13778
J. Phys. Chem. 1995,99, 13778-13786
Quantitative Spectroscopic Investigation of Enhanced Excited State Complex Formation in Supercritical Carbon Dioxide under Near-Critical Conditions: Inconsistency between Experimental Evidence and Classical Photophysical Mechanism Ya-Ping Sun* and Christopher E. Bunker Department of Chemistry, Howard L. Hunter Chemistry Laboratory, Clemson University, Clemson, South Carolina 29634-1905 Received: March 16, 1995; In Final Form: June 8, 1 9 9 9
Fluorescence spectra and quantum yields of pyrene in supercritical C02 are determined systematically as functions of temperature, CO2 density, and pyrene concentration. Under near-critical conditions, contributions of the pyrene excimer emission in observed fluorescence spectra are abnormally large. The results cannot be explained in the context of the classical photophysical mechanism well-established for pyrene in normal liquid solvents. It is thus demonstrated experimentally that the photophysical behavior of pyrene in a supercritical fluid is indeed unusual. The experimental results can be rationalized with a proposal that the local concentration of pyrene monomer in the vicinity of an excited pyrene molecule is higher than the bulk in a supercritical solvent environment. It is shown that the calculated ratios between the local and bulk concentrations deviate from unity more significantly under near-critical conditions. The implication of the proposed local solute concentration augmentation to the issue of solute-solute clustering in supercritical fluids is discussed.
Introduction Supercritical fluids are unique solvent systems which have found widespread applications,'-2especially in separation and ~hromatography.~The most important properties of a supercritical fluid include low densities and so-called clustering effects. The densities of a supercritical fluid are between those of a gas and a normal liquid and are easily tunable with a variation of experimental conditions. The high molecular diffusivities as a result of low fluid densities have profound effects on diffusion-controlled chemical processes in supercritical fluids. Two kinds of clustering effects (solute-solvent and solute-solute) in supercritical fluids have been considered. The solute-solvent clustering refers to a phenomenon in which the local density of solvent molecules in the vicinity of a solute molecule is higher than the bulk in a supercritical fluid s ~ l u t i o n . ~Experimental -~ evidence for the clustering behavior includes observations that the solvent effect experienced by a solute in a supercritical fluid solution as probed experimentally is more significant than what is predicted using the bulk properties of the f l ~ i d . ~ -The ' ~ clustering behavior is strongly dependent on the fluid density. For a correlation of extensive spectroscopic and solubility results in supercritical fluids, theoretical models have been developed to establish the microscopic bases of solute-solvent interactions in supercritical fluid solution^.^^'^-'^ Altematively, experimental observations concerning the characteristic behavior of molecular probes in supercritical fluid solutions can also be accounted for by an empirical three-density-region solvation model' ',I4 which is based on a pictorial description of the microstructure of nearcritical fluids.20 It seems that the existence of solute-solvent clustering in supercritical fluid solutions is widely recognized. However, the issue concerning the existence and definition of solute-solute clustering is still somewhat controversial in supercritical fluid research. It was found2' that the presence of a small amount of liquid cosolvent can dramatically increase the solubility of solids in @Abstractpublished in Advance ACS Absfrucfs, September 1, 1995.
