Supercritical fluid tuning of reactions rates: The cis-trans isomerization of 4-4′-disubstituted azobenzenes

Article abstract of DOI:10.1021/jp981634j

Remarkable tuning of reaction rates has been achieved for the isomerization of several dye molecules in supercritical fluid solvents using both small pressure changes and small additions of cosolvents. Rates of the thermal cis-trans relaxation were measured spectroscopically following irradiation for three dyes in supercritical carbon dioxide and ethane, pure and with several polar and protic cosolvents. The results are explained in terms of local density and composition enhancements, as well as by a change of mechanism due to strong hydrogen bonding. This study demonstrates the versatility of supercritical fluid solvents both to examine reaction mechanisms and as a means to tune rates.

Full text of DOI:10.1021/jp981634j

J. Phys. Chem. A 1998, 102, 7609-7617
7609
Supercritical Fluid Tuning of Reactions Rates: the Cis-Trans Isomerization of
4-4′-Disubstituted Azobenzenes
Angela K. Dillow,† James S. Brown, Charles L. Liotta, and Charles A. Eckert*
Schools of Chemical Engineering and Chemistry and Specialty Separations Center, Georgia Institute of
Technology, Atlanta, Georgia 30332-0100
ReceiVed: March 25, 1998; In Final Form: June 26, 1998
Remarkable tuning of reaction rates has been achieved for the isomerization of several dye molecules in
supercritical fluid solvents using both small pressure changes and small additions of cosolvents. Rates of the
thermal cis-trans relaxation were measured spectroscopically following irradiation for three dyes in supercritical
carbon dioxide and ethane, pure and with several polar and protic cosolvents. The results are explained in
terms of local density and composition enhancements, as well as by a change of mechanism due to strong
hydrogen bonding. This study demonstrates the versatility of supercritical fluid solvents both to examine
reaction mechanisms and as a means to tune rates.
Introduction
state (see Figure 1). However, the isomerization in polar and/
or protic solvents, where the large solvent effects could stabilize
A remarkable range of tunability is one of the enormous
advantages of supercritical fluid (SCF) solvents as reaction
media. Not only do small pressure variations give large density
changes with concomitant changes in solvent power, but SCFs
can be further tailored with the addition of small amounts of
cosolvents selected for their specific intermolecular interactions.
Here we demonstrate the tuning of the rate of the thermal cis-
trans isomerization of 4-(diethylamino)-4′-nitroazobenzene (DE-
NAB) and some related compounds in SCF solutions.
Azobenzene compounds have been of both mechanistic and
practical importance; many applications stem from their special
push-pull properties.1,2 The strong charge-transfer process
resulting from the electron-donating and electron-withdrawing
groups of the disubstituted azobenzenes produce strong absorp-
tion bands in the visible region, and consequently represent a
large group of dyes.3 Polymers impregnated with push-pull
azobenzenes have been commonly used as molecular probes,
triggers, and liquid crystals, and for nonlinear optics.4,5 The
reversible, photoinduced isomerization of these push-pull
azobenzenes is the rate-limiting step of the trans/cis cycle used
in reversible optical storage.4-6
Although the thermal cis-trans isomerization follows first-
order kinetics in solution,1-7 the mechanism of this isomerization
is still disputed in polar or protic (hydrogen bond donating
(HBD)) solvents. The kinetics of this isomerization in polymeric
environments would be more accessible if the mechanism of
isomerization in a variety of solvent environments were
determined unequivocally.
While unsubstituted or push-push azobenzenes generally
isomerize through an inversion mechanism,8-11 debate still exists
concerning the isomerization mechanism of push-pull azoben-
zenes such as 4-(dialkylamino)-4′-nitroazobenzenes. In non-
polar, aprotic (non-HBD) solvents, it is generally agreed that
the isomerization of this class of compounds proceeds through
an inversion mechanism characterized by an isopolar transition
a highly dipolar transition state, is thought to proceed through
a rotation mechanism after the rupture of the azo double bond
(see Figure 1).
One side of the debate argues that the isomerization reaction
for 4-(dialkylamino)-4′-nitroazobenzene proceeds by inversion
in all solvents,11 based on the following studies:
1. Both push-push and push-pull reaction rate constants
correlate with Taft polarity-polarizability parameters, where
the solvent dipole/solvent-induced dipole have equal importance
on the push-push and push-pull azobenzenes and this is
responsible for the sizable solvent effects.12
2. Another investigator justifies the solvent effects through
coplanar resonance structures of the transition state.13 However,
in this same work it was reported that for a series of
4′-(diethylamino)-nitroazobenzenes in DMF, a Hammet type plot
of log k versus σ+ and σ- produced two distinct linear regions
with F values of -3.25 and 10.2. This normally would be a
clear indication of a change in mechanism, but the authors
claimed the experimental data were evidence for the inversion
mechanism in all cases.
