Enhanced cage effects in supercritical fluid solvents. The behavior of diffusive and geminate caged-pairs in supercritical carbon dioxide

Article abstract of DOI:10.1021/ja002800f

The behavior of geminate and diffusive radical caged-pairs arising from the photolysis of dicumyl ketone in conventional and supercritical carbon dioxide (SC-CO₂) solvents has been examined. The results suggest that locally enhanced solvent density about a solute (solvent/solute clustering) can lead to an enhanced cage effect near the critical pressure in supercritical fluid solvents. This enhanced cage effect is similar in magnitude for both diffusive and geminate caged-pairs.

Full text of DOI:10.1021/ja002800f

J. Am. Chem. Soc. 2001, 123, 5703-5709
5703
Enhanced Cage Effects in Supercritical Fluid Solvents. The Behavior
of Diffusive and Geminate Caged-Pairs in Supercritical Carbon
Dioxide
James M. Tanko* and Ryszard Pacut‡
Contribution from the Department of Chemistry, Virginia Polytechnic Institute and State UniVersity,
Blacksburg, Virginia 24061-0212
ReceiVed July 28, 2000
Abstract: The behavior of geminate and diffusive radical caged-pairs arising from the photolysis of dicumyl
ketone in conventional and supercritical carbon dioxide (SC-CO2) solvents has been examined. The results
suggest that locally enhanced solvent density about a solute (solvent/solute clustering) can lead to an enhanced
cage effect near the critical pressure in supercritical fluid solvents. This enhanced cage effect is similar in
magnitude for both diffusive and geminate caged-pairs.
There is a need to reduce or eliminate toxic chemical waste
and/or byproducts which arise in the course of chemical
synthesis and manufacture.1 One way to accomplish this is to
replace toxic, environmentally threatening solvents utilized in
many chemical processes with nontoxic, “environmentally-
benign” alternatives. Supercritical carbon dioxide (SC-CO2)
has emerged as a suitable, “environmentally benign” alternative
for a variety of solvents.2,3 The supercritical state of CO2 is
easily attained (Tc ) 31 °C, Pc ) 74 bar),4 and being nontoxic,
CO2 is a viable alternative to traditional solvents which are either
carcinogenic (e.g., benzene) or damaging to the environment
(e.g., CFC’s, CCl4).
For these reasons, there is considerable interest in the physical
aspects of chemistry conducted in supercritical fluid (SCF)
solvents. In addition to the considerations discussed above, there
are several advantages associated with the use of supercritical
fluids as solvents for chemical reactions from the standpoint of
reactivity and selectivity. Changes in rate arising from the direct
effect of pressure (and temperature) are governed by transition
state theory, and pertain to reactions in both SCF medium and
conventional solvents. However, what is special about SCF
solvents is that important solvent parameters such as dielectric
constant, viscosity, and solubility parameter vary dramatically
with temperature and pressure,5,6 thereby providing a unique
element of control over the kinetics of a chemical process.7
Scheme 1
Solvent viscosity is one example of a manipulable parameter
that can affect the outcome of a chemical process. For example,
consider two highly reactive species A and B generated
simultaneously in a solvent cage as a geminate caged-pair from
a common precursor molecule M (Scheme 1). Further, suppose
that reaction within the (A/B) caged-pair gives rise to a unique
product P and the rate constant for this process is ko; counter-
diffusion (k-diff) yields free A and B, which give rise to different
products. Because the magnitude of k-diff is related to solvent
viscosity, increased viscosity will favor production of product
P (k-diff < ko), while at lower viscosity, products arising from
individual reactions of free A and free B will be formed.
According to the Noyes model, the ratio of products arising
from the ko and k-diff pathways varies linearly with the inverse
of viscosity (1/η.)8
Rather than being formed from a common precursor, a
diffusiVe caged-pair is produced by diffusion of free A and free
B together (with diffusion-controlled rate constant kdiff), i.e.,
Afree + Bfree f (A/B)cage. Thus, while a geminate caged-pair
may have a history associated with it (i.e., the orientation of A
and B with respect to each other and the solvation shell may
be similar to the precursor), the orientation within a diffusive
caged-pair will be random. In accordance with theory, the
diffusion-controlled rate constant kdiff is expected to vary linearly
with inverse viscosity.9
‡ Current address: Department of Chemistry, Agricultural University,
Wroclaw, Poland.
(1) Benign by Design. AlternatiVe Synthetic Design for Pollution PreVen-
tion; Anastas, P. T., Farris, C. A., Eds.; American Chemical Society:
Washington, DC, 1994; Vol. 577.
(2) Eckert, C. A.; Knutson, B. L.; Debenedetti, P. G. Nature 1996, 383,
313-318.
(3) Chemical Synthesis Using Supercritical Fluids; Jessop, P. G., Leitner,
W., Eds.; Wiley-VCH: Weinheim, 1999.