0022-365419512099-13778$09.00/0
supercritical fluids. Similarly, it was reported7a that there are preferred interactions between the solute and cosolvent molecules. These results served as the precursor for the concept of solute-solute clustering in supercritical fluids.22 In a fluorescence study of excited state complexes, Eckert and coworkers o b ~ e r v e dthat ~ ~ the , ~ ~formation of pyrene excimer and naphthalene-triethylamine exciplex happens at much lower concentrations in supercritical fluids than in normal liquid solvents. It was proposed that the unusual excited state complex formation is due to enhanced interactions of solute molecules in a supercritical solvent environment. Subsequently, observation of solute-solute clustering in supercritical fluids has been reported for other system^.^^,^^ The existence of solute-solute clustering has also been supported by results from theoretical c a l c u l a t i ~ n s . ' ~ ~ 'However, ~ ~ ' ~ ~ ~ ~there ~ ~ ~ are also other experimental studies that show no unusual solute-solute interactions in supercritical f l ~ i d s . ~ ~ -For ~ O pyrene excimer formation, Bright and c o - w o r k e r ~carried ~ ~ . ~ ~out time-resolved fluorescence studies and concluded that the observed efficient pyrene excimer formation in supercritical COz is simply due to efficient diffusion as a result of low viscosities in the fluid. But they also reported3' that the excimer formation in supercritical fluoroform or a CO2-polar cosolvent system is up to an order of magnitude slower than the diffusion-controlled limit. Recently, there was a suggestion30 that the time scale of the concerned reaction process may also play a significant role. It was proposed that a reaction must occur on a time scale comparable to the time scale that the local environment maintains its integrity for it to be influenced by that environment. Following our earlier work on the subject,32we have carried out comprehensive fluorescence spectral and quantum yield studies of excited state complexes in supercritical fluids. In this paper, we report that the formation of pyrene excimer in supercritical C02 does not follow the prediction of the classical photophysical model commonly used in normal liquid solvents if the diffusion-controlled rate constant is expressed in terms of the Debye equation. It is thus established experimentally that the photophysical behavior of pyrene is indeed unusual in 0 1995 American Chemical Society
Complex Formation in Supercritical Carbon Dioxide supercritical C02 with respect to that in normal liquid solvents. It is shown that the results can be rationalized with a proposal that the local concentration of pyrene monomer in the vicinity of an excited pyrene molecule is higher than the bulk in the supercritical solvent environment, and the calculated ratios between the local and bulk concentrations deviate from unity more significantly under near-critical conditions. The implication of the proposed local solute concentration augmentation to the issue of solute-solute clustering in supercritical fluids is discussed.
Experimental Section Materials. Pyrene (Aldrich, 99%) was purified through repeated recrystallization from hexane. Hexane (Burdick & Jackson, spectrophotometry grade) was used as received. Carbon dioxide (AirProducts, 99.9999%) was purified by being passed through a column filled with silica gel and activated carbon and repeatedly through oxygen traps (Alltech Associates) to remove trace amounts of oxygen. It is estimated that the oxygen content of the carbon dioxide used in all measurements is lower than 1 ppm. Measurements. Absorption spectra were measured on a computer-controlled Shimadzu UV-2101PC spectrophotometer. Fluorescence and fluorescence excitation spectra were recorded on a Spex Fluorolog-2 photon-counting emission spectrometer equipped with a 450 W xenon source and a R928 photomultiplier tube in a cooled housing. A right-angle geometry was used in fluorescence measurements. Unless specified otherwise, the fluorescence spectra were corrected for nonlinear instrumental response of the emission spectrometer using predetermined correction factors. The fluorescence excitation spectra were recorded using the ratio mode of the instrument and corrected using predetermined excitation correction factors. The fluorescence quantum yields were determined using 9-cyanoanthracene (CJF = 1.0 in hexane)33as a standard. Fluorescence quantum yields of 9-cyanoanthracene in hexane and in supercritical C02 at reduced densities higher than 0.8 are very close. The experimental conditions for spectral measurements of the standard and the samples were kept the same. The absorption and fluorescence spectra of the standard and samples were measured in the same optical cells at the same geometry (following the established principle for fluorescence quantum yield measurement^^^). It was found that fluorescence spectra of pyrene in supercritical C02 are excitation wavelength independent. Therefore, fluorescence quantum yield measurements were