B. Pyrene and the Py Scale

Several research groups have used pyrene as a fluorescent probe in the

study of supercritical fluid properties (2,3,40–48). In particular, the density dependence of the Py scale has been examined systematically in a number of

supercritical fluids such as CO2 (2,3,40–43,45,46), ethylene (40,41,47), fluoroform (3,40,41,43,47), and CO2 -fluoroform mixtures (43). The Py values obtained

in various supercritical fluids correlate well with the polarity or polarizability

parameters of the fluids (3,40,41,43,47). For example, Brennecke et al. (40)

found that the Py values obtained in fluoroform were consistently larger than

those obtained in CO2 , which were, in turn, consistently larger than those found

in ethylene over the entire density region examined. In addition, the Py values

obtained in the liquid-like region (reduced density ∼1.8) indicate that the local polarity of fluoroform is comparable to that of liquid methanol, CO2 with

xylenes, and ethane with simple aliphatic hydrocabons (15,16).

For the density dependence of solute–solvent interactions in supercritical

fluids, the Py values were found to increase with increasing density in a nonlinear

manner (2,3,40–43). For example, Sun et al. reported Py values in supercritical

CO2 over the reduced density (ρr ) range 0.025–1.9 at 45◦ C (Figure 5) (2). At

low densities (ρr < 0.5), the Py values are quite sensitive to density changes,

increasing rapidly with increasing density. However, at higher densities, the Py

values exhibit little variation with density over the ρr range ∼0.5–∼1.5, followed

by slow increases with density at ρr > 1.5. The nonlinear density dependence

was attributed to solvent clustering effects in the near-critical region of the



Figure 5 Py values in the vapor phase (᭿) and CO2 at 45◦ C with excitation at 314 nm

(᭺) and 334 nm (᭝). (From Ref. 2.)



Copyright 2002 by Marcel Dekker. All Rights Reserved.



supercritical fluid. Quantitatively, the clustering effects were evaluated using the

dielectric cross-term f (ε, n2 ) (2):

f (ε, n2 ) = [(ε − 1)/(2ε + 1)] ∗ [(n2 − 1)/(2n2 + 1)]



(2)



Extrapolation of the data obtained in the liquid-like region to the gas-phase

values confirmed that significant deviation of the experimental data from the

prediction of Eq. (2) for the low-density region of supercritical CO2 was occurring (Figure 6). The results are consistent with those obtained from investigations

using other polarity-sensitive molecular probes. It appears that the largest deviation (or the maximum clustering effect) occurs at a reduced density of about

0.5 rather than at the critical density, as was naturally assumed (40,42,43).

The investigation of high-critical-temperature supercritical fluids is a more

challenging task. One of the significant difficulties associated with these studies is probe-molecule thermal stability; many molecular probes commonly used

with ambient supercritical fluids decompose at the temperatures required by

these high-critical-temperature fluids. Fortunately, pyrene can be employed for

such tasks. Several reports have been made of the use of pyrene as a molecular probe to investigate solute–solvent interactions in high-critical-temperature

supercritical fluids (e.g., pentane, hexane, heptane, octane, cyclohexane, methcyclohexane, benzene, toluene, and water) (44,48,49). In supercritical hexane



Figure 6 Py values in CO2 at 45◦ C plotted against a dielectric cross term f (ε, n2 ).

The line, Py = 0.48 + 0.02125 f (ε, n2 ), is a reference relationship for the calculation

of local densities. (From Ref. 2.)



Copyright 2002 by Marcel Dekker. All Rights Reserved.



Figure 7 Pyrene fluorescence excitation spectral shifts (᭺), and hexane C-H Raman

shifts (ᮀ) and Raman intensities (᭞) in supercritical hexane at 245◦ C. The y axis represents normalized spectral responses, with Z G being the spectral response obtained in the

gas phase, Z C the spectral response at the critical density, and Z the observed responses.

(From Ref. 49).



the pyrene fluorescence spectrum is very broad, lacking the characteristic structural detail observed in the room-temperature spectrum (49). The fluorescence

spectrum for low and high densities is essentially the same; however, the fluorescence excitation spectrum maintains its characteristic vibronic structure and

displays a small but measurable red shift with increasing fluid density (49). A

plot of the fluorescence excitation spectral maximum as a function of the reduced density of supercritical hexane (Figure 7) shows the same characteristic

pattern observed for pyrene in supercritical CO2 (2,3); and the results can be

explained in terms of the three-density-region solvation model (1–3). It appears

that even in the high-temperature supercritical fluids, solute–solvent clustering is

prevalent. This is supported by results obtained from the investigation of supercritical hexane using Raman spectroscopy, where the spectral shifts and relative

intensities of the C-H stretch transition of hexane were measured at different

densities (Figure 7) (49).