3. Similar kinetic behavior between push-pull and other
types of azobenzenes suggests that the single mechanism is
inversion.14
4. A study of 15 “bipolarity” azobenzenes (none of which
were 4-(dialkylamino)-4′-nitroazobenzenes) reports no depen-
dence of the rate constants on the solvent order.11
Other evidence supports isomerization via a rotation mech-
anism in highly dielectric or protic solvents.,1,15-19 Here the
two mechanisms compete; the inversion mechanism will
dominate in nonpolar, aprotic solvents, which could not ef-
fectively solvate the highly dipolar transition state of rotation
mechanism. Such a hypothesis is consistent with the near-zero
activation volume observed in nonpolar solvents such as
hexane.8 However, when protic or polar solvents are used, large
negative activation volumes (-25.9 mL/mol in chloroform,
-29.6 mL/mol in acetone) suggest a change in mechanism to
rotation through a highly polar transition state stabilized by
solvation.8 Additionally, Kirkwood-type plots indicate strong
* Corresponding author.
† Present address: Department of Chemical Engineering and Materials
Science, University of Minnesota, Minneapolis, MN.
S1089-5639(98)01634-X CCC: $15.00 © 1998 American Chemical Society
Published on Web 09/09/1998

7610 J. Phys. Chem. A, Vol. 102, No. 39, 1998
Dillow et al.
TABLE 2: Molecular Structures of Azo Reactants
CH2CH3
N
N
N
N
CH2CH3
4-(diethylamino)-4′-nitroazobenzene (DENAB)
CH3
N
N
N
N
CH3
4-(dimethylamino)-4′-nitroazobenzene (DMNAB)
CH2CH2OH
N
N
N
N
CH2CH3
Disperse Red (DR)
TABLE 3: Cosolvent Structures and Properties
cosolvent
Ra âa
methanol (CH3OH)
Figure 1. Isomerization by inversion mechanism (isopolar transition
state) and rotation (dipolar transition state).
πa
ꢀ
0.93 0.62 0.6
32.7d
TABLE 1: SCF Solvents and Reaction Conditions for Each
Solvent
1,1,1,3,3,3-hexafluoro-2-propanol
(CF3CH(OH)CF3)
1.96 0.00 0.65 16.6b
SCF
density range (mol/L)
dielectric range
acetone (CH3COCH3)
0.08 0.48 0.71 20.7c
dimethylacetamide (CH3CON(CH3)2) 0.00 0.76 0.88 37.8e
carbon dioxide (CO2)
ethane (C2H6)
7-19
6-13
1.2-1.5
1.2-1.5
a Reference 58. b Reference 59. c Reference 18. d Reference 8. e Ref-
erence 60.
positive deviations from linearity at large values of the dielectric
constant, additional evidence for a change in mechanism (i.e.,
from inversion to rotation).8
in solvent properties. The high compressibility leads to large,
negative solute partial molar volumes, which may give large
negative activation volumes. Local composition enhancements
of a cosolvent about the reactant(s) further affect the rate in
this highly compressible region.28-35
The purpose of this work is 2-foldsdetermination of the
kinetics and mechanism and a demonstration of solvent tuning
in SCFs. First, the reaction kinetics of the thermal cis-trans
isomerization of a series of push-pull 4-(diethylamino)-4′-
nitroazobenzenenes in pure SCFs ethane and CO2 are deter-
mined. Reactant structures are given in Table 2. Ethane does
not interact specifically with the solutes and exhibits little change
in solvent dielectric with density; therefore, the effects of
pressure can be isolated. Supercritical CO2 also has little change
in solvent dielectric with density, but may engage in specific
interactions with the solutes.36
Second, through the use of small amounts of specifically
chosen cosolvents (1 mol % and less), we may vary solvent
properties substantially. Cosolvents used in this experiment and
their properties are shown in Table 3. Through the use of polar/
aprotic and polar/protic cosolvents, the effects of polarity/
hydrogen-bonding ability (i.e., specific interactions) may be
separated, and the effect on reaction kinetics will aid in the
definition of reaction mechanism. Since the small amount of
cosolvent affects the (low) SCF bulk dielectric constant very
little, the effect of hydrogen bonding on the reaction rate is also
separable.
Whitten and co-workers1 contend that the rate enhancement
for polar, aprotic solvents is due to stabilization of the transition
state by dielectric effects. However, specific interactions
between the protic solvent and the hydrogen bond accepting
(HBA) nitro group provides additional stabilization of the
transition state when protic solvents are used, enhancing the
charge transfer within the molecule.
Leffler and Sigman used the variable, density-dependent
properties of SCF carbon dioxide (CO2) to try to determine the
mechanism of isomerization of 4-(diethylamino)-4′-nitroazoben-
zene (DENAB).19 Although the density, viscosity, and diffu-
sivity of SCF CO2 change dramatically in the near-critical
region,20 the dielectric constant and π* (Kamlet-Taft polarity/
polarizability solvent parameter) vary only modestly. Therefore,
determining mechanistic changes in a single solvent through
adjustable, density-dependent properties was not possible.
