2698 J. Phys. Chem. A, Vol. 108, No. 14, 2004
Oum et al.
TABLE 3: Kinetic Parameters for the CCl3 + Br (+ M) f CCl3Br (+ M) Reaction at 300 K
ET
kdiff
RC (A ) CCl3, B ) Br)
kE∞T
kAM+B
kBM+A
kAM+BM
k0,RC
Keq(AM)
Keq(BM)
M
(cm3 s-1
)
ø2′
(cm3 s-1
)
(cm3 s-1
)
(cm3 s-1
)
(cm6 s-1
)
(cm3)
(cm3)
Ar
N2
He
2.0 × 10-11
2.0 × 10-11
2.0 × 10-11
0.28
0.24
0.24
5.8 × 10-11
4.5 × 10-11
3.9 × 10-11
6.2 × 10-11
4.4 × 10-11
3.9 × 10-11
9.8 × 10-11
8.8 × 10-11
6.8 × 10-11
2.7 × 10-32
1.9 × 10-32
1.9 × 10-33
2.9 × 10-22
2.7 × 10-22
3.0 × 10-23
1.7 × 10-22
1.6 × 10-22
1.7 × 10-23
E. Density-Dependent Electronic Quenching, rspin(M). The
approach of two CCl3 radicals in their doublet electronic ground
states may lead to the electronic ground-state singlet C2Cl6 or
to the excited triplet C2Cl6. The pure spin statistics (Rspin(M))
tells us that only one-fourth of the CCl3 + CCl3 encounters
succeed to form ground-state C2Cl6, whereas three-fourths of
the encounters are unsuccessful because they separate before
they can attain the “correct” spin configuration. Such a situation
is most probable in low-pressure environments and not-too-high
densities. Similarly, Rspin(M) studies indicate that one-eighth of
the CCl3 + Br encounters have been included.51,52 For an
enhancement of the recombination probability at high densities
(i.e., an increase of Rspin(M) f 1), at least two reasons must be
considered. The underlying condition is that the rate constant
of the electronic transition (here, triplet to singlet), kISC, of the
reagents approaching each other not in the singlet ground state
must become fast, compared to relevant translational motion,
e.g., the diffusion process. With the asymptotically isoenergetic
electronic states of our systems at very large distances, there is
a range of moderate separations of the radicals where the
energetic splitting between ground and excited states is really
small and favorable for transitions. In many cases, collisions,
especially with heavier atoms, increase spin-orbit coupling in
the combined system (known as “external heavy atom effect”)
and thus accelerate electronic quenching. The number of bath-
gas collisions, even within the time interval of very small
diffusional displacements, becomes very high at high densities,
which leads to the increasing probability to enter the ground-
state surface in connection with multiple encounters. Increased
spin-orbit coupling should also be considered, with respect to
eventual “internal heavy atom effects” in RC units AMn.
Even without collision-induced electronic quenching, how-
ever, the increase of density alone must lead to a breakdown of
such that the limiting “high-pressure” rate constants of the
ET
ET
energy-transfer (ET) mechanism k and k could be deter-
1,∞
2,∞
mined over a sufficiently wide pressure range. Our results can
be represented by
ET
1,∞
k
) (1.0 ( 0.2) × 10-11(T/300 K)-0.17
(cm3 molecule-1 s-1)
and
ET
2,∞
k
) (2.0 ( 0.2) × 10-11(T/300 K)-0.13
(cm3 molecule-1 s-1)
These values were analyzed in terms of statistical adiabatic
channel/classical trajectory (SACM/CT) theory. An interpreta-
tion of the observed increase in the rate constants between ∼40
bar and the onset of diffusion-limited dynamics was given in
terms of a radical-complex mechanism. Our analysis provides
a consistent description. However, more-quantitative conclusions
must wait until more theoretical information on the potentials
and dynamics of the radical complexes involved is available.
A better understanding of the collision-induced electronic
quenching is also required.
