6616 J . Org. Chem., Vol. 66, No. 20, 2001
Mulder et al.
Sch em e 4
ficiently fast. We can estimate that with the inherently
elevated concentration of benzanthrenyl (see above),
which is a direct consequence of the low BDE(C-H) in
1, a pseudo-first-order rate constant of 105 s-1 or higher
for the incipient radical species is required to circumvent
the reversibility. These findings also explain why the rate
for reductive cleavage of R-phenoxyl-acetophone (see
Introduction) is accelerated only modestly when adding
1 to 3. The actual RRD by 1 is faster (eq 3) but the
following fragmentation of the ketyl radical into phenoxyl
and acetophenone (eq 4) is too slow to compete effectively
with the back hydrogen atom transfer to the benzanthre-
nyl radical. In the past, we have estimated a rate
constant for eq 4 as about 106 M-1 s-1 24
Now, an upper
.
for disappearance of benzanthrone (6) can now be pre-
limit of 104 M-1 s-1 seems to be more in line with the
current insights and can be related to the high intrinsic
activation barrier for the reverse of eq 4, the addition of
a phenoxyl radical to a double bond.25
sented as:
-d[6]/dt ) [k9K6K10/K11][3][6]
(12)
With the enthalpic data from Table 3, eq 12 is reduced
Hyd r ogen a tion of Ben za n th r en e. The hydrogena-
tion of benzanthrene (1) follows a second order (in 1)
reaction mechanism. At the high temperatures employed,
an appreciable radical concentration can be envisaged to
establish a dynamic equilibrium between 1 and its radical
(20). Delocalization of the unpaired electron26 in 20
creates a number of reactive sites and hydrogen transfer
yields an isomeric mixture of 7H-benz[d,e]anthracene (1),
6H-benz[d,e]anthracene (21), 4H-benz[d,e]anthracene (22),
3H-benz[d,e]anthracene (23), and 1H-benz[d,e]anthracene
(24). It seems reasonable to postulate that the concentra-
tions of the isomers are established by an overall
thermodynamic equilibrium (eq 14, Scheme 5), which is
corroborated by the degree of H/D exchange in benzan-
threne when a deuterated solvent is used.
Provided that the entropy changes are negligible, the
relative concentrations can be approximated by using the
benzylic BDE(C-H)s from Table 3 as 1/21/22/23/24 ) 3.5
× 104:3.9 × 102:9.4 × 102:1:5.8 at 300 °C. This ratio
agrees with the general feature that phenanthrene
derivatives are thermodynamically more stable than the
isomeric compounds with a (linear) anthracene backbone.
Compound 7, the product of hydrogenation of 1, emerges
through two distinct RRD reactions: hydrogen transfer
to -d[6]/dt )1.8 × 10-12k9[3][6].17 Combination with the
experimentally determined kexp,6 of 7.1 × 10-5 M-1 s-1
,
furnishes a rate constant for disproportionation of 9,10-
dihydroanthracenyl (19) with ketyl 18 of k9 ) 3.9 × 107
M-1 s-1at 300 °C.
In the absence of significant steric interactions, the rate
for disappearance of carbon-centered radicals by radical-
radical interaction is at the diffusion-controlled limit. The
rate constant (kdis) merely reflects the transport proper-
ties of the solvent rather than the nature of the encoun-
tering species.18,20 Typically, kdis is about 2 × 1010 M-1
s-1 at 300 °C. The two product channels are recombina-
tion (kr) and disproportionation (kd); the ratio (kd/kr)
strongly depends on the type of radicals involved.21
linear relationship between ln(kd/kr) and the reaction
enthalpy for disproportionation (∆dH) has been sug-
gested, which can be rewritten as eq 13.21,22
A
ln(kd) ) 13.6 - 0.16∆dH
(13)
With ∆9H of -16.5 kcal mol-1, eq 13 yields a k9 () kd)
of 1 × 107 M-1 s-1, in good agreement with our experi-
mental value of 3.9 × 107 M-1 s-1
.