(4) McHugh, M.; Krukonis, V. Supercritical Fluid Extraction. Principles
and Practice; Butterworth: Boston, 1986.
(5) Supercritical Fluid Science and Technology; Johnston, K. P., Pen-
ninger, J. M. L., Eds.; American Chemical Society: Washington, DC, 1989;
Vol. 406.
(6) Supercritical Fluid Technology. ReViews in Modern Theory and
Applications; Bruno, T. J., Ely, J. F., Eds.; CRC Press: Boca Raton, 1991.
(7) Savage, P. E.; Gopalan, S.; Mizan, T. I.; Martino, C. J.; Brock, E. E.
AIChE J. 1995, 41, 1723-1778.
The viscosity of a supercritical fluid varies dramatically with
pressure and temperature. For CO2 at 37 °C, a change in pressure
(8) Koenig, T.; Fischer, H. In Free Radicals; Kochi, J. K., Ed.; Wiley:
New York, 1973; Vol. 1, pp 157-189.
(9) Tanko, J. M.; Suleman, N. K. In Energetics of Organic Free Radicals,
4th ed.; Simo˜es, J. A. M., Greenberg, A., Liebman, J. F., Eds.; Blackie
Academic & Professional: New York, 1996; pp 224-293.
10.1021/ja002800f CCC: $20.00 © 2001 American Chemical Society
Published on Web 05/25/2001

5704 J. Am. Chem. Soc., Vol. 123, No. 24, 2001
Tanko and Pacut
from just above the critical pressure (74 bar) to 300 bar results
in a change in viscosity from 0.02 to 0.12 cP.10 Thus, for
reactions which are sensitive to solvent viscosity, a relatively
small variation in pressure may significantly influence the
outcome of the reaction. However, because of the unique nature
of supercritical fluids, there are yet additional factors which
may lead to deviations in rate/viscosity correlations, specifically
the possibility that cage lifetimes may be enhanced at pressures
near the critical point.
the photo-Fries rearrangement of naphthyl acetate in SC-CO2.35
Near the critical pressure, an enhanced cage effect was observed
that was attributed to solvent/solute clustering. In contrast, for
the free radical chlorination of alkanes, there was no indication
of an enhanced “chlorine atom cage effect” near the critical
pressure in SC-CO2 solvent.37,38 Moreover, the magnitude of
the cage effect observed in SC-CO2 at all pressures examined
was within what is anticipated based upon extrapolations from
conventional solvents.
Assuming that enhanced cage effects near the critical point
in supercritical fluids are the consequence of clustering and not
experimental artifacts, then the important issue to address is
why are they observed in some cases, but not in others. There
are two likely explanations: The magnitude of the effect may
be related to the strength of the interaction between the solute-
(s) and solvent (i.e., specific functional groups on A or B may
interact more strongly with solvent). In the case of geminate
caged-pairs, interactions between the precursor molecule M and
the solvent may lead to formation of a cluster into which the
A/B pair is born.
It has been suggested that cage lifetimes may be enhanced
near the critical point because of an increase in the local solvent
density around the solute.11,12 This phenomenon, known as
“solvent/solute clustering”, is well-documented, particularly in
the spectroscopic literature.13-23 In addition, there is good
evidence to suggest that such clustering may affect the rates of
chemical phenomena.17,18,24-30 It is thus reasonable to suppose
that increased local solvent density (and implicitly, increased
local viscosity) about Afree, Bfree, or (A/B)cage would diminish
kdiff and/or k-diff to a greater extent than expected based upon
bulk solvent properties.
It is possible that enhanced cage effects arising from solvent/
solute cluster formation may be especially important in systems
which possess aromatic rings. The local solvation behavior of
aromatic compounds (specifically naphthalene,39 benzene, and
toluene)40 in SC-CO2 has been examined theoretically, and has
been found to form ordered structures with CO2. Hence it is
possible that because of the naphthalene ring, solvent/solute
clustering led to the enhanced cage effect observed in the
photolysis of naphthyl acetate. For the chlorine atom cage effect
study, because there was no specific functional group for CO2
to interact strongly with, there was little or no local density
enhancement near the critical pressure. Consequently, an
enhanced cage effect was not observed.
To test these hypotheses, cage effects were examined in a
system (a) that possesses aromatic rings and (b) that generates
both a diffusive and geminate caged-pair (each of which give
rise to unique products). In this chemistry, a geminate caged-
pair is formed by photolysis of a ketone: RCOR f (R•/•COR).
A diffusive caged-pair is formed by the self-reaction of R•: 2R•
f (R• •R).