carried out by adjusting excitation wavelengths in the 325-340 nm range for pyrene solutions of different concentrations, so as to maintain the optically thin condition (absorbance at the excitation wavelength < 0.1). The high-pressure setup for spectroscopic studies in supercritical C02 is similar to the one reported p r e v i o u ~ l y . ~The ~ system pressure was generated by a Teflon-packed syringe pump (High Pressure Equipment Co., 87-6-5) and monitored by a precision pressure gauge (Dresser Industries, Heise-901A). The calibrated accuracy of the pressure gauge is better than f l psia at 1100 psia. The system temperature was controlled and monitored by an RTD temperature controller (Omega, 4200A) coupled with a pair of cartridge heaters (Gaumer, 150 W) inserted into the optical cell body. Most fluorescence spectral and quantum yield measurements were carried out using a cubic shape high-pressure optical cell made from stainless steel. The cell chamber (calibrated volume 1.87 mL) consists of four channels which open at the four side walls of the cell. Three of the channels are for accommodating optical windows, and the fourth one is for cell cleaning. The three quartz windows (12.7 mm diameter and 5 mm thick) are sealed using Teflon
J. Phys. Chem., Vol. 99,No. 38, 1995 13779 O-rings. The optical paths of the cell for absorption (180") and fluorescence (90") measurements are 30.5 mm (calibrated) and 7.5 mm, respectively. Absorption spectra for determining solubilities as a function of C02 densities were obtained using a cylindrical high-pressure optical cell. The stainless steel cell has two openings at 180" to accommodate two quartz windows (25.4 mm diameter and 9.5 mm thick). The windows are also sealed using Teflon O-rings. The cylindrical cell was also used in measurements of the excitation spectra of concentrated pyrene solutions. The front surface geometry of the emission spectrometer (22.5" angle between the excitation and emission light beams) was used in order to minimize inner-filter effects. For sample preparation, a pyrene solution of known concentration in hexane was loaded into the optical cell, followed by evaporation of the solvent with a slow stream of nitrogen gas. The cell was purged repeatedly with low-pressure nitrogen and C02 gases to eliminate trace amounts of oxygen trapped in the optical cell chamber and then sealed and thermostated at the desired temperature before C02 fluid was introduced. The actual pyrene concentration in the optical cell was verified spectroscopically using the predetermined molar absorptivities of pyrene in supercritical C02. Variations of experimental conditions were achieved by changing the system pressure and temperature. The densities of supercritical C02 were calculated from observed pressures and temperatures using a modified B W R equation of state.36 Experimental viscosity values of supercritical COZare available at selected temperatures and pressure^.^' Interpolation for obtaining the values under our experimental conditions were made using the empirical equation due to Jossi, Stiel, and Thodos,38
where 7;1 and vo are viscosities of the fluid and low pressure gas, respectively, Pc and Tc are the critical parameters, M is the fluid molecular weight, and er is reduced density. The parameters ai in eq 1 generalized for nonpolar fluids are available in the l i t e r a t ~ r e . ~However, ~ in order to be more accurate specifically for C02 under our experimental conditions, the parameters were obtained from the experimental viscosity data through a least-squares regression. For C02 in the temperature range 35-57 "C and pressure up to 400 bar,37the parameters are a0 = 0.9975, al = 0.2061, a2 = 0.6998, a3 = -0.5258, and a4 = 0.1372. The result of regression is shown in Figure 1. Data Treatment. With the formation of pyrene excimer, the observed fluorescence spectra are mixtures of the monomer and excimer emission bands. An overlapping of the two emission bands makes a quantitative determination of their relative contributions in the observed spectra somewhat difficult, especially at low pyrene concentrations where contributions of the excimer emission are relatively small. At constant temperature and density, relative contributions of the monomer and excimer emissions in the observed fluorescence spectra vary with pyrene concentration, but spectral profiles of the two underlying emission bands remain unchanged. Therefore, this is an ideal case for an application of the chemometric method principal component a n a l y s i ~ . A ~ ~detailed . ~ ~ description of the method can be found elsewhere.@ Briefly, principal component analysis allows a representation of a complicated linear system in a simplified coordinate established on the basis of the principal eigenvectors of the system. In the analysis of the
Sun and Bunker
13780 J. Phys. Chem., Vol. 99, No. 38, 1995 I
/I 0.8
Y u 0.6 L
3
0.4
+ " k-,e
0
F
-
F
Y
0.7
1.4
350
2.1
Figure 1. Result of fitting experimental CO2 viscosity data to the
500
550
600
-
