and B can be factored into an enthalpy difference ( M A B ) , an entropy difference without statistical factors (SIAB and),a ratio of statistical factors (N*,A/ZV*,B):
Kq = exp(-AG,,/Rq = Ws,JNs,Bl e x ~ W k ~ / ex~kAffABlRT) Rl
(6)
To evaluate this hypothesis, the thermodynamic energies of these PCBs need to be obtained. Experimental data are available for only a small number of PCBs and must be precise to account for the small energy differences between isomers. Thus, various estimation methods were considered. At one extreme, the group additivity method is attractive because of its simplicity, but appropriate groups for differentiating PCB isomers have not been defined. At the other extreme, ab initio calculation methods are attractive because they do not rely on the input of empirical data. The enormouscomputational time requirement of applying these methods to large molecules, however, makes it prohibitively expensiveto carry out a large number of calculations. Therefore, we used a semiempirical molecular orbital modeling technique. We have calculated the enthalpies and entropies of biphenyl and all 209 PCB congeners, and we have used them to derive a small set of parameters that can be used for group additivity estimation of relative isomer stability. We then compare these
thermodynamiccalculations with the experimental measurementss to test the hypothesis that PCBs produced by low-temperature o-dichlorobenzenepyrolysis are thermally distributed. Similar calculationsare being comparedwith experimentalmeasurements of biaryls formed during pyrolysis of pure anthracene738and pure pyrene.9J0
Calculation Method The thermodynamic stabilities of biphenyl and all 209 PCBs were estimated using the semiempirical quantum mechanical molecular orbital modeling package MOPAC.11J2 First, an appropriate method, or set of empircally-derivedparameters, was selected. Three alternative methods based on the neglect of diatomic differential overlap approximation were evaluated: MNDO, AM1, and PM3. MNDO (modified neglect of diatomic overlap) was developed by Dewer and Thiel13 and has been used extensively. A common cause of error in MNDO, according to Dewer's group, is an overestimationof nonbonded repulsions. As a result, MNDO overestimates the rotational barrier about the aryl-aryl bond in biaryls, favoring a nearly perpendicular arrangement of the two aryl parts. AM1 (Austin model 1) was developed to overcome this weakness in MNDO by modification of the core repulsion f~ncti0n.l~ It has also been used extensively and is a significant improvement over MNDO in calculations of preferred conformations of biaryls and rotational barriers about their aryl-aryl single bond.15 PM3 (parametric method 3) is the newest of the methods and has been used much less extensively.*b Biphenyl was studied as a test molecule because there are experimental data available on its vapor-phase torsional angle (42")" and on its rotational energy barriers at Oo (2 kcal/mol) and 90° (1 kcal/mol).18 These measurements were used to assess the predictive capability of each method because they are quite sensitive to steric interactionsat ortho sites and, therefore, address important aspects of PCB formation thermochemistry. Our semiempirical calculations of the preferred conformation and rotational energy barriers of biphenyl were also compared with ab initio calculations, often used as a benchmark against which semiempirical methods are evaluated when experimental data are not available. Biphenyl energy profiles with respect to torsional angle (Oo = planar), calculated by each of the three methods, are shown in Figure 3. Predictions of the preferred conformation of biphenyl, with symmetry about 90°, could not have been more different. At one extreme, MNDO predicts an optimum angle of 90°, as was expected since MNDO has a tendency to overestimate repulsions between o-hydrogen atoms, causing the molecule to bevery twisted. A large energy barrier of almost 7 kcal/mol was predicted for rotation through the plane. At the other extreme, PM3 predictsan optimum angleof Oo (that is, completely planar), apparently overestimating the stabilizing effect of conjugation between rings relative to the destabilizing effect of o-hydrogen atom repulsion. Moreover, the shape of the energy profile, with two minima, is perplexing. AM1 predicts a torsional angle of 41°, in close agreement with the measured value. Furthermore, the calculated energy barriers at Oo and 90° (2.1 and 1.1 kcal/ mol, respectively) are surprisinglysimilar to the measured values. Calculations by the ab initio method GAUSSIAN-SO give an accurate value of torsional angle (42O), but less accurate values of energy barriers at Oo and 90° (3.76 and 2.26 kcal/mol, re~pectively).~9Other ab initio methods (employing other basis sets) might yield different results. On the basis of these results, AM1 was selected for quantum mechanical simulation of PCBs. This choice is appropriate not only becauseof the agreement with experimentaldata on biphenyl described above, but also becauseof well-documented deficiencies in MNDO and, in the case of PM3, due to both the inexplicable behavior of the biphenyl energy profile (Figure 3) and the lack of a reliable track record.