Alkyl radical pairs react either via dimerization (kdim) or
disproportionation (kdisp) pathways: 2R• f R-R and/or R-H
+ R-H. Fischer demonstrated that for diffusiVe tert-butyl radical
caged-pairs in a series of n-alkane solvents, the rate constant
ratio (kdim/kdisp) varies as a function of solvent viscosity.41,42
Thus, the rate constant ratio kdim/kdisp is a sensitive probe for
cage effects involving a diffusive caged-pair. Cumyl radicals
self-react at a diffusion-controlled rate constant (2kT ) 1.6 ×
1010 M-1 s-1),43 yielding cumene and R-methylstyrene (dis-
There are a number of seemingly contradictory reports in the
literature pertaining to enhanced cage lifetimes near the critical
point in SCF solvents.31-38 For example, Andrew et al. examined
(10) Stephan, K.; Lucas, K. Viscosity of Dense Fluids; Plenum: New
York, 1979.
(11) Brennecke, J. F. In Supercritical Fluid Engineering: Fundamentals
and Applications; Erdogan, K., Brennecke, J. F., Eds.; American Chemical
Society: Washington, DC, 1993; pp 201-219.
(12) Brennecke, J. F.; Chateauneuf, J. E. Chem. ReV. 1999, 99, 433-
452.
(13) Johnston, K. P.; McFann, G. J.; Peck, D. G.; Lemert, R. M. Fluid
Phase Equilib. 1989, 52, 337-346.
(14) Kim, S.; Johnston, K. P. Ind. Eng. Chem. Res. 1987, 26, 1206-
1213.
(15) Sun, Y.-P.; Fox, M. A.; Johnston, K. P. J. Am. Chem. Soc. 1992,
114, 1187-1194.
(16) Sun, Y.-P.; Fox, M. A. J. Am. Chem. Soc. 1993, 115, 747-750.
(17) Rhodes, T. A.; Fox, M. A. J. Phys. Chem. 1996, 100, 17931-17939.
(18) Kajimoto, O.; Futakami, M.; Kobayashi, T.; Yamasaki, K. J. Phys.
Chem. 1988, 92, 1347-1352.
(19) Brennecke, J. F.; Tomasko, D. L.; Peshkin, J.; Eckert, C. A. Ind.
Eng. Chem. Res. 1990, 29, 1682-1690.
(20) Betts, T. A.; Zagrobelny, J.; Bright, F. V. J. Am. Chem. Soc. 1992,
114, 8163-8171.
(21) Sun, Y.-P.; Bunker, C. E.; Hamilton, N. B. Chem. Phys. Lett. 1993,
210, 111-117.
(22) Sun, Y.-P.; Bunker, C. E. Ber. Bunsen-Ges. Phys. Chem. 1995, 99,
976-984.
(23) Urdahl, R. S.; Rector, K. D.; Myers, D. J.; Davis, P. H.; Fayer, M.
D. J. Chem. Phys. 1996, 105, 8973-8976.
(24) Gehrke, C.; Schroeder, J.; Schwarzer, D.; Troe, J.; Voss, F. J. Chem.
Phys. 1990, 92, 4805-4816.
(25) Randolph, T. W.; Carlier, C. J. Phys. Chem. 1992, 96, 5146-5151.
(26) Ganapathy, S.; Carlier, C.; Randolph, T. W.; O’Brien, J. A. Ind.
Eng. Chem. Res. 1996, 35, 19-27.
(27) deGrazia, J. L.; Randolph, T. W.; O’Brien, J. A. J. Phys. Chem.
1998, 102, 1674-1681.
proportionation) and bicumyl (dimerization), with kdisp/kdim
)
0.05.8 Accordingly, this paper describes the behavior of geminate
and diffusive radical pairs, generated via photolysis of dicumyl
ketone, in supercritical solvent as a probe for enhanced cage
effects near the critical point.
(28) Anderton, R. M.; Kauffman, J. F. J. Phys. Chem. 1995, 99, 13759-
13762.
(29) Heitz, M. P.; Bright, F. V. J. Phys. Chem. 1996, 100, 6889-6897.
(30) Batchelor, S. N. J. Phys. Chem. B 1998, 102, 615-619.
(31) O’Shea, K. E.; Combes, J. R.; Fox, M. A.; Johnston, K. P.
Photochem. Photobiol. 1991, 54, 571-576.
(32) Combes, J. R.; Johnston, K. P.; O’Shea, K. E.; Fox, M. A. In
Supercritical Fluid Technology: Theoretical and Applied Approaches in
Analytical Chemistry; Bright, F. V., McNally, M. E. P., Eds.; American
Chemical Society: Washington, DC, 1992; Vol. 488, pp 31-47.
(33) Roberts, C. B.; Zhang, J.; Brennecke, J. F.; Chateauneuf, J. E. J.
Phys. Chem. 1993, 97, 5618-5623.