However, the CO2 rate data were used along with the data from
several nonpolar and polar liquid studies to generate a plot of
∆Gq (Gibb’s energy of activation) versus π*. This plot revealed
two linear regions: the liquid alkanes and SCF CO2 formed
one line with a small, positive slope, while the liquid polar
solvents formed a second line with a large, negative slope. The
difference in value of these slopes suggests a change in
mechanism from inversion to rotation.
Supercritical fluids have solvent properties between those of
gases and liquids - near liquid-like densities (and corresponding
solubilizing power) and diffusivities and viscosities which
approach those in gases. In the near-critical region, these
properties are a strong function of density, and large changes
in solvent properties can be obtained with very small changes
in pressure. For some SCFs (e.g., SCF CO2 and SCF ethane)
the dielectric constant changes only modestly as a function of
density (see Table 1).
Experimental Section
Materials. The materials used are listed in Table 4. The
4-(diethylamino)-4′-nitroazobenzene (DENAB) was synthesized
as described elsewhere19 and was recrystallized from toluene 3
times. The disperse red (DR) was also recrystallized from
toluene 3 times. NMR spectra confirmed the structure of these
compounds. All other materials were used as received. All
cosolvents were used as received.
Apparatus. A schematic of the modified UV-vis diode
array spectrophotometer (Hewlett-Packard 8453) is shown in
Figure 2. The spectrophotometer was modified to accommodate
a stainless steel high-pressure cell with 3 quartz windows
Even more profound tunability is achieved with the addition
of small amounts of specifically chosen cosolvents (typically
1-5 mol %). Cosolvents can enhance solubility in supercritical
fluids by orders of magnitude through specific interactions
coupled with local composition enhancements.21-27 Also reac-
tion rates may be tuned in this near-critical region due to changes

Supercritical Fluid Tuning of Reactions Rates
J. Phys. Chem. A, Vol. 102, No. 39, 1998 7611
Figure 2. Schematic of experimental apparatus.
TABLE 4: Materials, Sources, and Purities
Figure 3. ln(A - A∞/A0 - A∞) vs time (slope ) rate constant (1/s)).
DENAB in SCF CO2. T ) 35.6 °C.
compound
source
purity (%)
4-(diethylamino)-4′-nitroazo- synthesized
benzenenitroazobenzene
4-(dimethylamino)-4′-
nitroazobenzene
Disperse Red
carbon dioxide
ethane
methanol
acetone
dimethylacetamide
1,1,1,3,3,3-hexafluoro-2-
propanol
Aldrich Rare
Chemical Library
Aldrich
Matheson, SCF Grade
Matheson, C. P. Grade
Aldrich, HPLC Grade
Aldrich, HPLC Grade
Aldrich, HPLC Grade
Aldrich
99
99.99+
99.9+
99.9+
99.9+
99.9+
99+
(Heraeus Amersil). The path length of the cell was 3 cm and
the volume was 19.3 ( 0.15 mL. The windows were sealed
with indium.37 The cell was stirred continuously using a mini
stir plate (Variomag) and a Teflon-coated stir bar (Fisher) placed
inside the cell.
Figure 4. Sample time-based spectra of DENAB in SCF CO2 modified
with 0.056 M DMA. P ) 158 bar, T ) 35 °C.
negligible. The rates calculated from the changes in absorbance
were measured at 415, 433, and 455 nm simultaneously for
DENAB in SCF CO2 are shown in Figure 3; rate constants
calculated from all wavelengths are well within experimental
error. Errors resulting from monitoring the absorption of DR
at the wavelength of maximum absorption for the trans form
would be negligible since only 3-5% of the compound was
photoisomerized to the cis form in each decay experiment. This
was verified by comparing the measurements of the rate of
isomerization from both the wavelength of maximum absorption
of the cis and trans isomers; the rate constants agreed within
experimental error. Because the change in absorbance was
much greater for the trans isomer, the errors associated with
the rate constant measured at this wavelength were much
smaller, and rate constants reported are based on measurements
at this wavelength of maximum absorbance.
Two to seven time-based absorbance spectra were obtained
at every pressure point. Sample time-based spectra, representa-
tive of the time-based spectra throughout this experiment, are
shown in Figure 4.
Sample Preparation. All measurements were made at a
constant temperature of 35 °C ((0.1 °C) and were carried out
in the single-phase region, as confirmed by separate miscibility
experiments.38-41 Time-based spectra were obtained, starting
at low pressures and incrementally going to higher pressures.
The pressure varied less than 1 psi within a single spectral scan,
and data sets were taken with increasing pressure to ensure that
the solute concentration remained constant.
The cell temperature was monitored with an internal ther-
mocouple and an external thermocouple within the steel block
(Omega, type K, calibrated within (0.1 °C) The cell was
controlled by a PID controller (Omega) and backup heat was
supplied constantly using an EPSCO DC power supply (Model
D-612T) with thermoelectric Peltier heaters (Melcor). The
pressure was controlled using either a 60 cm3 piston type high-
pressure generator (High Pressure Equipment, Model 87-6-5)
or a high-pressure syringe pump (ISCO, 500D) and measured
to within (2 psi with a Heise digital pressure gauge (Model
901B). A Valco 6-port sampling valve with external sample
loops ranging in size from 50 to 100 µL was used to inject
cosolvent directly into the high-pressure cell. Visible light used
to induce photoisomerization was supplied by a 500 W tungsten
light passed through a UV filter.