Mulholland et al.
6892 The Journal of Physical Chemistry, Vol. 97, No. 26, 1993 CLS',~~.,AB
CLShr,AB
+ CLShr,AB
= R W Q h i r ~ Q f i r ~ AQhir,BQfir,BI / (9) The relative rigid body enthalpies of PCB isomers were found to have a negligible dependenceon temperature. Furthermore, rigid body entropy differenceswere found to be small relative to Miot; therefore, rigid body entropy differences were ignored. The role of statistical factors in these thermodynamic calculations is now explained. Consider the number of tetrachlorobiphenyls that can be formed by dimerization of the two o-dichlorophenylradicals (1,2-dichloro-4-phenyl and 1,2-&chloro3-phenyl). Statistically, there are 16 combinations of this type since there are four possible radical sites on each ring. Due to radical site and reaction path degeneracy, however, only three of the dimers are unique. The 2,3,3',4' isomer is formed by 8 combinations, and the 2,2',3,3' and 3,3',4,4' isomers each are formed by 4 combinations. Therelationshipbetweenthestatistical factor and symmetry has been described by Bishop and Laidler.2' They have shown that for any chemical equilibrium the ratio of statistical factorsis equal to the inverse ratio of symmetry numbers ( c ) . In thisexample, thesymmetry number for the2,3,3',4'isomer is 1 and the symmetry number for both the 2,2',3,3' and 3,3',4,4' isomers is 2. The equilibrium constant describing the ratio of abundances of any two PCB isomers A and B can be expressed as follows:
1 MNDO PARAMETERIZATION I
Kq = eXp{-AGAB/RT)
E?= 47.6 kcal/mol
c VB,A/Ns,Bl
~XP{-MAB/R~'I ex~{M:ot,~B/Rl
(10)
Relative Stability of PCB Isomers
'$
(degrees)
Figure 3. Comparison of molecular orbital calculationsof energy changes in biphenyl for conformationalvariation about its dihedral angle using three semiempirical methods.
For each of the 209 PCB congeners, the standard heat of formation, E f O , was calculated as a function of torsional angle, Geometries were optimized over all possible bond lengths, bond angles, and dihedral angles, or 60 degrees of freedom in all (3N- 6,N = 22). The torsional angle for the minimum heat of formation, Efomin, represents the preferred conformation of the molecule. MOPAC can handle only fixed conformations of molecules with internal rotors, such as PCBs. Therefore, an entropy partition function due to hindered internal rotation, Qhir, was calculated by averaging over all torsional angles, assuming a Boltzmann distribution of energy states:
+.
(7)
+
Here, AEfo(+)is the difference between Efo at and Efodn. Normalized in this manner, Qhir has a value of unity for free rotation and a value of zero for no rotation. The free internal rotation partition function ( Q d is found from a moment calculation using the unsymmetrical top approximate method of Pitzer.20 Noting that all of the PCBs are symmetric about r ,and that many are also symmetric about r / 2 , this integration can be carried out over a smaller range of torsional angles. The enthalpy and entropy differences between two isomers (A and B) were calculated as follows: MAB
= EfOmin,A-
Efomin.B
(8)
The standard heat of formation was calculated as a function of torsional angle for biphenyl and each of the 209 PCB congeners. To illustrate some general features of the results, energy diagrams for all dichlorobiphenyl isomers are shown in Figure 4. The shapes of the curves for PCBs with the same number of o-chlorineatoms are very similar. The optimum gymetry, minimum heat of formation, and degree of hindered rotation, Q k , for these 12 isomers are listed in Table I. When a PCB contains no o-chlorine atoms, its optimum torsional angle is approximately 41' and it has energy barriers of approximately 2 kcal/mol through its planar conformation (OO) and 1 kcal/mol through 90' (as was the case for biphenyl). The value of Qbir is less by about 23% than that of free rotation. When one o-chlorine atom is present, the preferred conformation is less planar (ICofl of approximately 60°) and the energy barrier through the planar conformation increases to about 7 kcal/mol. Here, Q b is about 34% less than that of free rotation. When two o-chlorine atoms are present, the preferred conformation of the PCB is nearly 90° out of plane, and the energy barrier through the plane is approximately 15 kcal/mol. In this