C. TICT State Probes

Molecules that form a TICT state serve as excellent probes to elucidate solute–

solvent interactions in condensed media (17). Upon photoexcitation, the excitedstate processes of TICT molecules in polar solvents are characterized by a ther-



Copyright 2002 by Marcel Dekker. All Rights Reserved.



modynamic equilibrium between the locally excited (LE) singlet state and the

TICT state (Figure 8) (50). Because of the two excited states, TICT molecules

often exhibit dual fluorescence, with the fluorescence band due to the TICT

state being extremely sensitive to solvent polarity. The spectral shifts of the

TICT emission band can be used to establish a polarity scale similar to the Py

and π∗ scales.



Structure 3



Kajimoto et al. used the classic TICT molecule p-(N ,N -dimethylamino)

benzonitrile (DMABN) to investigate solute–solvent interactions in supercritical

fluoroform (51–54) and ethane (55). In fluoroform, the TICT emission was

readily observed. The emission band shifted to the red with increasing fluoroform

density. The shift was accompanied by an increase in the relative contribution

of the TICT emission to the observed total fluorescence (Figure 9) (51). The

solvent effects were evaluated by plotting the shift in the TICT band maximum

as a function of the dielectric cross-term [Eq. (2)]:

P = [(ε − 1)/(ε + 2)] − [(n2 − 1)/(n2 + 2)]



(3)



The shifts of the TICT band maximum in normal liquid solvents correlated

well with those of P , confirming the linear relationship predicted by classical continuum theory. However, the results in supercritical fluoroform deviated



Copyright 2002 by Marcel Dekker. All Rights Reserved.



Figure 8 Energy diagram for the formation and decay of a TICT state in DEAEB and

related molecules. The coordinate is for the twisting of amino-phenyl linkage. The diagram represents a mechanism in which fast and slow emission processes are considered.

The fast process is restricted in the region surrounded by dashed lines. (From Ref. 50.)



significantly from the relationship, indicating that the effective polarities in supercritical fluoroform were significantly larger than expected (Figure 10) (51).

According to Kajimoto et al. (51), the deviation may be attributed to unusual

solute–solvent interactions (or solute–solvent clustering) in supercritical fluid

solutions. From the results at low fluid densities, they were able to determine

the number of solvent molecules about the solute using a simple model with

solute–solvent interaction potentials (51,52,54,55).

Sun et al. carried out a more systematic investigation of the TICT molecules

DMABN and ethyl p-(N ,N -dimethylamino)benzoate (DMAEB) in supercritical

fluoroform, CO2 , and ethane as a function of fluid density (1). They found

that the absorption and TICT emission spectral maxima shifted to the red with

increasing fluid density. The results were comparable to those reported by Kajimoto et al. (51–55). More importantly, the spectral shifts and the fractional

contribution of the TICT state emission changed with fluid density following the

characteristic three-density-region pattern (Figures 11 and 12) (1). In fact, these

results furnished the impetus for the development of the three-density-region solvation model for solute–solvent interactions in supercritical fluid solutions (2,3).



Copyright 2002 by Marcel Dekker. All Rights Reserved.



Figure 9 Dependence of the relative intensity of the CT emission of DMABN on the

density of the supercritical solvent, CF3 H (in g/mL). (From Ref. 51.)



Another TICT molecule, ethyl p-(N ,N -diethylamino)benzoate (DEAEB),

was used to probe solute–solvent interactions in supercritical ethane, CO2 , and

fluoroform (3,50,56). Unlike DMABN and DMAEB, DEAEB forms a TICT

state even in nonpolar solvents (Figure 13) (50), resulting in dual fluorescence

emissions. Because of the excited-state thermodynamic equilibrium, the relative

intensities (or fluorescence quantum yields) of the LE-state (xLE ) and TICT-state

(xTICT ) emissions may be correlated with the enthalpy ( H ) and entropy ( S)

differences between the two excited states:

K = (xTICT /xLE )(kF,LE )/(kF,TICT )

ln(xTICT /xLE ) = − H /RT +



S/R + ln[(kF,TICT )/(kF,LE )]



(4)

(5)



where kF,LE and kF,TICT are the radiative rate constants of the two excited states.