(37) Tanko, J. M.; Suleman, N. K.; Fletcher, B. J. Am. Chem. Soc. 1996,
118, 11958-11959.
(38) Fletcher, B.; Suleman, N. K.; Tanko, J. M. J. Am. Chem. Soc. 1998,
120, 11839-11844.
(39) Koga, K.; Tanaka, H.; Zeng, X. C. J. Phys. Chem. 1996, 100,
16711-16719.
(34) Materny, A.; Lienau, C.; Zewail, A. H. J. Phys. Chem. 1996, 100,
18650-18665.
(40) Ferreira Coelho, L. A.; Marchut, A.; de Oliveira, J. V.; Balbuena,
P. B. Ind. Eng. Chem. Res. 2000, 39, 227-235.
(41) Schuh, H.; Fischer, H. Int. J. Chem. Kinet. 1976, 8, 341-356.
(42) Schuh, H.-H.; Fischer, H. HelV. Chim. Acta 1978, 61, 2463-2481.
(43) Ingold, K. U. In Free Radicals; Kochi, J. K., Ed.; Wiley: New
York, 1973; Vol. I, pp 37-112.
(35) Andrew, D.; Des Islet, B. T.; Margaritis, A.; Weedon, A. C. J. Am.
Chem. Soc. 1995, 117, 6132-6133.
(36) Batchelor, S. N.; Henningsen, B.; Fischer, H. J. Phys. Chem. A 1997,
101, 2969-2972.

Enhanced Cage Effects in Supercritical Fluid SolVents
J. Am. Chem. Soc., Vol. 123, No. 24, 2001 5705
Scheme 2
Table 1. Photolysis of Dicumyl Ketone in Conventional Solvents
at 50 °C
Table 2. Photolysis of Dicumyl Ketone in Supercritical Carbon
Dioxide at 50 °C
solvent η (cP) 9 (µmol) 8 (µmol) 4 (µmol) kdim/kdisp kesc/kH
pressure
(psi)
η (cP) 9 (µmol) 8 (µmol) 4 (µmol) kdim/kdisp kesc/kH
hexane
heptane 0.30
octane
CCl4
C2F2Cl4 0.91
0.24
9.96
11.2
8.30
2.88
3.33
0.375
0.5
0.509
0.193
0.212
0.177
0.291
0.236
0.154
0.129
26.6
22.4
16.3
14.9
15.7
58.4
40.2
37.3
20.0
27.5
1110 0.0205
1125 0.0207
1130 0.0208
1134 0.0208
1230 0.0225
1305 0.0241
1390 0.0263
1465 0.0305
1473 0.0310
1560 0.0358
1600 0.0378
1728 0.0433
1756 0.0444
2134 0.0557
2644 0.0656
2740 0.0670
3946 0.0814
4005 0.0820
6194 0.101
7456 0.110
7936 0.114
8534 0.118
5.32
4.39
5.63
4.02
8.25
7.01
6.04
4.96
3.00
3.64
9.18
6.04
7.95
6.03
6.41
5.53
6.29
4.33
9.89
6.34
4.77
5.27
0.282
0.240
0.314
0.230
0.378
0.286
0.235
0.163
0.082
0.106
0.295
0.192
0.255
0.188
0.208
0.174
0.227
0.159
0.418
0.297
0.247
0.307
0.237
0.211
0.174
0.174
0.324
0.271
0.136
0.071
0.029
0.030
0.120
0.066
0.070
0.059
0.069
0.063
0.086
0.061
0.165
0.121
0.124
0.144
18.9
18.3
17.9
17.5
21.8
24.5
25.7
30.5
36.6
34.4
31.1
31.5
31.2
32.1
30.8
31.8
27.7
27.2
23.7
21.4
19.3
17.1
23.6
21.9
34.2
24.4
26.6
26.9
46.2
72.2
106
125
79.0
94.4
117
106
95.8
90.5
75.8
73.5
62.5
54.9
40.5
38.7
0.38
0.71
Results and Discussion
Solubility of Dicumyl Ketone in SC-CO2. Because SC-
CO2 is nonpolar, polar compounds tend not to be very soluble
(especially at lower pressures where the dielectric constant and
Hildebrand solubility parameter are low). To ensure that the
results of these experiments would not contaminated by
unanticipated and unnoticed phase behavior, it was deemed
critical to examine the solubility behavior of dicumyl ketone in
SC-CO2 at the same concentration that would be used in this
study, and especially, at pressures nearing the critical pressure.
Solubility was checked using a view cell. The starting ketone
was dissolved in a tiny quantity of diethyl ether, and the resulting
solution was placed on one of the sapphire windows of the view
cell to create a film. The view cell was assembled, the system
was pressurized with CO2 and equilibrated at the desired
temperature and pressure, and the dissolution of the starting
material was observed visually. Without agitation, it was found
that the starting material was fully dissolved in less than 25
min.