case, Qhir is half that of free rotation. The relationship of the number of o-chlorine atoms and PCB twist is summarized in Table 11. There is very little variation in and Qhir for the 21 PCB congeners (including biphenyl) that have no o-chlorine atoms; nor is there much variation in these values for the 48 PCB congeners that have one o-chlorine atom, the 72 PCB congeners that have two o-chlorine atoms, the 48 PCB congeners that have three o-chlorine atoms, or the 21 PCB congeners that have four o-chlorine atoms. Thus, to a good approximation, the internal rotation entropy difference in PCB isomers can be estimated by valuesgiven in the right-hand column of Table 11. Effects of steric crowding of non-ortho C1 atoms within a ring on Efodncan also be seen in Figure 4. In the set of dichlorobiphenyl isomers that have no o-chlorine atoms, a slight destabilizing effect (on the order of 0.1 kcal/mol) is observed for each meta interaction between C1atoms and phenyl group (comparing 4,4'-, 3,4'-, 3,3'-, and 3,5-dichlorobiphenyls),and a more sub-
PCBs Modeled by AM1
The Journal of Physical Chemistry, Vol. 97, No. 26, 1993 6893
TABLE II: Effects of &blorine Atoms on PCB Twist &at no. of t& ,,, (deg), 1350 K, As'b" no. of 0-C1 atoms PCB congeners mean [SD] mean [SD] [cal/(mol.K)]
no o-chlorine atoms
37
/
0
21 41[1] 0.77[0.01] 48 60[2] 0.66[0.01] 2 72 88[2] 0.48[0.02] 90[1] 0.38[0.01] 3 48 90[1] 0.31[0.01] 4 21 Entropy decrease due to hindered internal rotation. 1
33-
:
:
:
:
:
~
:
:
:
:
:
.
;
,
~
;
one o-chlorine atom 45 --
/
.I
r
/
two o-chlorine otoms
3
5 0
1 : 20
:
'
40
:
' 60
:
L,L
: 80
:
:
100
: : ; : ; : : : 120 140 160 1-J
(degrees)
0.00 -0.31 -0.94 -1.4 -1.8
On the other hand, the 2,6 isomer is symmetric about 90°, having two o-chlorinelo-hydrogenatom interactions in each of its planar conformations, whereas the 2,2' isomer has an o-chlorinelochlorineinteraction in its less stable planar conformations(180'). Hence, the energy barrier through that planar conformation is higher (by about 3 kcal/mol) than the energy barrier through the more stable planar conformation (0'). Because the probability of these isomers being in their planar conformation is small, the contribution that this interaction between o-chlorine atoms has to Qhir is small (order 0.01). Therefore, no distinction is made in Table I1 between isomers with two o-chlorine atoms on the same ring versus one o-chlorine atom on each ring. The relative heats of formation (hEfomin),calculated using AM1, are shown in Table I11 for all PCB congeners that have more than one isomer. The isomer with the lowest Elominis listed first in each isomer grouping and is the reference molecule in that isomer set. In most cases, this isomer is the one that has both the fewest number of o-chlorine atoms and the minimum steric interaction within each ring. The isomer of a given set with the highest Efomin(listed last) generally has a maximum number of C1 atoms on one ring located on carbon atoms adjacent to each other and to the aryl-aryl bond, as this configuration maximizes steric effects. This molecule can be as much as 8 kcal/mol higher in Efomhthan the reference isomer.
Derivation of Additivity Groups
&'mi.
isomer
u
4,4' 3,4' 3,3' 3,4
8 2 2 4 2
2,4' 2,3' 2,s 2,4 2,3
2 1 2 2 2
2,2' 2,6
2 4
395
lLan(dea) (kcal/mol) No o-ChlorineAtoms 40.8 33.4 41.3 33.5 40.5 33.7 41.3 34.1 41.1 35.0 One &ChlorineAtom 58.4 35.5 57.0 35.7 58.9 36.0 59.2 36.1 62.0 37.4 Two o-ChlorineAtoms 86.9 37.1 90.0 37.8
Qmt
at
1350 K 0.778 0.775 0.779 0.767 0.778 0.680 0.662 0.663 0.665 0.648 0.497 0.501
stantial destabilizing effect (on theorder of 1 kcal/mol) is observed for an ortho interaction between C1 atoms (comparison with the 3,4 isomer). These effects are also seen in the set of dichlorobiphenyl isomers that have one o-chlorine atom. The two dichlorobiphenyl isomers that have two o-chlorine atoms demonstrate two other effects: the interaction of three neighboring large groups and the interaction of two o-chlorine atoms in the planar conformation. The 2,6-isomer has a greater steric interaction in its optimal conformation (and, hence, a higher value of Efo-) due its having large neighbors (Cl atom, phenyl group, C1 atom) on three adjacent carbon atoms, whereas the 2,2' isomer has large neighbors on only two adjacent carbon atoms.