Kinetic Measurements. Single-beam diode array spectros-
copy was used to monitor absorbance as a function of increasing
pressure at constant probe and cosolvent concentrations. Samples
were irradiated with visible light for approximately 1 min, time-
based absorbance measurements by the UV-vis diode array
were initiated, the light was then blocked by a shutter (to give
and accurate zero time), and the relaxation of the trans isomer
to the cis isomer was monitored. Reaction rates were indepen-
dent of irradiation time (after a minimum time) and independent
of the percent reactant isomerized to the cis form, as was
reported previously.13
The absorbance was recorded at the wavelength of maximum
absorption for the trans isomer, where the change in absorbance
is a maximum and where the contribution from the cis isomer
is negligible for DENAB and DMNAB.1,12,16,19 The rate
constants were calculated from the absorbance measurements,
assuming Beer’s law. The absorbance was measured at two
additional wavelengths to ensure that the contributions to the
rate constant from the absorbance of the cis isomer were
The high-pressure cell was loaded with a solution of solute
dissolved in acetone using a micrometering pipet to obtain a
probe concentration below the solubility limit at experimental
conditions as determined spectroscopically. Experimental solute
concentrations are given in Table 5. The cell was flushed with
multiple volumes of low-pressure SCF solvent to evaporate the
acetone and to displace air from the system. In the experiments
with pure SCF solvents the cell was then pressurized with SCF

7612 J. Phys. Chem. A, Vol. 102, No. 39, 1998
Dillow et al.
TABLE 7: Critical Properties and Acentric Factors Used
for PR EOS61
compound
TC (K)
PC (bar)
ω
carbon dioxide
ethane
304.1
305.4
508.1
655.7
512.6
461.6
73.8
48.8
47.0
42.11
80.9
37.3
0.225
0.099
0.304
0.147
0.556
0.66
acetone
dimethylacetamidea
methanol
1,1,1,3,3,3-hexafluoro-2-propanola
Figure 5. Fit of experimental absorbance data to a first-order
exponential decay model for DENAB in SCF CO2 modified with 0.126
M MeOH. P ) 155 bar, T ) 35 °C.
a Reference 62.
TABLE 8: Rate Constants for Cis to Trans Thermal
Relaxation of DENAB in SCF Ethane and SCF Ethane
Cosolvent Modified Solvents at 35 °Ca
TABLE 5: Solute Concentrations
solute
concentration (M)
density (mol/L)
k (1/s)
density (mol/L)
k (1/s)
DENAB
DMNAB
Disperse Red
1.4 × 10-5
1.5 × 10-5
1.35 × 10 -5
DENAB/Pure Ethane
8.94
9.50
10.25
10.51
10.98
0.115
0.103
0.080
0.078
0.072
11.49
0.070
0.062
0.058
0.051
11.98
12.48
13.00
TABLE 6: Experimental Cosolvent Compositions
SCF
cosolvent
conc (M)
mol %
ethane
ethane
ethane
ethane
CO2
MeOH
HFIP
acetone
DMA
MeOH
MeOH
HFIP
0.128
0.049
0.07
0.056
0.064
0.128
0.025
0.049
0.056
0.97-1.48
0.25-0.3
0.54-0.86
0.43-0.63
0.35-0.45
0.67-1.1
0.13-0.25
0.27-0.36
0.58-0.9
DENAB/0.128 M MeOH
8.63
8.82
9.62
0.154
0.134
0.136
0.126
0.121
0.122
0.117
10.83
0.105
0.106
0.093
0.084
0.075
0.064
0.057
11.14
11.46
11.97
12.26
12.74
13.14
9.83
CO2
CO2
CO2
CO2
10.11
10.36
10.54
HFIP
DMA
DENAB/0.056 M DMA
8.86
9.07
9.31
9.62
9.82
10.09
10.30
0.158
0.122
0.119
0.112
0.124
0.116
0.113
10.58
0.113
0.104
0.098
0.088
0.080
0.071
0.063
to the desired initial pressure. In cases where cosolvent was
added, the cell was charged with 100 psig of SCF after removing
air from the system. The cell was then isolated from the rest
of the system, and the lines leading to the cell were pressurized
with 450 psig of SCF. The external sample loop was then rinsed
and filled with the cosolvent, and the sampling valve and the
valve leading to the cell were opened simultaneously to force
the cosolvent into the cell using the pressure differential. The
cell was further pressurized with SCF to the desired pressure
set point, and after equilibration of temperature and pressure,
absorbance spectra were measured as described above. Con-
centrations and mole percents of cosolvents used for the various
SCF solvents are given in Table 6.