Reaction Mechanism. Photolysis of dicumyl ketone (0.01
M in either conventional solvents or SC-CO2) yields the
products depicted in Scheme 2 (compounds 3, 4, 8, and 9). The
results are summarized in Tables 1 and 2. Reactions were run
to low (<8%) conversion to avoid further reaction of the primary
reaction products. In addition to the expected products arising
from dimerization and disproportionation of the cumyl radical
(i.e., 9 from dimerization; 3 and 8 from disproportionation),
significant yields of aldehyde 4 were produced.
rate constant for decarbonylation is 2 × 108 s-1 44,45
)
and it is
unlikely that the aldehyde is formed by reaction of free acyl
radical 6 because (a) there is not a good hydrogen atom donor
present and (b) reactions are run to low percent conversion
(meaning that the reaction products are not formed in sufficiently
high yields to serve as H-atom donors). The fact that the yield
of aldehyde varies as a function of viscosity (vide infra) strongly
supports the suspicion that aldehyde 4 is formed via a cage
process.
A somewhat simplified mechanism for decomposition of 1
is summarized in Scheme 2. Norrish Type I photocleavage yields
a geminate acyl radical/cumyl radical caged-pair (2), which can
either diffuse apart (kesc, inevitably leading to two free cumyl
(44) Turro, N. J.; Gould, I. R.; Baretz, B. H. J. Phys. Chem. 1983, 87,
Aldehyde 4 is formed as the result of hydrogen abstraction
by an intermediate acyl radical produced by the Norrish I
photocleavage of 1. This acyl radical is very short-lived (the
531-532.
(45) Gould, I. R.; Baretz, B. H.; Turro, N. J. J. Phys. Chem. 1987, 91,
925-929.

5706 J. Am. Chem. Soc., Vol. 123, No. 24, 2001
Tanko and Pacut
Scheme 3
Figure 1. Partitioning of geminate caged-pair 2: kesc/kH vs 1/η in
conventional solvents and SC-CO2.
radicals) or undergo in-cage reaction (kH) yielding R-methyl-
styrene (3) and aldehyde 4. Bimolecular reaction of free cumyl
radicals leads to diffusive caged-pair 7, giving rise to dispro-
portionation and dimerization products, 3 + 8 and 9, respec-
tively. Thus, this system is especially interesting in that it allows
the behavior of two caged radical pairs to be monitored: the
geminate acyl radical/cumyl radical pair (2) and a diffusiVe
cumyl radical pair (7).
The mechanism for the photolysis of 1 is actually a bit more
complicated than that depicted in Scheme 2. In addition to the
benzylic (R) carbon, radicals can couple with cumyl radical at
the ortho and para positions yielding semibenzenes. The
semibenzenes are known to decompose via a free radical,
addition/elimination pathway (Scheme 3).46
Thus, in addition to dimer 9, cumyl radical caged-pair 7 also
leads to small amounts of R-ortho and R-para coupling products,
10a and 11a, respectively. In our runs, these compounds were
detected by GC/MS, formed in quantities comparable to earlier
reports,46 and not included in the calculation of kdim/kdisp
.
Similarly, for geminate acyl radical/cumyl radical caged-pair
2, CIDNP studies suggest that caged-pair 2 also combines
regenerating 1 and also forming R-p-semibenzene 11b.47 It is
thus conceivable that small amounts of dimer 9 may actually
result from geminate acyl radical/cumyl radical caged-pair 2
via cumyl radical addition to 11b. However, it is expected that
this problem is minor because (a) these reactions were carried
out in dilute solution and to low percent conversion and (b) the
gem-dimethyl groups on 11b should retard the rate of addition
(steric effects).
Behavior of the Geminate Acyl Radical/Cumyl Radical
Caged-Pair 2. For 2, the rate constant ratio kesc/kH is propor-
tional to the yield of products formed in-cage relative to those
formed via reaction of free cumyl radicals (kesc/kH ) ([8] +
[9])/[4]). Because R-methylstyrene (3) is formed both by reaction
of geminate caged-pair 2 and by the disproportionation of cumyl
radicals, this product is uninformative in the determination of
Figure 2. Partitioning of geminate caged-pair 2 in SC-CO2: kesc/kH
vs pressure.
pertaining to the mass, radius, and translational energy of the
components of the caged-pair, and b is the diffusional radius.8
Ro - 2b Ro AT + RAE 1
ATAE 1
2
F )
+
+
(1)
[
]
( )
( )
2b
2b
R
η
R
η
Equation 1 predicts that F will vary linearly with 1/η, except
perhaps at low viscosities where upward curvature may be
observed if the 1/η2 becomes important. Cage efficiency
represents the fraction of reaction that occurs within the cage,
and applied to Scheme 2 is equal to kH/(kH + kesc); F ) kesc/kH.