Also shown in Table I11 are relative enthalpies calculated by group additivity, with functional groups defined in Table IV.The group additivity technique for estimating thermodynamic properties has two advantages over molecular orbital modeling. First, group additivity is much simpler to use, with almost no computationalrequirements. Second, insight is gained as to which molecular features affect thermodynamic properties most. For example, the lowest energy conformationof a PCB and the degree to which its rotation is hindered are determined almost entirely by the number of o-chlorine atoms it contains (as already discussed, and shown in Table 11). On the other hand, differences in the heats of formation of PCB isomers are not only due to the steric interactions of o-chlorine atoms that cause them to be less planar (and, hence, less conjugated), but also due to C1-atom steric repulsions. We derived a minimum set of groups and group values that would closely match the heats of formation calculated via AM1. The results are tabulated in Table IV. Three types of effects were considered: reduced aryl-aryl conjugation due to twist, primary steric interactions within each ring due to neighboring large atom or group repulsions,and secondary steric interactions within each ring due to meta interactionsof large atoms or groups. We found that the presence of one o-chlorine atom results in an increase in twist angle from 41' to 60' and an increase in due to decreased aryl-aryl conjugation of 0.8 kcal/mol. When more o-chlorine atoms are added, the PCB becomes almost completely nonplanar (90°), resulting in an additional 0.2 kcal/ mol decrease in Efominby reduced aryl-aryl conjugation. Within each ring, repulsion between neighboring C1 atoms results in a 0.8 kcal/mol increase in Efominfor each interaction; o-chlorine atom steric interactions with its neighboring phenyl group result
Mulholland et al.
6894 The Journal of Physical Chemistry, Vol. 97, No. 26,1993
TABLE III: Relative Heat8 of Formation of PCB Isomers kcal/mol kcal/mol kcal/mol isomer AM1 group isomer AM1 group isomer AMI group Monochlorobiphenyls Tetrachlorobiphenyls Pentachlorobiphenyls 4 3 2
0.0
0.0
0.1 2.3
0.1 1.8
Dichlorobiphenyls 4,4f 3,4f 3,3' 3,5 3,4 2,4' 2,3' 2,5 2,4 2.2' 2,3 2,6
0.0 0.1 0.3 0.7 1.6 2.1 2.3 2.6 2.7 3.7 4.0 4.4
0.0 0.1 0.2 0.3 1.1 1.8 1.9 2.1 2.1 3.0 3.2 3.6
Trichlorobiphenyls 3,4',5 3,3',5 3,4,4' 3,3',4 2,4',5 2,4,4' 2,3',5 2,3',4 2',3,5 3,4,5 2',3,4 2,3,4' 2,3,3' 2,2',5 2,2',4 2,4',6 2,3',6 2,4,5 2,3,5 2,4,6 2,2',3 2,2',6 2,3,4 2,3,6