The reaction entropy for disproportionation is close to
zero, and on the basis of microscopic reversibility, eq 13
can also be used to calculate the preexponential factor
for the RRD, kRRD ) kdexp(-Ea,RRD/RT). This implies that
the variation in the reactivity of a hydrogen donor cannot
be derived exclusively on an activation enthalpy consid-
eration.23
(23) Using eq 13 to derive the ARRD implies that both ARRD and Ea,RRD
depend on the reaction enthalpy. This phenomenon is commonly
referred to as the isokinetic relationship but may also be imposed by
a
small enthalpic barrier for disproportionation (Evans-Polanyi
principle). Indeed, the factor of 0.16 is quite common for exothermic
hydrogen atom abstraction reactions.20 The rate constant for RRD is
presented by kRRD ) ARRDexp(-Ea, RRD/RT); with ln(ARRD) ) ln(kd) )
13.6 + 0.16∆RRDH and Ea,
) ∆RRDH + 3 with ∆RRDH the reaction
RRD
enthalpy for RRD and a diffusional enthalpy barrier of 3 kcal mol-1
Thus, benzanthrene can be applied as a hydrogen
transfer agent only when the subsequent step is suf-
for the reverse reaction.18
(24) Huang, Y.; Page´, D.; Wayner, D. D. M.; Mulder, P. Can. J .
Chem. 1995, 73, 2079-2085.
(16) Savage, P. E. Energy Fuels 1995, 9, 590-598.
(25) (a) In this particular experiment, the 1/3 ratio was 1/16,5 and
according to ref 23 the relative v3,RRD is expected to be 70. Experimen-
tally, a rate enhancement of only a factor of 5 was found. (b) With a
(17) Assuming ∆6S ) 0 and with ∆6H ) 21.0 kcal mol-1 from Table
3, renders K6 ) 9.8 × 10-9 at 300 °C (see also ref 14).
(18) The kdis for, e.g., cumyl radicals, measured in tert-butylbenzene
∆4H of 12 kcal mol-1 24 log(A4) ) 13.4,25c and a rate constant, k4, of 104
,
as the solvent, is determined as 4 × 1011exp(-3.4/RT), i.e., at 300 °C
s-1 leads to Ea4 ) 25 kcal mol-1, thus Ea-4 ) 13 kcal mol-1 the reverse
reaction: the addition of the phenoxyl radical to the styrene derivative
(the enol form of acetophenone). This high activation barrier for
phenoxyl may be associated with the extended delocalozation of the
free electron into the aromatic ring. In the recombination reaction with
methyl, primarily the carbon-carbon coupling occurs,25d addition of a
phenoxyl to styrene with the spin on carbon yields an adduct with a
weak carbon-carbon bond, which will decompose to reactants. (c)
Autrey, S. T.; Alnajjar, M. S.; Nelson, D. A.; Franz, J . A. J . Org. Chem.
1991, 56, 2197-2202. (d) Arends, I. W. C. E.; Louw, R.; Mulder, P. J .
Phys. Chem. 1993, 97, 7914-7925.
kdis ) 2 × 1010 M-1 s-1
.
The temperature dependence for a diffusion-
19a
controlled rate constant is associated with the change in the solvent’s
viscosity (η). The viscosity of pure anthracene is 0.39 cP at 300 °C.19b
(19) (a) Korthe, T.; Marque, S.; Martschke, R.; Popov, M.; Fischer,
H. J . Chem. Soc. Perkin Trans 2, 1998, 1553-1559. (b) Landolt-
Bo¨rnstein, 6. Auf. Zweiter Band, 5. Teil, Bandteil a (Transportpha¨-
nomene I); Scha¨fer, K., Ed; Springer-Verlag: Berlin, Heidelberg, New
York, 1969; p 174.
(20) Arends, I. W. C. E.; Mulder, P.; Clark, K. B.; Wayner, D. D. M.
J . Phys. Chem. 1995, 99, 8182-8189.
(21) Manka, M. J .; Stein, S. E. J . Phys. Chem. 1984, 88, 5914-5919.
(26) According to our DFT calculations, the Mulliken spin densities
at positions C-7, C-6, C-4, C-3, and C-1 in the benzanthrenyl radical
(20) are 0.29, 0.23, 0.23, 0.10, and 0.15, respectively, in good agreement
with an EPR study to provide 0.31, 0.22, 0.21, 0.13, and 0.13.27
(22) Equation 13 is derived from ln(kd/kr) ) -10.1 - 0.16∆dH.21 Since
kdis kr > kd, it can be rewritten as ln(kd) ) -10.1-0.162 ∆dH + ln-
≈
(kdis) ) 13.6 - 0.16∆dH, with kdis from ref 18.