D. Other Systems and Methods

Figure 13 Absorption and fluorescence spectra of DEAEB in supercritical ethane (—)

and CO2 (-··-). Absorption in ethane: 580 psia and 53◦ C. Absorption in CO2 : 800 psia

and 50◦ C. Fluorescence in ethane (in the order of increasing band width): the vapor

phase, 340, 470, and 750 psia at 45◦ C. Fluorescence in CO2 : 600 psia and 50◦ C. The

fluorescence spectrum in room-temperature hexane (· · ·) is also shown for comparison.

(From Ref. 50.)



the equilibrium is inert to density changes in both fluids. In supercritical CO2

neither extreme applies; therefore, the equilibrium is strongly density dependent,

favoring the azo tautomer at low densities and the hydrazone tautomer at high

densities. Using the equilibrium between the azo and hydrazone tautomers as

a solvation scale, the authors concluded that the solvent strength of supercritical CO2 is similar to that of liquid benzene and that the solvent strength of

supercritical fluoroform is similar to that of liquid chloroform. The results are

consistent with the findings based on the π∗ and Py scales. (See Scheme 1.)

Lee et al. investigated the photoisomerism of trans-stilbene in supercritical

ethane to observe the so-called Kramer’s turnover region where the solvent

effects are in transition from collisional activation (solvent-promoting reaction)

to viscosity-induced friction (solvent-hindering reaction) (76). In the experiments

the Kramer’s turnover was observed at the pressure of about 120 atm at 350 K.

(See Scheme 2.)



Copyright 2002 by Marcel Dekker. All Rights Reserved.



Figure 14 Solvatochromatic shifts of the TICT band maximum for DEAEB in supercritical CHF3 at 35◦ C (᭺) and 50◦ C (᭝), and the relative contributions of the TICT

and LE emissions, ln(xTICT /xLE ), for DEAEB in supercritical ethane at 50◦ C (᭿) as a

function of reduced density. (From Ref. 3.)



Randolph and coworkers (79,80) used electron paramagnetic resonance

(EPR) spectroscopy to determine the hyperfine splitting constants AN for di-tbutylnitroxide radicals in supercritical ethane, CO2 , and fluoroform. Plots of AN

as a function of reduced density clearly revealed the three-density-region pattern.

The solute–solvent clustering issue was evaluated using the [(ε − 1)/(2ε + 1)]

term as a measure of solvent polarity. Again, it was found that the maximum

clustering effects occurred at a reduced density around 0.5.

2. Vibrational Spectroscopy

A number of investigations of supercritical fluids have been conducted using

vibrational spectroscopy methods, including infrared absorption (19,84–89), Raman scattering (90–100), and time-resolved vibrational relaxation and collisional

deactivation (101–112). The results of these investigations have significantly

aided the understanding of solute–solvent interactions in supercritical fluid systems. For example, Hyatt used infrared absorption to examine the spectral shifts

of the C=O stretch mode for acetone and cyclohexanone and those of the NH stretch mode for pyrrole in liquid and supercritical CO2 to determine the

solvent strength of CO2 relative to normal liquid solvents (19). Blitz et al.



Copyright 2002 by Marcel Dekker. All Rights Reserved.



Figure 15 A plot of the DEAEB TICT band maxima vs. the PRODAN fluorescence

spectral maxima in a series of room-temperature solutions. The result in CHF3 at the

reduced density of 2 and 35◦ C (᭿) follows the empirical linear relationship closely.

(From Ref. 3.)



utilized infrared and near-infrared absorption to study CO2 under supercritical conditions in both neat CO2 and CO2 –cosolvent mixtures (84). For neat

CO2 at 50◦ C, plots of the frequency shifts and the absorption bandwidths as

a function of fluid density were clearly nonlinear, similar to the plots made

using data obtained with the π∗ polarity probes (22–25). Ikushima et al. used



Scheme 1



Copyright 2002 by Marcel Dekker. All Rights Reserved.