0.0 0.2 0.8 1.0 1.8 1.9 2.0 2.0 2.2 2.9 3.0 3.2 3.3 3.3 3.4 3.5 3.7 3.7 4.0 4.5 4.6 4.9 5.2 5.5
0.0 0.1 0.8 0.9 1.8 1.8 i n
i:;
1.8
iyi 3.0 3.0 3.0 3.0 3.3 3.4 3.3 4:1 4.3 4.5 4.9
3.3' . .5.5' ,. 3,3' . ,4,5'. 3,3',4,4' 2,3',5,5' 2,3',4,5' 3,4,4',5 3,3',4,5 2,3',4',5 2,3',4,4' 2,4,4',5 2,2',5,5' 2,2',4,5' 2,2',4,4' 2,3',4,5 2,3,3',5' 2,3,4',5 2,3,3',5 2,3',5',6 2,4,4',6 2,3',4,6 2,3,3',4' 2,2',3,5' 2',3,4,5 2,3',4',6 2,2'.3,4' 2;3,4,4/ 2,2',4,5 2,2',5,6' 2,3,3',4 2,2',4,6' 2,3,4',6 2,2',3,5 2,3,3',6 2,2',4,6 2,2',3,3' 2,2',3,4 2,2',3,6' 2,2',6,6' 2,2',3,6 2,3,4,5 2,334 2,3,4,6
0.0 0.8 1.6 1.7 1.8 2.0 2.2 2.5 2.6 2.8 2.8 2.9 2.9 3.0 3.0 3.1 3.2 3.3 3.5 3.7 3.8 4.1 4.1 4.2 4.2 4.2 4.2 4.3 4.3 4.4 4.5 4.5 4.7 4.8 5.4 5.6 5.6 5.8 5.8 6.5 6.8 6.9
0.0 0.8 1.6 1.8 1.8 2.2 2.2 2.6 2.6 3.0 3.0 3.0 3.0 3.1 2.9 3.2 3.3 3.3 3.6 3.7 3.7 4.1 4.0 4.1 4.2 4.2 4.2 4.3 4.3 4.3 4.6 4.4 4.7 4.6 5.2 5.4 5.4 5.6 5.6 6.5 6.9 6.9
3.3'.4.5.5' 2;3';4;5;5' 3,3',4,4',5 2,3,3',5,5' 2,3',4,5',6 2,3',4,4',5 2',3,4,4',5 2',3,4,5,5' 2,2',4,5,5' 2,3,3',4',5 2,2',4,4',5 2,2',3,4',5 2,2',3,5,5' 2,3,3',4,5' 2,3',4,4',6 2,2',4,5',6 2,3,3',5',6 2,2',4,4',6 2,3,3',4,4' 2',3,3',4,5 2,2',3',4,5 2,2',3,4,5' 2,2',3,4,4' 2,3,3',4',6 2,2',4,5,6' 2',3,4,5,6' 2,2',3,5',6 2,2',3,3',5 2,2',3,4',6 2,2',3,5,6' 2,3,4,4',5 2,2',3',4,6 2,3,3',4,5 2,2',4,6,6' 2,3,4',5,6 2,3,3',5,6 2,3,4,4',6 2,3,3',4,6 2,2',3,3',4 2,2',3,4,6' 2,2',3,3',6 2,2',3,6,6' 2,2',3,4,5 2,2',3,5,6 2,2',3,4,6 2,3,4,5,6
0.0 0.7 0.8 1.0 1.4 1.7 1.8 1.8 1.8 1.8 1.8 2.1 2.1 2.1 2.2 2.3 2.4 2.5 2.9 3.0 3.1 3.1 3.2 3.2 3.2 3.3 3.3 3.3 3.3 3.5 3.6 3.6 3.8 3.8 3.9 4.1 4.1 4.1 4.4 4.6 4.6 4.8 4.9 5.2 5.3 7.7
in a 1.O kcal/mol increase in Efomin(not including the increase in Efomin due to reduced ring conjugation). Additional steric hinderance due to meta interaction repulsions ranges from 0.1 kcal/mol for an isolated m-chlorine atom to 4.9 kcal/mol for the total effect of a fully chlorinatedring (not including the repulsions between ortho neighbors, which are calculated separately). An example of a group additivity calculation is given in the Appendix. As shown by the comparison presented in Table 111, the group additivity results provide a good fit with the AM1 results. Thus, our groups includethe important molecular features that affect thermodynamic stability; however, for a more precise determination of thermodynamic stability, the full molecular orbital simulation should be used.