10.91
11.27
11.68
12.21
12.58
13.08
DENAB/0.049 M HFIP
11.68
12.10
0.490
0.499
12.56
13.04
0.524
0.449
DENAB/0.07 M Acetone
8.25
8.41
8.55
9.60
9.88
10.16
10.56
0.126
0.131
0.113
0.116
0.110
0.095
0.088
10.82
0.088
0.095
0.085
0.075
0.074
0.063
11.22
11.69
12.13
12.57
13.07
Blank runs (no azobenzene) were made for each experiment
to ensure that cosolvent was injected properly and that no
contaminants were present. Replicate experiments with and
without cosolvent resulted in rate constants within experimental
error, ensuring that the method of cosolvent injection and
experimental procedure were reproducible.
a The uncertainty of the data is (5%.
Results and Discussion
Rate constants were obtained for
Data Analysis. All experiments followed first-order kinetics,
and the rate constants were obtained by a fit of the time-based
absorbance data to an exponential model (see Figure 5).
(1) DENAB in SCF ethane; (2) DENAB, DMNAB, and DR
in SCF CO2; (3) DENAB in SCF ethane modified with
cosolvents acetone, dimethylacetamide (DMA), methanol
(MeOH), and 1,1,1,3,3,3-hexafluoro-2-propanol (HFIP); (4)
DENAB, DMNAB, and DR in SCF CO2 modified with DMA,
MeOH, and HFIP.
The rate constants as a function of density are listed in Tables
8-12. There were no significant differences in the isomeriza-
tion rates for DENAB, DMNAB, and DR in the pure SCF
solvents; therefore DENAB was chosen as the focus solute for
this work and the subsequent work with cosolvents because it
exhibited the greatest solubility at low solvent densities in pure
SCF solvents.
Since the azobenzene reactants were very dilute, mixture
densities for the systems with no added cosolvent were assumed
to be equal to the pure SCF density, calculated from the
Benedict-Webb-Rubin (BWR) EOS. For the cosolvent-
modified SCF mixture densities, we calculated the ratio of
mixture density to pure SCF density from the Peng-Robinson
(PR) EOS,42 and used this ratio to correct the pure SCF density
calculated from the BWR EOS. The mixture densities calcu-
lated by this method are reasonably accurate when less than 1
mol % cosolvent is used as determined by comparison with
measured SCF/cosolvent mixture density data obtained in a
separate experiment.38 Critical properties and acentric factors
used in the PR EOS calculations are listed in Table 7.
Reaction Rates of DENAB in Pure SCF CO2 Pure SCF
Ethane. The rate constant of the thermal cis-trans relaxation
of DENAB in both pure SCF CO2 and SCF ethane decreased

Supercritical Fluid Tuning of Reactions Rates
J. Phys. Chem. A, Vol. 102, No. 39, 1998 7613
TABLE 9: Rate Constants for Cis to Trans Thermal
Relaxation of DENAB in SCF CO2 and Cosolvent-Modified
Solvents at 35 °Ca
TABLE 11: Rate Constants for Cis to Trans Thermal
Relaxation of DR in SCF CO2 and Cosolvent-Modified
Solvents at 35 °Ca
density (mol/L)
k (1/s)
density (mol/L)
k (1/s)
density (mol/L)
k (1/s)
density (mol/L)
k (1/s)
DENAB/PURE CO2
DR/Pure CO2
9.1
9.9
10.5
12.4
13.5
0.123
0.104
0.099
0.076
0.071
14.5
0.058
0.052
0.046
0.038
0.032
14.09
15.05
15.63
0.100
0.082
0.084
16.07
17.03
17.69
0.081
0.071
0.066
15.1
16.1
17.1
18
DR/0.064 M MeOH
14.36
14.65
15.16
15.45
0.134
0.093
0.100
0.091
15.75
0.091
0.089
0.077
0.071
DENAB/0.025 M HFIP
16.52
17.32
18.24
10.06
10.56
11.43
11.78
12.19
12.37
12.76
0.298
0.253
0.220
0.202
0.190
0.187
0.176
13.79
0.165
0.137
0.128
0.113
0.099
0.085
0.078
14.48
15.29
16.17
17.22
18.18
18.81
DR/0.049 M HFIP
13.53
14.43
15.26
16.34
0.346
0.305
0.284
0.199
17.12
17.82
18.76
0.183
0.165
0.132
a The uncertainty of the data is (5%.
13.93
14.71
15.39
0.322
0.243
0.218
TABLE 12: Rate Constants for Cis to Trans Thermal
a
Relaxation of DMNAB in SCF CO2
density (mol/L)
k (1/s)
density (mol/L)
k (1/s)
11.49
11.85
12.32
12.62
12.94
13.31
13.50
13.79
13.96
0.088
0.087
0.082
0.074
0.067
0.061
0.057
0.047
0.042
12.55
13.00
13.51
14.31
0.101
0.076
0.069
0.064
15.11
16.08
17.08
18.05
0.060
0.044
0.038
0.031
a The uncertainty of the data is (5%.