fluorescence spectral mixtures in this study, a series of observed fluorescence spectra that consist of varying contributions of the monomer and excimer emissions are used to form a data matrix Y. Two significant eigenvectors VI and V 2 are obtained from a treatment of the matrix using principal component analysis. Within experimental uncertainties, an observed fluorescence spectrum Y , can be represented as a combination of the two eigenvectors,
the wavelength region of longer than 400 nm only can be treated in the same way as described above, yielding ( x D ~ / x M ~ ) ~ > ~nm. w The ratio X D ~ / X Mcan ~ be calculated as follows,
where r is a factor that can be obtained from integrated areas over the full and a portion (A > 400 nm) of the pure monomer and excimer fluorescence spectra.43b
(3) where and . 5 2 are combination coefficients. The pure monomer and excimer fluorescence spectra can also be represented by eq 3 using two sets of combination coefficients (6MI96M2)and ( & J ~ , ~ D Z )respectively. , The monomer spectrum is available experimentally, and the coefficients ~ D and I 6 ~ for the excimer spectrum are determined using a known spectral property. Due to a distribution of transitions from the excimer state to the repulsive part of the ground state potential energy curve, the shape of the excimer emission band can be best approximated as a Gaussian (on the wavenumber scale), -
450
Figure 2. Fluorescence spectra of pyrene in supercritical CO1 (1180 psia and 35 "C) at concentrations of 1.7 x M (-), 3.5 x M (- - -), and 6.2 x M (- -). The insert is the dependence of Py values on CO:, densities for a dilute pyrene solution at 35 "C.
Jossi-Stiel-Thodos equation (eq 1).
zD(ij) = (o/JT)"~ exp[-a(ij
400
WAVELENGTH ( n m )
REDUCED DENSITY
(4)
where u and Fmaxare the two parameters of a Gaussian function. The coefficients 601 and 6 D 2 are obtained from a least-squares regression by requiring that the excimer spectrum from eq 3 be best fitted to the Gaussian function in eq 4.43aUpon the pure monomer and excimer fluorescence spectra becoming available, their relative contributions in the observed fluorescence spectral mixtures are easily determined using the combination coefficients.
where XD~/,XM~represents the ratio of excimer and monomer emission contributions. For the observed fluorescence spectra at different densities, the underlying monomer spectral profile varies due to changes in the relative intensities of the vibronic bands. A direct application of the principal component analysis method is conceptually not feasible because the system is nonlinear. However, it can be assumed that the monomer spectral changes are primarily at the structured portion of the spectrum.@ Thus, a data matrix consisting of observed fluorescence spectra for
Results 2
Emission Spectra and Quantum Yields. In C02, pyrene fluorescence spectra are similar to those observed in roomtemperature solvents such as cyclohexane (Figure 2). For the monomer spectrum at a very low pyrene concentration, the relative intensities of the vibronic bands are sensitive to fluid d e n ~ i t y . ~ ~As. ' C~ 0. 2~ density ~ increases, the intensity ratio of the first ZI and the third 13 vibronic bands (often called Py scale4) becomes larger as a result of increasing solvent dielectric field. In the low-density gaslike region of the fluid (er< -OS), the Py values increase rapidly with increasing C 0 2 density.I4 However, in the near-critical density region (-0.5 < er < -lS), the Py values are much less sensitive to C 0 2 density change^.^^,^^ The fluorescence spectra exhibit contributions from excimer at pyrene concentrations as low as 5 x M, which is more than 2 orders of magnitude lower than those required for excimer formation in normal liquid solvents. The excimer band is Gaussian-like (Figure 2 ) and overlaps with the monomer spectrum. The relative contributions of pyrene monomer and excimer emissions to the observed fluorescence spectra are determined using the principal component analysis method. The fluorescence spectra are excitation wavelength independent, except for those at low COZ densities (er < 0.4) due to interference of pyrene microcrystals. The monomer fluorescence excitation spectrum at a very low pyrene concentration is close to the corresponding absorption spectrum. For a comparison of the monomer and excimer fluorescence excitation spectra, special experimental conditions are required because of the high pyrene concentrations. At a pyrene concentration of only 1 x loT5M and an optical path length of 1 cm, there is nearly no light transmission at the first intense absorption band. Thus, measurements of the fluorescence excitation spectra are subject to severe inner-filter effect^.^^.^',^^^ Even with the use of the front surface geometry in the emission spectrometer (a 22.5" angle between the exciting and emitting beams), the observed fluorescence excitation spectra for a pyrene solution
Complex Formation in Supercritical Carbon Dioxide
A
m
I\ i
e/ f
J. Phys. Chem., Vol. 99,No. 38, 1995 13781
0'5 0.4
W
0.3 .