Comparison with Experimental Data Returning to our experimental measurements of o-dichlorobenzene pyrolysis products, we compare the relative yields of the PCB isomers that were measured with the thermodynamic distribution as predicted by semiempirical molecular orbital modeling. This comparison is shown in Table V at one temperature (1375 K) and in Figure 5 over temperatures ranging from 1100 to 1400 K. The reference isomer in the comparisons
0.0 0.8 0.8 1.o 1.4 1.6 1.8 1.8 2.0 1.8 2.0 2.2 2.2 2.0 2.2 2.4 2.4 2.4 2.8 2.9 3.1 3.2 3.2 3.2 3.3 3.3 3.4 3.3 3.4 3.5 3.9 3.5 4.1 3.7 4.4 4.5 4.4 4.5 4.3 4.5 4.5 4.7 5.2 5.4 5.4 8.0
kcal/mol isomer AMI group Hexachlorobiphenyls 3.3' . ,4.4' . ..5.5'. . 2,3',4,4',5,5' 2,2',4,4',5,5' 2,3,3',4',5,5' 2,2',3,4',5,5' 2,2',4,4',5,6' 2,2',3,3',5,5' 2,3',4,4',5',6 2,2',3,4',5,6' 2,3,3',4,5,5' 2,2',4,4',6,6' 2,3,3',5,5',6 2,3,3',4,5',6 2,2',3,4,4',5' 2,3,3',4,4',5' 2,2',3',4,5,6' 2,3,3',4,4',5 2,3,3',4',5',6 2,2',3,3',4,5' 2,2',3,4,5,5' 2,2',3,4,4',5 2,2',3,3',5,6' 2,2',3,4,4',6' 2,3,3',4',5,6 2,3,3',4,4',6 2,2',3,5,5',6 2,2',3,4',5,6 2,2',3,4',6,6' 2,2',3,4,5',6 2,2',3,4,4',6 2,2',3,3',4,4' 2,2',3,3',4,6' 2,2',3,3',6,6' 2,2',3,3',4,5 2,2',3,4,5,6' 2,2',3,3',5,6 2,2',3,3',4,6 2,2',3,4,6,6' 2,2',3,5,6,6' 2,3,4,4',5,6 2,3,3',4,5,6 2,2',3,4,5,6
0.0 0.7 0.7 1.o 1.o 1.2 1.2 1.3 1.5 1.5 1.7 1.8 1.8 2.0 2.1 2.2 2.2 2.3 2.3 2.4 2.5 2.5 2.5 2.5 2.6 2.7 2.7 2.7 2.7 2.7 3.4 3.5 3.7 3.7 3.8 4.0 4.0 4.1 4.1 4.7 5.0 6.0
0.0 0.8 1.o 1.o 1.2 1.4 1.4 1.4 1.6 1.8 1.8 2.2 2.2 2.2 2.0 2.2 2.6 2.4 2.4 3.0 3.0 2.6 2.6 3.0 3.0 3.2 3.2 2.8 3.2 3.2 3.4 3.6 3.8 4.1 4.3 4.3 4.3 4.5 4.5 5.5 5.6 6.5
kcal/mol isomer AM1 group Heptachlorobiphenyls 2.2'.3.4.4'.5.5' 2;3,?;4;4';5;5' 2,2',3,4',5,5',6 2,2',3,3',4,5,5' 2,3,3',4',5,5',6 2,3',4,4',5,5',6 2,2',3,4,4',5',6 2,2',3,4,4',5,6' 2,2',3,3',5,5',6 2,2',3,3',4,5',6 2,2',3,4',5,6,6' 2,2',3,4,4',6,6' 2,3,3',4,5,5',6 2,2',3,3',4,4',5 2,2',3,3',4,5,6' 2,2',3,3',4,4',6 2,2',3,3',4',5,6 2,2',3,3',5,6,6' 2,2',3,3',4,6,6' 2,3,3',4,4',5,6 2,2',3,4,5,5',6 2,2',3,4,4',5,6 2,2',3,3',4,5,6 2,2',3,4,5,6,6'
0.0 0.1 0.2 0.3 0.3 0.4 0.4 0.5 0.5 0.6 0.7 0.7 1.3 1.3 1.5 1.6 1.6 1.7 1.7 2.0 2.1 2.1 3.4 3.5
0.0 -0.2 0.2 0.2 0.2 0.2 0.2 0.4 0.4 0.4 0.6 0.6 1.3 1.2 1.4 1.4 1.4 1.6 1.6 2.1 2.3 2.3 3.4 3.6
Octachlorobiphenyls 2,2',3,3',4,4',5,5' 2,2',3,3',4,5,5',6' 2,2',3,3',4,4',5,6' 2,2',3,4,4',5,5',6 2,2',3,3',4,5',6,6' 2,2',3,3',5,5',6,6' 2,2',3,3',4,4',6,6' 2,3,3',4,4',5,5',6 2,2',3,3',4,5,5',6 2,2',3,4,4',5,6,6' 2,2',3,3',4,4',5,6 2,2',3,3',4,5,6,6'
0.0 0.2 0.2 0.4 0.4 0.4 0.4 0.5 0.7 0.8 1.7 1.8
0.0 0.2 0.2 0.3 0.4 0.4 0.4 0.3 0.5 0.7 1.5 1.7
Nonachlorobiphenyls 2,2',3,3',4,4',5,5',6 2,2',3,3',4,5,5',6,6' 2,2',3,3',4,4',5,6,6'
0.0 0.2 0.2
0.0 0.2 0.2
of tetrachlorobiphenyls is 3,3',4,4'; for the trichlorobiphenyls, the reference isomer is 2',3,4. These results indicate that the PCB products may indeed be equilibrated, Further evidence supporting the hypothesis of thermodynamic control of biaryl formation during pyrolysis of fused arenes has been obtained. We have estimated the thermodynamic distribution of two other sets of biaryl isomers for which we have experimental data: those produced during pyrolysis of pure anthracene's8 and pure pyrene9J0between 1200 and 1500 K. The thermodynamic predictions agree with the experimental data in each of these systems.