DENAB/0.056 M DMA
10.92
11.32
11.65
12.07
12.43
12.80
13.22
13.50
0.140
0.096
0.076
0.080
0.079
0.082
0.077
0.072
13.99
0.067
0.062
0.058
0.051
0.044
0.039
0.034
0.030
14.64
15.16
15.74
16.46
17.25
18.18
18.86
a The uncertainty of the data is (5%.
TABLE 10: Rate Constants for Cis to Trans Thermal
Relaxation of DENAB in SCF CO2 45 °Ca
Figure 6. Rate constant vs reduced density for DENAB in SCFs CO2
and ethane (b, CO2, 9, ethane).
density (mol/L)
k (1/s)
density (mol/L)
k (1/s)
8.474
8.97
9.52
10.21
10.55
0.178
0.102
0.084
0.124
0.111
11.06
11.69
11.98
12.55
13.00
0.102
0.092
0.099
0.087
0.075
a The uncertainty of the data is (5%.
with increasing solvent density (shown in Figure 6 as a function
of reduced density). The activation volume observed is positive,
and relatively small for SCF reactions: ∆νq ) +170 ( 225
mL/mol for ethane and +560 ( 350 mL/mol for CO2.
The rate constants, even at the highest measured density (i.e.,
slowest rate), are approximately an order of magnitude greater
than the corresponding rate constant in cyclohexane (0.0071
s-1), even though the dielectric constant in the pure SCFs is
smaller than that of cyclohexane.1 The viscosity of cyclohexane
is approximately an order of magnitude greater than that of the
SCF solvents, and the rate constant varies inversely with solvent
viscosity for thermal isomerization in both pure SCF CO2 and
ethane (illustrated when comparing Figure 7 to Figure 6).43 It
is tempting to attribute the solvent effects to viscosity, especially
with a positive activation volume.
Figure 7. Viscosity as a function of reduced density for SCFs CO2
and ethane (b, CO2, 9, ethane).
Since the solvents are aprotic and the dielectric constant is
low (1.2-1.5 in this region for both solvents), the reaction most
likely proceeds via an inversion mechanism, which has not been
reported to be viscosity dependent. While positive activation
volumes in liquids can signal mass-transfer-limited reactions,
the activation volume in SCFs is of little significance in
determining mechanism. In liquids, structural and solvation

7614 J. Phys. Chem. A, Vol. 102, No. 39, 1998
Dillow et al.
In the case where k2 . k-1 the rate equation reduces to
rate ) k1[C]
which indicates that the solvent shell reorganizes very rapidly
and that the rate is kinetically controlled. In the case where
k-1 (in the case of equilibrium k-1 ) k1) . k2, the rate becomes
Figure 8. Schematic of two-step mechanism with solvent rearrange-
ment.
contributions are roughly comparable in size, about (30 cm3/
mol; in SCFs the structure contributions are presumably the
same size, but they are virtually always overwhelmed by the
solvation contributions, which can be hundreds of mL/mol or
even L/mol. Thus, all the activation volume really tells us is
that the difference of large numbers for solvation between
transition state and substrate is positive by as little as only a
few percent of their absolute values. Since the viscosity of SCFs
is a strong function of their density, it seems consistent to
consider the rates as density dependent.
The viscosity effect on unimolecular isomerization reactions
in SCF solvents is relatively unexplored. The ratio of cis-/trans-
stilbene was reported to be a strong function of SCF CO2
viscosity in the near-critical region.44 It is possible that this
strong dependence on the solvent viscosity observed is actually
due to the dependence of viscosity on solvent density. In this
case, the trend of the ratio of cis-/trans-stilbene may be described
as a function of density.
The viscosity effects on the thermal isomerization of DENAB
were recently investigated by Sumi and co-workers45 in methyl
acetate and in two relatively viscous liquids, 2-methyl-2,4-
pentanediol (MPT) and glycerol triacetate (GTA), where it was
possible to vary the viscosity by many orders of magnitude by
adjusting the pressure. In these two solvents, the rates initially
increased with pressure due to normal transition state electros-
triction of the solvent about the very polar (rotational) transition
state. At a certain point, the viscosity becomes great enough
that the rate begins to slow with additional pressure. However,
viscosities many orders of magnitude higher than those in SCFs
were required to see this effect.
k1k
rate ) 2[C]
k-1
and the structural step occurs much faster than the solvent
reorganization and the rate is then partially dependent on this
rate of solvent reorganization. In this experiment, the solvent
rearrangement step is believed to occur on a comparable or
slower time scales than the reaction time. In this case, the rate
of solvent rearrangement enters into the rate expression. In this
case, at the lower solvent densities, where there are fewer solvent
molecules, the rate increases due to increases in k2.
The ability to “tune” the reaction rate of this thermal
relaxation by over 4 times in a very limited density region of
SCF CO2 is remarkable. In a single solvent, the reaction rate
is tuned to an extent that could only be achieved by changing
from liquid solvents with increasing polarities. This experiment
demonstrates that solvent density is a very important tunable
property for isomerization reactions, as well as other unimo-
lecular reactions, in near-critical SCF solvents. Opportunities
exist for further tunability of the reaction rate with small
additions of cosolvents, due to local composition enhancements
near the critical point of the system.