As anticipated based upon the Noyes model, in conven-
tional solvents kesc/kH varies linearly with inverse viscosity (1/
η, Figure 1).
kesc/kH (or kdisp/kdim). The trend in kesc/kH observed in conven-
In SC-CO2 solvent, the value of kesc/kH was examined as a
function of pressure at constant temperature (50 °C), and the
rate constant ratio kesc/kH was found to be pressure dependent.
At high pressures (>1800 psi), kesc/kH decreases smoothly with
increasing pressure (Figure 2). This observation makes sense
because the viscosity increases with increasing pressure (dashed
line in Figure 2), and thus, the rate constant for diffusion of the
species out of the cage (kesc) decreases. However, a significant
divergence is noted at lower pressures. At pressures less than
ca. 1800 psi, the rate constant ratio kesc/kH begins to decrease
with decreasing pressure (reaching values similar to that
observed at higher bulk viscosities).
tional solvents (Table 1) supports the supposition that aldehyde
4 is formed via a cage process...higher viscosity favors aldehyde
formation (in-cage); lower viscosity favors products arising from
the free cumyl radical.
The behavior of geminate caged-pairs is typically quantified
in terms of the Noyes model. Koenig and Fischer8 derived a
general expression based upon the Noyes model (eq 1), where
F ) (1/cage efficiency) - 1, Ro is the separation between the
two reactive components of the caged-pair, R the probability
(per collision) that the components will react, and η the viscosity
of the solvent. AE and AT are constants which incorporate terms
Ignoring the deviation observed near the critical point for
the moment, the magnitude of the cage effect in SC-CO2 is
greater than expected based upon extrapolations from conven-
(46) Skinner, K. J.; Hochster, H. S.; McBride, J. M. J. Am. Chem. Soc.
1974, 96, 4301-4306.
(47) Hany, R.; Fischer, H. Chem. Phys. 1993, 172, 131-46.

Enhanced Cage Effects in Supercritical Fluid SolVents
J. Am. Chem. Soc., Vol. 123, No. 24, 2001 5707
Figure 3. Partitioning of diffusive caged-pair 7: kdim/kdisp vs 1/η in
conventional solvents and SC-CO2.
Scheme 4
Figure 4. Partitioning of diffusive caged-pair 7 in SC-CO2: kdim
/
kdisp vs pressure.
viscosity (as anticipated), but are about 2-3 times less than
predicted on the basis of behavior in conventional solvents, and
(b) divergent behavior is observed near the critical pressure (i.e.,
the rate constant ratios approach values observed similar to those
observed at higher bulk viscosities).
An understanding of why the observed cage effects are
generally larger in SC-CO2 than anticipated can be achieved
by considering the relationship between the diffusion coefficient
of a solute, and viscosity. According to the Stokes-Einstein
equation, the diffusion coefficient (D) and viscosity (η) are
inversely related (eq 2, where k is the Boltzmann constant, T is
the temperature in Kelvin, and r is the radius of the solute).9
On the basis of eq 2, a plot of D vs 1/η is expected to be linear.
tional solvents. This point is illustrated in Figure 1 which plots
k
esc/kH vs 1/η for both conventional and SC-CO2 solvents
(excluding data points near the critical pressure in SC-CO2).
In SC-CO2, although kesc/kH varies linearly with 1/η as
expected, the magnitude of the rate constant ratio is about half
that expected based upon the results in conventional solvents.
Behavior of the Diffusive Cumyl Radical Caged-Pair 7.
For 7, the rate constant ratio kdim/kdisp is directly related to the
yields of disproportionation vs dimerization products (kdim/kdisp
) [9]/[8]). In conventional solvents, kdim/kdisp is found to
decrease with increasing viscosity (Table 1), and kdim/kdisp varies
linearly with inverse viscosity (Figure 3). These observations
are consistent with the behavior of diffusive tert-butyl radical
caged-pairs in conventional solvents as reported by Fischer, who
also found dimerization decreased with increasing viscosity.42
The reason that kdim/kdisp varies with viscosity is because for
dimerization to occur, the combining radicals must line up along
the principal axis and reorientation (rotation) of the radicals in
the caged-pair may be required (Scheme 4). As viscosity
increases, this rotation is hampered (kdim decreases with increas-
ing viscosity). In contrast, the geometric requirements for
disproportionation are less stringent; kdisp is less sensitive to
viscosity.42
kT
6πrη
D )
(2)
However, for SC-CO2, the Stokes-Einstein equation, as well
as other empirical relationships predicting an inverse relationship
between D and η, tends to overestimate the diffusion coefficient
of aromatic compounds (by a factor of 1.2-1.5 for benzene
and 1.3-2.2 for naphthalene).48,49 Of course the diffusion
coefficient in the Stokes-Einstein equation is in reference to
translational diffusion, whereas the cage effects discussed herein
are related to rotational diffusion (in the case of diffusive caged-
pair 7) or separation (in the case of geminate caged-pair 2). It
is reasonable to suppose that similar (but not necessarily
identical) considerations pertain.
