1774 J. Phys. Chem. A, Vol. 107, No. 11, 2003
Arita and Kajimoto
arise from the viscosity term through the increase in the Stokes
radius due to the strong ion-dipole interaction between the
solute ion and solvent molecules.
Conclusion
The diffusion-controlled recombination rate of 1-(4-methoxy-
phenyl)-2,2-diphenyl cation with Br- has been determined in
SC CF3H. Although the rate constant as a whole decreased with
increasing density as a function of 1/(ꢀη) according to the SES
equation, a severe downward deviation of the rate constant from
the 1/(ꢀη) curve was observed near the critical density where
the clustering is most significant. To our best knowledge, this
is the first unambiguous observation of the clustering effect on
the diffusion-controlled reaction in contrast to the ambiguous
results for the recombination of neutral species. The reason for
this successful observation in ion recombination lies in the
participation of Coulomb attraction in determining the mutual
diffusion of recombining partners. The Coulomb attraction is
severely suppressed when the clustering solvent molecule
enhance the dielectric constant around the ionic species. This
study demonstrated that, between the factors for determining
the diffusion-controlled reactions, the reactant diffusion against
the solvent viscosity suffers no significant disadvantage by
enhanced clustering near the critical density whereas the
diffusion caused by the Coulomb attraction is considerably
suppressed by the enhanced clustering.
Figure 5. Density dependence of the observed rate constant (O) and
the estimated tendency (-) from eq 12.
In the diffusion-controlled recombination of the ionic species
such as the vinyl cation and Br-, the second factor, Coulomb
interaction, should be taken into account. For the conditions
T ) 295 K, rC ) 0.5 nm, and ꢀ e 10, eqs 6-9 can be simplified
as
-ZAZBe2
6πηꢀꢀ0 rA rB
1
1
kbi )
+
(11)
(
)
Acknowledgment. The authors thank Prof. S. Kobayashi
of Kyushu University for his kindly providing the vinyl bromide
sample. This work was partially supported by Japan Science
and Technology Cooperation under the CREST project.
This equation indicates that the recombination rate is propor-
tional to the reciprocal of (ηꢀ). Figure 5 shows the plot of the
measured rate constant as a function of the bulk solvent density
together with the plot according to the prediction by eq 11. The
viscosity data was taken from the literature.23 The recombination
rate constant of the vinyl cation as a whole decreased with
increasing solvent density. The most noticeable feature is the
large downward deviation of the observed recombination rate
from the predicted value near the critical density. Since neutral
species did not show such s-shaped dependence, the density
enhancement or clustering definitely affects the recombination
rate of ionic species in contrast to the neutral species.
References and Notes
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(3) See, e. g., (a) Kajimoto, O.; Futakami, M.; Kobayashi, T.; Yamasaki,
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Ind. Eng. Chem. Res. 1987, 26, 1206-1213. (g) Sun, Y.-P.; Fox, M. A.;
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Koda, S. Chem. Phys. 1999, 242, 241-252.
(4) See, e. g., (a) Supercritical Fluid Technology: Theoretical and
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To interpret the remarkable difference in the clustering effect
between the neutral species and ions, we have to consider how
the above-mentioned two critical factors, viscosity and Coulomb
interaction, are modified and work when the clustering becomes
significant. For the contribution of the viscosity term in ionic
species, the interaction between the ion and the clustering solvent
molecules is probably strong enough to increase the Stokes
radius and hence reduces the rate of the recombination reaction
to some extent. The Coulomb interaction suffers the much more
significant effect by the clustering. The enhancement of
dielectric constant by the clustering causes considerable reduc-
tion of the attraction between the ionic species as apparent from
eq 11. Note that such deduction in Coulomb attraction has
nothing to do with the exchange of the clustering molecules
because only the time-averaged number of clustering molecules
is essential to determine the dielectric constant. Thus, local
density enhancement always weakens the Coulomb attraction
and slows down the rate of the recombination reaction between
the ionic species of opposite charges.
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Phys. Chem. 1993, 97, 5618-5623. (b) Roberts, C. B.; Zhang, J.; Brennecke,
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Roberts, C. B.; Zhang, J.; Brennecke, J. F.; Chateauneuf, J. E. J. Am. Chem.
It becomes apparent that the unambiguous observation of the
clustering effects in diffusion-controlled recombination reaction
can only be possible for ionic species because of the significant
contribution of the enhanced dielectric constant to the Coulomb
interaction. Less significant contribution to the diffusion may