Scheme 2



frequency shifts of the C=O stretch mode in cyclohexanone, acetone, N ,N dimethylformamide, and methyl acetate to probe the solvent strength in supercritical CO2 (85); Wada et al. used the molar absorptivity changes of the C-C ring

stretch and the substituent deformation stretch in several substituted benzenes to

study solvation effects in supercritical CO2 (89). Both investigations yielded results that are characteristic of solute–solvent clustering. The results of Wada et al.

again suggest that the maximum clustering effects occur at a reduced density of

around 0.5 (89).

The collisional deactivation of vibrationally excited azulene was recently

investigated in several supercritical fluids for a series of fluid densities (106,

108,109). Theoretically, the rate constant of collisional deactivation kc should

be proportional to the coverage of azulene by the collision (solvent) molecules,

and thus kc should be a function of the local solvent density in a supercritical fluid. A plot of kc as a function of reduced density in propane shows the

characteristic three-density-region solvation behavior (Figure 16). The results

correlate well with the observed shifts in the absorption maximum of azulene

under the same solvent conditions (106). Similarly, Fayer and coworkers (101–

103) examined the vibrational relaxation of tungsten hexacarbonyl W(CO)6 in

supercritical ethane, CO2 , and fluoroform as a function of fluid density. Their results show that the lifetime of the T1u asymmetric C=O stretch mode decreases

with increasing fluid density in the characteristic three-density-region pattern. A

concept similar to the solute–solvent clustering, “local phase transitions,” was

introduced by these authors to explain the experimental results. The results were

also discussed in terms of a mechanistic scheme in which the competing thermodynamic forces may cancel out the density dependence of the lifetimes of

the vibrational modes in the near-critical density region. However, the validity

of such a scheme remains open to debate (113,114).

3. Rotational Diffusion

Another important topic in the study of supercritical fluids is viscosity effects.

Several research groups have used well-established probes to examine the effect

of viscosity on rotational diffusion in supercritical fluid systems.



Copyright 2002 by Marcel Dekker. All Rights Reserved.



Figure 16 (a) Density dependence of collisional deactivation rate constants of azulene

in propane at various temperatures (full line: extrapolation from dilute gas phase experiments). (b) Density dependence of the shift of the azulene S3 ← So absorption band in

propane at various temperatures. (From Ref. 106.)



The time for rotational diffusion τrot can be related to the viscosity η using

the modified Stokes–Debye–Einstein equation (115):

τrot = (ηVp /kB T )f C



(6)



where Vp is the volume of the probe molecule, kB is the Boltzmann constant,

T is the temperature in K, and f and C are correction factors. The factor f

corrects for the shape of the probe molecule, whereas the factor C takes into

account variations in hydrodynamic boundary conditions. In the absence of these

corrections (both factors being unity), the rotational diffusion time τrot is linearly



Copyright 2002 by Marcel Dekker. All Rights Reserved.



dependent on the viscosity (115). Experimentally, rotational diffusion times of

the probes in supercritical fluids have been determined via various spectroscopic

techniques, including infrared absorption and Raman scattering (116–125), NMR

(126–133), fluorescence depolarization (66,115,134,135), and EPR (136). For

example, Betts et al. used the fluorescence depolarization method to obtain rotation reorientation times of PRODAN in supercritical N2 O (66). The results show

that, contrary to the behavior predicted by Eq. (6), τrot actually increases with decreasing pressure and density (lower bulk viscosity of the fluid). As unusual as it

seems, the observation that rotation reorientation times increase with decreasing

density in supercritical fluids has been reported in other investigations. Heitz and

Bright (135) reported similar behavior for the rotational diffusion of N ,N -bis(2,5-tert-butylphenyl)-3,4,9,10-perylenecarboxodiimide (BTBP) in supercritical

ethane, CO2 , and fluoroform; and deGrazia and Randolph (136) made similar



Structure 5



Copyright 2002 by Marcel Dekker. All Rights Reserved.



observations in their EPR (electron paramagnetic resonance) study of copper

2,2,3-trimethyl-6,6,7,7,8,8,8-heptafluoro-3,5-octanedionate in supercritical CO2 .