Both kesc/kH and kdim/kdisp deviate as the critical pressure is
approached. These observations suggest that movement (trans-
lational and rotational) of the caged-pairs is impeded, and
solvent/solute clustering emerges as a plausible explanation for
these phenomena. (Heitz and Bright recently probed the extent
of local density enhancement in the critical region in SC-CO2,
SC-CHF3, and SC-CH3CH3 by examining the rotational reori-
entation kinetics of N,N′-bis(2,5-di-tert-butylphenyl)-3,4,9,10-
perylenecarboxodiimide (BTBP). Near the critical density,
rotational times were longer than predicted on the basis of bulk
solvent properties because of solvent/solute clustering.29 Analo-
gous results have been reported for other systems.)27,28 Thus, it
is reasonable to conclude that solvent/solute clustering has a
In SC-CO2, diffusive cage-pair 7 behaves as expected at
pressures >1800 psi:
kdim/kdisp decreases with increasing
pressure (increasing viscosity, Figure 4). Excluding data at
pressures <1800 psi, a plot of kdim/kdisp vs 1/η (Figure 3) is
linear, but the magnitude of kdim/kdisp in SC-CO2 is about half
that expected based upon extrapolations from conventional
solvents. At lower pressures (<1800 psi), anomalous behavior
is observed: kdim/kdisp decreases with decreasing pressure; near
the critical pressure, the observed kdim/kdisp values are similar
to those observed at higher viscosities (Figure 4).
Cage Effects in SC-CO2 vs Conventional Solvents. Pho-
tolysis of dicumyl ketone in both conventional and SC-CO2
solvents yields unique products which arise from two discrete
radical-radical caged-pairs. Geminate caged-pair 2 partitions
between two pathways, cage-escape and hydrogen abstraction
(kesc/kH); diffusive cumyl radical caged-pair 7 undergoes dimer-
ization and disproportionation (kdim/kdisp). In SC-CO2, as
measured by the variation in both kesc/kH and kdim/kdisp with
pressure, (a) the rate constant ratios vary linearly with inverse
(48) Debenedetti, P. G.; Reid, R. C. AIChE J. 1986, 32, 2034-2046.
(49) Clifford, A. A.; Coleby, S. E. Proc. R. Soc. London A 1991, 433,
63-79.

5708 J. Am. Chem. Soc., Vol. 123, No. 24, 2001
Tanko and Pacut
similar effect on the behavior of diffusive caged-pair 7 (and
kdim/kdisp) near the critical pressure.
Although these results are consistent with the notion that the
local viscosity is higher than in the bulk, it does not necessarily
hold that the rate constant ratios are a measure of local viscosity,
or that the term “local viscosity” has any meaning in this context.
The structure of these clusters (if they even haVe a defined
structure) is unknown, and it is possible that translational and
rotational motion is not random (e.g., does motion occur within
a cluster, or does the cluster behave as a single entity?). Thus,
although the Noyes model provides a useful quantitative
treatment of cage effects in terms of a macroscopic solvent
property (i.e., viscosity), it would be unwise to overextend this
theory to describe the microscopic behavior of clusters.
Nature of the Interaction between CO2 and the Cumyl
Radical. The nature of the intermolecular interaction between
CO2 and aromatic molecules was examined theoretically in order
to better understand the nature of solvent/solute clusters in SC-
CO2 solvent. Using density functional theory (DFT), it was
found that for the interaction of benzene with CO2, the binding
energies were 0.40, 1.12, 1.35, and 2.87 kcal/mol for the addition
of one, two, three, and four CO2’s, respectively.40 For PhH +
CO2, the structure of the complex is one in which the CO2
molecule lies approximately 3.6 Å above the plane of aromatic
ring, with one of the C-O bonds nearly lined up with a C-H
bond of benzene (e.g., 12). As more CO2’s are added, the new
molecules build upon this general structure, maximizing the most
favorable interactions.40
Figure 5. Structure of cumyl radical/CO2 complexes.
involves polarization of one of the CdO bonds of CO2 by the
aromatic ring, but that there is no significant amount of spin
and/or charge-transfer involved. The fact that an enhanced cage
effect is observed both for diffusive caged-pair 7 and geminate
caged-pair 2 and is similar in magnitude suggests that this
phenomenon is not restricted to geminate caged-pairs which are
“born” into a cluster arising from interactions between the
precursor molecule (dicumyl ketone in this instance) and CO2
solvent.