Conclusion The pyrolysis of pure o-dichlorobenzene at temperatures between 1100 and 1400 K produced a small number of tri- and tetrachlorobiphenylswhose relative yields appear to be governed by the steric effects of o-chlorine atoms. The semiempirical molecular orbital model AM1 was able to predict differences in thermodynamic stability due to these steric interactions. A small set of group additivity parameters were derived from the quantum mechanical treatment of biphenyl and all 209 PCB congeners. The results of the thermodynamicmodeling support the hypothesis
PCBs Modeled by AM1
The Journal of Physical Chemistry, Vol. 97, No. 26, 1993 6895
TABLE I V PCB Isomer Group Additivity Parameters Derived from Molecular Orbital Modeling Reduced Conjugation between Rings Due to Twist no. of AH0 o-chlorine atoms (kcal/mol) 1 2-4
0.8 1.o
Primary Steric Interactions: Ortho Effects rwb interaction (kcal/mol) CI atom/Cl atom 0.8 CI atom/phenyl 1.o Secondary Steric Interactions: Meta Effects no. AHc no. of c1 (kcal/ ofC1 atoms interaction mol) atoms interaction 1 m 0.1 3 o+o+m 2 o + m o r m + m 0.3 3 o+o+o o+o
2 3
0.6
4
o+o+o+o
AHC
(kcal/ mol) 1.2 1.4 2.9 4.9
o+m+o 1.0 5 o+o+o+o+o a Enthalpy increase due to reduced conjugation between rings. bEnthalpy increase due to crowding by ortho groups within ring. Enthalpy increase due to all additional crowding within ring.
TABLE V Comparison of Relative PCB Isomer Yields from eMchlorobenzene Pyrolysis Experiments and from Thermodynamic Calculations experiment thermodynamiccalculation re1 AH hs'& Asffi,a yieldat (kcal/ [cal/ [cal/ K, at mol) (mol K)1 (mol Kll N. u 1375 K isomer 1375 K Tetrachlorobiphenyls 3,3',4,4' 1 2,3,3',4' 0.5 0.2 2,2',3,3' 0.14*0.06 2',3,4 2,2',3
1 0.2
0.0 2.3 3.8
0.0 -0.4
-1.0 Trichlorobiphenyls
0.0
0.0
0.0 0.2 0.5
4
0.0
4
2 1 2
0.19
4
1
1
8
1
0.78
1.7 -0.6 0.2 4 1 0.44 Entropy change due to internal rotation (hindered and free). 0.1
1 tL3.3'.4'lA3.3'.*41
T
-0 -0
122'.3MZ'A41
Figure 6. Chart illustratingthe use of group additivityfor estimating the
thermodynamicpropertiesof four tetrachlorobiphenylisomers. Entropy group additivity parametersare listed in Table11;enthalpy groupadditivity parameters are listed in Table IV. A comparison is made of group additivity and semiempirical (AM 1) results.