These rotational diffusion results are somewhat controversial, partially due to

the fact that the probes involved are complicated and subject to other effects

beyond viscosity-controlled rotational diffusion. deGrazia and Randolph suggested that solute–solute interactions might be responsible for the anomalous

density dependence of τrot in supercritical CO2 (136). Heitz and Maroncelli

(115) repeated the rotational reorientation study of BTBP in supercritical CO2

and also added two more probes, 1,2,6,8-tetraphenylpyrene (TPP) and 9,10bis(phenylethynyl)anthracene (PEA). They found that for all three probes, the

τrot values actually increase with increasing fluid density (115). More quantitatively, the PEA results clearly deviate from the prediction of Eq. (6). The

deviations were discussed in terms of significant solute–solvent clustering in

the near-critical density region, namely, that local solvent density augmentation

results in locally enhanced viscosities. Anderton and Kauffman (134) studied

the rotational diffusion of trans,trans-1,4-diphenylbutadiene (DPB) and trans4-(hydroxymethyl)stilbene (HMS) in supercritical CO2 and found that the τrot

values increase with increasing fluid density for both probes. The debate concerning the density dependence of rotational diffusion in supercritical fluids is

likely to continue.



E. The Three-Density-Region Solvation Model

The wealth of data characterizing solute–solvent interactions in supercritical

fluids show a surprisingly characteristic pattern for the density dependence. Even

more incredible is the fact that the same density dependence pattern has been

observed in virtually all supercritical fluids (from nonpolar to polar and from

ambient to high temperature) with the use of numerous molecular probes that

are based on drastically different mechanisms. These results suggest that three

distinct density regions are present in a supercritical fluid: gas-like, near-critical,

and liquid-like. The density dependence of the molecular probe response in a

supercritical fluid differs in each of the three density regions (Figure 1): strong

in the gas-like region, increasing significantly with increasing density; plateaulike in the near-critical density region, beginning at ρr ∼ 0.5 and extending to

ρr ∼ 1.5; and again increasing in the liquid-like region, in the manner predicted

by the dielectric continuum theory.

To account for the characteristic density dependence of the spectroscopic

(and other) responses in supercritical fluids, a three-density-region solvation

model was proposed, reflecting the different solute–solvent interactions in three

distinct density regions (Figure 17) (1–3). According to the model, the three

density-region solvation behavior in supercritical fluid solutions is determined



Copyright 2002 by Marcel Dekker. All Rights Reserved.



Figure 17 Cartoon representation of the empirical three-density-region solvation model

depicting molecular level interactions for the three density regions: (a) low-density region;

(b) near-critical density region; (c) liquid-like region.



primarily by the intrinsic properties of the neat fluid over the three density

regions.

The behavior in the gas-like region at low densities is probably dictated

by short-range interactions in the inner solvation shell of the probe molecule.

The strong density dependence of the spectroscopic and other responses is

probably associated with a process of saturating the inner solvation shell. Before saturation of the shell, microscopically the consequence of increasing the

fluid density is the addition of solvent molecules to the inner solvation shell

of the probe, which produces large incremental effects (Figure 17a). In the

near-critical region, where the responses are nearly independent of changes in

density, the microscopic solvation environment of the solute probe undergoes

only minor changes. Such behavior is probably due to the microscopic inhomogeneity of the near-critical fluid—a property sheared by all supercritical fluids. As discussed in the introduction, a supercritical fluid may be considered

macroscopically homogeneous (remaining one phase regardless of pressure) but

microscopically inhomogeneous, especially in the near-critical density region.

Although the solvent environment is highly dynamic, on the average the fluid in

the near-critical region can be viewed as consisting of solvent clusters and free

volumes that possess liquid-like and gas-like properties, respectively. Changes

in bulk density through compression primarily correspond to decreases in the

free volumes, leaving solute–solvent interactions in the solvent clusters largely

unaffected (Figure 17b). This explains the insensitivity of the responses of the

probe molecules to changes in bulk density in the near-critical region. Above

a reduced density of about 1.5, the free volumes become less significant (consumed), and additional increases in bulk density again affect the microscopic

solvation environment of the probe. The solvation in the liquid-like region at

high densities should be similar to that in a compressed normal liquid solvent

(Figure 17c).



Copyright 2002 by Marcel Dekker. All Rights Reserved.