Utilizing density functional theory implemented through PC
Spartan Pro (Becke-Perdew BP86 functional and DN** full
polarization basis sets),50 the interaction between CO2 and a
cumyl radical was examined. Because of the lower symmetry
of the cumyl radical compared to benzene, a larger set of
structures was considered. Of these, only two low-energy
structures were found, both of which place the CO2 about 3.6-
3.7 Å above the aromatic ring in a manner similar to the PhH/
CO2 complex, and with binding energies of 0.24 and 0.87 kcal/
mol (Figure 5a). For both of these structures, in the CO2 portion,
there is a shift of electon density toward the outer oxygen, but
no net transfer of electron density from the aromatic ring to the
CO2 (i.e., these are not donor/acceptor complexes). In addition,
there is no transfer of spin density from the cumyl radical to
CO2. As the spin density isosurface for this system reveals
(Figure 5b), the CO2 molecule prefers to associate with the
carbons at which the spin density is the smallest.
Experimental Section
General Considerations. Gas chromatographic analyses were
performed on a Hewlett-Packard 5890A instrument equipped with FID
detection and HP 3393A reporting integrator. Analyses were conducted
using either an Alltech SE-30 or SE-54 capillary column (30 m × 0.25
mm ID × 0.25 µm). Products were identified by comparison of retention
time with that of an authentic sample and by GC/MS. Product yields
were quantitated vs a measured internal standard and appropriate GLC
correction factors. All gas chromatographic analyses were performed
in triplicate.
Summary and Conclusions
Materials. Hexane, heptane, octane (Aldrich), CCl4 (JTBaker), and
CFCl2CFCl2 (PCR Inc.) were used as received. SFC-Grade carbon
dioxide was obtained from Scott Specialty Gases. Dicumyl ketone was
prepared according to literature procedures.51
Reactions in SC-CO2 Solvent. The details regarding the apparatus
for reactions conducted in supercritical carbon dioxide have been
previously reported.52 Briefly, the reactor is constructed of Hastelloy
C-276, and is equipped with a sapphire window (for irradiation) and a
This study lends support to the notion that locally enhanced
solvent density about a solute (solvent/solute clustering) can
result in an enhanced cage effect in supercritical fluid solvents.
The degree of this enhancement depends on the magnitude of
the interaction between the solvent and specific functional
groups on the solute, in this case, SC-CO2 and the aromatic
ring of the cumyl radical. DFT calculations suggest that the
nature of the interaction between CO2 and cumyl radical
(51) Dyllick-Brenzinger, R. A.; Patel, V.; Rampersad, M. B.; Stothers,
J. B.; Thomas, S. E. Can. J. Chem. 1990, 68, 1106-1114.
(52) Tanko, J. M.; Blackert, J. F.; Sadeghipour, M. In Benign by Design.
Alternate Synthetic Design for Pollution PreVention; Anastas, P. T., Farris,
C. A., Eds.; American Chemical Society: Washington, DC, 1994; Vol. 577,
pp 98-113.
(50) Hehre, W. J.; Yu, J.; Klunzinger, P. E.; Lou, L. A Brief Guide to
Molecular Mechanics and Quantum Chemical Calculations; Wavefunction,
Inc.: Irvine, 1998.

Enhanced Cage Effects in Supercritical Fluid SolVents
J. Am. Chem. Soc., Vol. 123, No. 24, 2001 5709
magnetic stir bar. In a typical experiment, 45.2 mg (169 µmol) of
dicumyl ketone (ca. 0.01 M in SC-CO2) was placed in a 1 mL ampule,
degassed 5× (freeze-pump-thaw), and sealed. The ampule was
introduced into the high-pressure reactor (50 °C) with magnetic stirring.
The system was closed and purged with argon followed by CO2 (30
min each). The system was pressurized with CO2 (causing the ampule
to rupture) and the reaction mixture was stirred overnight.
The reaction mixture was irradiated with a 150 W xenon arc lamp;
the reaction time was adjusted such that the percent conversion was
approximately 3-8%. After completion, the system was depressurized
by bubbling the contents of the reactor through 12 mL of ethyl acetate
at 0 °C. The reactor was opened and washed thoroughly with ethyl
acetate. These fractions were combined and an internal standard
(diphenylmethane) was added and analyzed by gas chromatography.
Reactions in Conventional Solvents. Dicumyl ketone (45.2 mg,
169 µmol) and the desired solvent were placed in a ca. 35 mL Pyrex
pressure tube; the concentration of dicumyl ketone was 0.01 M. The
reaction mixture was degassed 3-4× by the freeze-pump-thaw
method and irradiated at 50 °C with a 150 W xenon arc lamp. After
illumination, the pressure tube was cooled to room temperature, an
internal standard was added, and the reaction mixture was analyzed
by gas chromatography.
Acknowledgment. Financial support from the National
Science Foundation (CHE-9524986) is acknowledged and
appreciated.
JA002800F