Cosolvent Modified Experiments. The thermal cis-trans
relaxation kinetics for DENAB, primarily, and DR were
measured in SCF CO2 and ethane with small amounts of
acetone, DMA, methanol, and HFIP cosolvents.46 The con-
centrations and mole fraction ranges for the added cosolvents
are shown in Table 6. The experiments were carried out in
constant concentration of cosolvent. The mole fraction changed
as SCF was added throughout each experiment. The composi-
tion may be enhanced in the near-critical region where local
composition of cosolvent about the solute (i.e., reactant) may
be several times the bulk composition.32,47-53 By using cosol-
vents with varying degrees of acidity, basicity (HBD or HBA
ability, in this case), and polarity/polarizability, it is possible
to analyze the effect of these specific solvent properties while
maintaining bulk solvent properties much like that of the pure
SCF fluid. In liquid studies, high polarity/polarizability cannot
be easily separated from specific interactions because most acid
or basic (HBD or HBA) solvents also have large dielectric
constants or Kamlet-Taft polarity/polarizability parameters.
This is more readily accomplished in SCF/cosolvent media.
The cosolvent experiments revealed the following key
points: (1) small amounts of polar or protic cosolvents are
capable of tuning the reaction rate many times over that in the
pure SCF solvent; (2) rapid increases in the rate constant in the
near-critical region may be due to local composition enhance-
ments of cosolvent about the reactant; (3) polar, aprotic
cosolvents modestly enhance the reaction rate; (4) protic
cosolvents, regardless of polarity, enhance reaction rate dramati-
cally; (5) the data are consistent with a change in mechanism
to rotation in the presence of protic cosolvents.
We propose a mechanism similar to that developed by Sumi
to explain the rate behavior observed in the SCF experiments:
k2
98 T
C {kk } M
1
-1
In this equation, C is the cis isomer with its equilibrium solvent
shell and T is the trans isomer with its equilibrium solvent shell
as shown in Figure 8. We view the intermediate configuration
not as a transition state in the classical sense, but rather as the
isomerized molecule before the concomitant rearrangement of
the solvent shell. The first step is the structural change, where
the energy barrier must be crossed by rapid atomic vibrations.
The second step is the rearrangement of molecules to accom-
modate the new molecular species and is subject to a density
dependence. In cases where the electrical environment does
not change (solvent properties remain constant, isopolar transi-
tion state (polarities of C and M are constant), etc.) the changes
in the rate constant are due to the changes in solvent density.
This mechanism is strictly for the inversion process, while the
rotation process is envisioned to proceed through a one-step
mechanism.
This two-step mechanism can be illustrated by the following
rate equation
Each of these points will be discussed in detail below with
specific experimental results to serve as examples for each key
point.
When aprotic, polar cosolvents such as acetone and DMA
are added to SCF ethane and CO2, the rate of thermal cis-
k1k2
rate )
[C]
k-1 + k2

Supercritical Fluid Tuning of Reactions Rates
J. Phys. Chem. A, Vol. 102, No. 39, 1998 7615
Figure 9. First-order rate constants for the thermal cis-trans isomer-
ization of DENAB with cosolvent DMA as a function of reduced
density.
Figure 11. First-order rate constants for the thermal cis-trans
isomerization of DENAB and DR with cosolvent HFIP in SCF CO2 as
a function of density.
with 0.05 M HIFP, the data are limited because the rate constants
were so large (fast) that they could not be accurately measured
at lower pressures. In addition, there was a much smaller
percent of cis isomer present at the photostationary state.
However, the rate was found to increase over 15 times with the
addition of less than 0.4 mol % HFIP. This rate enhancement
is truly remarkable for such a small amount of added cosolvent;
it can be explained only by strong specific interactions of the
hydrogen-bonded cosolvent to the nitro group of the solute
molecules, going through a highly dipolar transition state
(associated with a rotation mechanism). The bulk dielectric
constant will remain very similar to that of SCF CO2 at these
concentrations, while the local dielectric may be several times
greater in the near-critical region due to local composition
enhancementssthis would lead to a local dielectric which is
still relatively low. In fact, the dielectric environment would
be lower than in the previous DMA, acetone, and methanol
experiments. Therefore, with no change mechanism (i.e., a
reaction proceeding by inversion), the reaction rate would be
expected to be similar to or lower than the previous experiments.
However, HFIP has a very large acidity parameter (R ) 1.96)
and no basic nature whatsoever (unlike the case of methanol,
which is a weak HBD and strong HBA molecule) and is capable
of strong hydrogen bonding interactions with the reactant.
Whitten and co-workers1 noted that in a correlation of rate
constants for the thermal isomerization of DENAB with the
Kosower parameter for 14 protic and aprotic solvents that the
plot broke up into two distinct linear regions for the protic and
aprotic solvents. This was attributed to the lowering of the
energy barrier of isomerization when the solvent interacts
specifically with the solute via the nitro group, thus enhancing
its ability to withdraw electrons. Our experimental data provides
additional evidence for the lowering of the energy barrier via
specific hydrogen bond interactions with the nitro group.