Acknowledgment. Financial support of this work by the
Deutsche Forschungsgemeinschaft (Sonderforschungsbereich
357 “Molekulare Mechanismen Unimolekularer Prozesse”), as
well as helpful discussions with T. Lenzer, V. Ushakov, A.
Maergoiz, M. Teubner, D. Schwarzer, J. Schroeder, and P.
Botschwina, are gratefully acknowledged. K. O. is deeply
indebted to V. Ushakov for generous and invaluable discussions
during this work. K. O. also thanks the Alexander von Humboldt
Foundation for the funding of her work within the “Sofja
Kovalevskaja Program”.
1
the condition of a “spin-statistic” Rspin (1/4 or /8). The strong
decrease of the diffusion rate with density alone is sufficient to
arrive at a point where it is not bigger than kISC. Unfortunately,
a quantitative understanding of this important problem in atom
and radical combinations is still lacking,53,54 and thus usable
predictions or calculations for which to compare are not
available. From our experimental evidence, we currently cannot
confirm the simple, extreme assumption that all changes in
References and Notes
(1) Rabinowitch, E. Trans. Faraday Soc. 1937, 33, 283.
(2) Porter, G.; Smith, J. A. Proc. R. Soc. London A 1961, 261, 28.
(3) Oum, K. W.; Sekiguchi, K.; Luther, K.; Troe, J. Phys. Chem. Chem.
Phys. 2003, 5, 2931.
(4) Hippler, H.; Rahn, R.; Troe, J. J. Chem. Phys. 1990, 93, 6560.
(5) Gao, D. F.; Stockwell, W. R.; Milford, J. B. J. Geophys. Res.,
[Atmos.] 1995, 100, 23153.
Rspin(M) in our systems occur only at much higher densities
than applied here. Contributions of changing Rspin(M) to our
observation cannot be ruled out; however, there is also no direct
experimental evidence for them. Further experimental studies
are planned to clarify the situation on the basis of, for example,
heavy-mass bath-gas influences in selected systems.
(6) Hansen, J. C.; Francisco, J. S. Chem. Phys. Chem. 2002, 3, 833.
(7) Hippler, H.; Luther, K.; Troe, J. Chem. Phys. Lett. 1972, 16, 174.
(8) Hippler, H.; Luther, K.; Troe, J. Ber. Bunsen Phys. Chem. 1973,
77, 1020.
(9) Hippler, H.; Troe, J. Int. J. Chem. Kinet. 1976, 8, 501.
(10) Baer, S.; Hippler, H.; Rahn, R.; Siefke, M.; Seitzinger, N.; Troe, J.
J. Chem. Phys. 1991, 95, 6463.
(11) Stark, H. Ph.D. Thesis, Go¨ttingen University, Go¨ttingen, Germany,
1999.
Conclusions
(12) Luther, K.; Oum, K.; Troe, J. J. Phys. Chem. A 2001, 105, 5535.
(13) Hahn, J.; Luther, K.; Troe, J. Phys. Chem. Chem. Phys. 2000, 2,
5098.
(14) Danis, F.; Caralp, F.; Veyret, B.; Loirat, H.; Lesclaux, R. Int. J.
Chem. Kinet. 1989, 21, 715.
(15) Ellermann, T. Chem. Phys. Lett. 1992, 189, 175.
(16) Sullivan, J. H.; Davidson, N. J. Chem. Phys. 1951, 19, 143.
(17) Amphlett, J. C.; Whittle, E. Trans. Faraday Soc. 1968, 64, 2130.
The combination reactions CCl3 + CCl3 (+ M) f C2Cl6 (+
M) and CCl3 + Br (+ M) f CCl3Br (+ M) (with rate constants
of k1 and k2, respectively) were studied at 250 and 300 K over
the pressure range of 0.01-1000 bar in the bath gases helium,
argon, xenon, N2, CO2, and SF6. The rate constants of reactions
1 and 2 reached a pressure-independent range at ∼1-10 bar,