Acknowledgment. This research was supported by the National Institute of Environmental Health Sciences through the Superfund Hazardous Substances Basic Research Program Grnat ES04675 and Environmental Health Sciences Center Grant ES02109. The computations were performed on the MIT CRAY X-MP. Appendix: Sample Group Additivity Calculation For the purpose of illustration, details of the calculations of relative entropies and enthalpies of four tetrachlorobiphenylsare shown in Figure 6. The 3,3',5,5' isomer is the most stable tetrachlorobiphenyl; the other three isomers shown (2,2',3,3'-, 2,3,3',4'-, and 3,3',4,4'-) were detected in the o-dichlorobenzene pyrolysis tars. Group values of the hindered internal rotation partition function, &, and the corresponding entropy change due to hindered internal rotation, ASh,, are taken from Table 11. Group values for enthalpy differences are taken from Table IV. For example, the 2,3,3',4' isomer has one o-chlorine atom and, thus, an energy cost due to reduced aryl-aryl conjugation of 0.8 kcal/mol. It has two ortho C1-atom/Cl-atom interactions (0.8 kcal/mol enthalpy cost each) and one ortho Cl-atom/phenyl interaction (1.O kcal/mol cost), resulting in a 2.6 kcal/mol energy cost for all ortho interaction repulsions. The ring with C1 atoms on the 2- and 3-carbon atoms has an ortho + ortho secondary repulsion (0.6 kcal/mol cost), and the other ring, with C1 atoms on the 3- and 4-carbon atoms, has an ortho meta secondary repulsion (0.3 kcal/mol cost). The total enthalpy reduction for this isomer is 4.3 kcal/mol, which is 3.7 kcal/mol more than that of the reference isomer, 3,3',5,5'. Thisvalue is in close agreement with the AM1 calculation of 3.8 kcal/mol.
+
References and Notes (1) Badger, G. M.; Jolad, S.D.; Spotswood,T. M. Aust. J . Chem. 1964,
0.01 1100
1200 1300 TEMPERATURE (K)
14c0
Figure 5. RelativePCB yields as a function of temperature. The points
represent measurements of relative PCB yields from o-dichlorobenzene pyrolysis. Error bars indicate data accuracy. Curves represent thermodynamic yields of PCB isomers predicted by AM1. Points: circles = [2,3,3',4']/[3,3',4,4']; triangles = [2,2',3,3']/[3,3',4,4']; square = [2,2',31/ [2',3,41.
that the pyrolytic aryl addition pathways are under thermodynamic control. Hence, prediction of the distribution of these combustion byproducts is significantly enhanced by the ability to estimate the relative stability of biaryl isomers.
17, 771. (2) Badger, G. M.; Donnelly, J. K.;Spotswood, T. M. Aust. J. Chem. 1964,17, 1138. (3) Lcwis. I. C. Carbon 1982. 20. 519. (4) Bruinsma, 0. S.L.; Tromp, P. J. J.; ddauvage Nolting, H. J. J.; Mouliin. J. A. Fuel 1988. 67. 334. (5)'Mulholland, J. A.; Sarofim, A. F.; Beer, J. M.; Lafleur, A. L. In Twenty-Fourth Symposium (International)on Combustion; The Combustion Institute: Pittsburgh, 1992; p 1091. (6) Van Dell, R. D.; Mahle, N. H. Combust. Sci. Tech. 1992,85, 327. ( 7 ) Wornat, M. J.; Sarofim, A. F.;Lafleur, A. L. In Twenty-Fourth Symposium (International) on combustion; The Combustion Institute: Pittsburgh, 1992, in press. (8) Mulholland, J. A.; Mukherjce, J.; Wornat, M. J.; Sarofim, A. F.; Rutledge, G. C. Combust. Flame, in press. (9) Mukherjee,J.; Sarofim,A. F.;Longwell,J. P. Manuscriptsubmitted to Combust. Flame.
6896 The Journal of Physical Chemistry, Vol. 97, No. 26, 1993 (10) Mukherjcc, J.; Mulholland, J. A.; Sarotim, A. F. Manuscript to be submitted to J . Phys. Chem. (1 1) Coolidge, M. B.; Stewart, J. J. P. MOPAC, Version 6.00,Quantum Chemistry Program Exchange, 1990. (12) Stewart, J. J. P. J . Comput.-Aided Mol. Des. 1990, 4, 1 . (13) Dewer, M. J. S.; Thiel, W. J . Am. Chem. Soc. 1977, 99, 4899. (14) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J. Am. Chem. Soc. 1985,107, 3902. (15) Fabian, W. M. F. J. Compur. Chem. 1988,9, 369.
Mulholland et al. (16) (17) (18) (19)
Stewart, J. J. P. J. Compur. Chcm. 1989, 10, 209. Bastiansen, 0. Acto Chcm. S c u d . 1949, 3, 408. Carreira, L. A.; Towns, T. G. J. Mol. Srrucr. 1977, 41, 1. McKinney, J. D.; Gottschalk, K. E.; Pedersen, L. J. Mol. Srrucr.
1983, 104, 445.
(20) Pitzer, K. S. Quunrum Chemistry; Prenticc-Hall: New York, 1953; p 436. (21) Bishop, D. M.; Laidler, K. J. J. Chcm. Phys. 1965,42, 1688.