If solvent effects on the entropy difference are assumed to be negligible, the

relative contributions of the LE-state and TICT-state emissions are dependent

primarily on the enthalpy difference H . The energy gap between the two excited states is obviously dependent on solvent polarity because the highly polar

TICT state is more favorably solvated than the LE state in a polar or polarizable

solvent environment. Thus, ln(xTICT /xLE ) serves as a sensitive measure for the

solvent-induced stabilization of the TICT state (Figure 14) (3). For DEAEB in

the supercritical fluids (ethane in particular), the LE and TICT emission bands



Copyright 2002 by Marcel Dekker. All Rights Reserved.



Figure 10 Shift of the maximum of the CT emission as a function of the polar parameter of the solvent. The open circle shows the data obtained in the liquid solvent: (1) bromobenzene, (2) n-butyl chloride, (3) THF, (4) butylnitrile, (5) cyclohexanol, (6) ethanol,

and (7) methanol. The solid circles represent the results of the supercritical experiments.

The polar parameters for the supercritical fluid were calculated based on the reported

dielectric constants. (From Ref. 51.)



overlap significantly. A quantitative determination of the xTICT /xLE ratio as a

function of the fluid density requires the separation of overlapping fluorescence

spectral bands. In the work of Sun et al. (50,56), the spectral separation was

aided by the application of a chemometric method known as principal component analysis—self-modeling spectral resolution (57–62). As shown in Figure 14, the plot of ln(xTICT /xLE ) as a function of reduced density in supercritical

ethane again shows the characteristic three-density-region pattern, which validates the underlying concept of the three-density-region solvation model for

solute–solvent interactions in supercritical fluid solutions.

Other investigations of supercritical fluid systems have been conducted

using TICT and TICT-like molecules as probes. For example, DMABN and

DMAEB were used to study solvation in two-component supercritical fluid

mixtures (63). Another popular probe has been the highly fluorescent molecule



Copyright 2002 by Marcel Dekker. All Rights Reserved.



Figure 11 Bathochromic shifts of νTICT max (relative to the LE band maximum in the

absence of solvent, 330 nm) of DMAEB as a function of the reduced solvent density in

CHF3 at 28.0◦ C (ᮀ), in CO2 at 33.8◦ C (᭺), and in CO2 at 49.7◦ C (᭝). (From Ref. 1.)



6-propionyl-2-(dimethylamine)naphthalene (PRODAN). Although it shares the

structural features of the TICT molecules discussed above, PRODAN apparently

forms no TICT state upon photoexcitation; however, the fluorescence spectrum

of PRODAN does undergo extreme solvatochromic shifts. The shifts also correlate well with those of the TICT emissions (Figure 15), implying that the

emissive excited state of PRODAN is similar to a typical TICT state (64). The

strong solvatochromism of PRODAN was the basis for its use in the study of

solute–solvent interactions in supercritical CO2 and fluoroform and other supercritical fluid systems (3,65). In addition, PRODAN was also used as probe

for rotational reorientation in supercritical N2 O through fluorescence anisotropy

measurements (66).



Structure 4



Copyright 2002 by Marcel Dekker. All Rights Reserved.



Figure 12 Fractional contribution of the TICT state emission of DMAEB as a function

of the reduced solvent density in CHF3 at 28.0◦ C (ᮀ), in CO2 at 33.8◦ C (᭺), and in

CO2 at 49.7◦ C (᭝). (From Ref. 1.)



D. Other Systems and Methods

The π∗ , Py, and TICT solvation scales discussed above have been the basic techniques used in the investigation of solute–solvent interactions in supercritical

fluid solutions. In addition, other methods have been applied for the same purpose, including the use of unimolecular reactions and vibrational spectroscopy

and the probing of rotational diffusion; the results obtained have been important

to the understanding of the fundamental properties of supercritical fluids.

1. Unimolecular Reactions

Unimolecular reactions that have been used to investigate the solvation properties of supercritical fluids include tautomeric reactions (67–71), rotational isomerization reactions (72–78), and radical reactions (79–83). O’Shea et al. used

the tautomeric equilibrium of 4-(phenylazo)-1-naphthol to examine the solvent

strength in supercritical ethane, CO2 , and fluoroform and to determine its dependence on density (67). The equilibrium is strongly shifted to the azo tautomer in

supercritical ethane and the hydrazone tautomer in supercritical chloroform; and



Copyright 2002 by Marcel Dekker. All Rights Reserved.



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.