A Kirkwood analysis was performed and was consistent with
the above hypothesis. The existence of local composition
enhancements in the near-critical region results in a need for a
“local” dielectric constant to be calculated for the analysis. Kim
and Johnston54 determined local composition enhancements for
several cosolvents in SCF CO2 as a function of pressure and
cosolvent composition spectroscopically by measuring the
transition energy of the solvatochromic dye, phenol blue. We
have used these data, which reveal local composition enhance-
ments up to 7.5 times that of the bulk composition at reduced
pressures of just over unity, to estimate “local” dielectric
constants for the CO2/methanol systems. Local dielectric
constants were calculated for the ethane/CO2 system using local
composition enhancement data from a separate experiment.55
Because the reactant used in this investigation is not identical
to the probe molecules used in these determinations of local
composition enhancement, this is only an estimation. The fluid
Figure 10. First-order rate constants for the thermal cis-trans
isomerization of DENAB with cosolvent MeOH as a function of
reduced density.
trans isomerization of DENAB is very close to that in the pure
SCFs until the near-critical region is approached (Figure 9).
Cosolvent DMA enhances the rate in ethane slightly more than
in CO2 at the same reduced densities, perhaps because of the
lack of specific interactions between the ethane and DMA,
which may strengthen the interactions between the polar solute
molecule and the cosolvent. In both solvents, in the very near-
critical region, we suggest that local composition enhancements
cause a disproportional increase in the local concentration of
the cosolvent about the DENAB in relation to the bulk
concentration, giving marked increases in the rate constant.
These trends with respect to pressure (or density) are
consistent with the two-step rate hypothesis above. In the case
of cosolvent/SCF solvents, the rate is always greater than that
in the pure SCF. Here, the change in rate due to the density
effect (solvent rearrangement) is similar to that in the pure SCF;
however, the increased dielectric constant of the media resulting
from the addition of the polar cosolvent causes an increase in
the reaction rate (i.e., an increase in the structural rate constant,
k1).
In experiments involving the isomerization of DENAB in SCF
CO2 and ethane modified with methanol, similar results are
found for DMA and acetone (see Figure 10). With MeOH
cosolvent, the rate enhancements, as compared to the pure SCF
solvents, are greater at all reduced densities than with the DMA
or acetone, probably due to the ability of MeOH to hydrogen
bond weakly to the nitro group of DENAB that enhances this
group’s electron withdrawing capability. The same result was
found for DR.
The experiments with HFIP cosolvent were very difficult to
analyze at the high cosolvent concentrations with non-flash
photolytic analysis methods because of the extreme enhance-
ments of the isomerization rate of both DENAB and DR. In
Figure 11 the rate constants for DENAB and DR in HFIP
modified SCF CO2 are shown. In the case of pure DR, the
lower pressure limit for the data is high because of the low
solubility of DR in pure CO2; however, for DR and DENAB

7616 J. Phys. Chem. A, Vol. 102, No. 39, 1998
Dillow et al.
region. It seems clear that extreme rate enhancements occur
due to strong specific hydrogen bond interactions of protic
cosolvents with the nitro group of the solutes which result in a
change in mechanism from inversion to rotation.
These results also show the tremendous potential for SCFs
as reaction solvents; very often they provide environmentally
benign alternatives to undesirable liquid solvents, and they
permit precise tuning not only of rates, but also of yields or
product distributions55-57
Acknowledgment. The authors are grateful for the financial
support of the National Science Foundation and of the DuPont
Co.
Figure 12. Kirkwood plot for DENAB in SCF CO2 and SCF ethane
modified with cosolvents: 9, methanol-CO2; 2, HFIP-CO2, low
concentration; 1, HFIP-CO2, high concentration; [, DMA-CO2; b,
acetone-ethane; 0, methanol-ethane; O, DMA-ethane; 4, HFIP-
ethane.
Notation
k ) rate constant (s-1
)
was treated as having finite spaces about the central solute, and
the local dielectric was calculated by a linear sum of the
contributions from the supercritical fluid and the cosolvent.
The Kirkwood plot for DENAB in SCF CO2 with 0.128 M
MeOH using the “local” dielectric constant (Figure 12) shows
a linear relationship, indicating that the sharp rate increase in
the near-critical region may be due to an enhanced dielectric
environment arising from local composition enhancements of
cosolvent about DENAB in this region. However, the “local”
dielectric constant never exceeds ∼4 in the region with greatest
local composition enhancements, so the mechanism of isomer-
ization should remain dominantly inversion. For this reason,
no deviations in the Kirkwood plot occur.
Greek Letters
R ) Kamlet-Taft acidity parameter
â ) Kamlet-Taft basicity parameter
∆Gq ) Gibbs energy of activation
∆Vq ) activation volume
ꢀ ) dielectric constant
π* ) Kamlet-Taft polarity/polarizability parameter
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