t? V
z W
V
m
2
0.2
0
P
0
2 280
300 320 340 WAVELENGTH ( n m )
Figure 3. Fluorescence excitation spectra of pyrene in supercritical
COz (1180 psia and 35 "C) at a concentration of 3.5 x M with the monitored emission wavelengths of 390 nm (- - -) and 470 nm
-
(- -). The absorption spectrum (-)
obtained under the same conditions
I 1
2
0.1
.
'
0.0 1.0
1.2
1.4
1.6
1.8
REDUCED DENSITY
Figure 4. Fluorescence quantum yields of pyrene in supercritical COz (35 "C) at concentrations of 2 x M (0)and 6 x M (total, 0 ;monomer, A; and excimer, v)as a function of CO2 reduced densities.
is also shown for comparison.
of only 2 x M are still distorted significantly due to selfabsorption. The fact is that in a front surface geometry the observed spectra are a collection of emissions from molecules located at different distances from the front surface in the optical cell. Emission contributions from those molecules further away from the front surface are subject to more severe inner-filter effects. In order to eliminate the effects completely, a cell with a short optical path is required. For a pyrene solution of 2 x lov5M, the optical path length should be less than 1 mm. Due to constraints associated with high-pressure operating conditions, designing a cell with such a short optical path is difficult. Thus, in this study, the requirement of a short optical path in measurements of fluorescence excitation spectra of concentrated pyrene solutions is satisfied by adjusting the position of the optical cell in the emission spectrometer. The optimization of the cell position is such that only a thin layer of the sample near the front surface of the cell can be seen by the detector. The excitation spectra thus obtained are nearly free from innerfilter effects. At a pyrene concentration of 3.5 x M, the excitation spectra obtained by monitoring at the monomer (390 nm) and excimer (470 nm) fluorescence bands are the same (Figure 3).45 They are also in excellent agreement with the pyrene absorption spectrum obtained under the same experimental conditions (Figure 3). However, at a higher pyrene concentration such as 6 x lop5M, the requirement for the cell position becomes so extreme that a precise execution of the approach becomes very difficult. The fluorescence excitation spectra obtained at higher pyrene concentrations are still influenced by residual inner-filter effects. Fluorescence quantum yields of pyrene in C02 are determined using 9-cyanoanthracene (@F = l.0)33as a reference. The yield of the monomer in a very dilute solution is 0.34 f 0.05. Further treatment of the C02 fluid by repeatedly passing through oxygen traps has little effect on the result. Density Dependence. Fluorescence quantum yields are also determined as a function of C02 density. For a dilute pyrene solution of 2 x M, for which excimer formation is negligible, the observed fluorescence yields increase slightly with increasing COZ density (Figure 4). At higher pyrene concentrations, contributions of excimer emission become significant, and total fluorescence yields decrease slightly with increasing C02 density (Figure 4). As a result of separating the spectral mixtures of the monomer and excimer emissions using the principal component analysis method, fluorescence yields of the monomer and excimer are determined quantitatively. The monomer fluorescence yields at a pyrene
0
1.5
'
0.0 0.5
1 .o
I
1.5
2.0
REDUCED DENSITY Figure 5. Ratios of pyrene excimer and monomer fluorescence quantum yields as a function of COz reduced densities at 35 "C (6.2 x and 6.8 x M, 0). M, 0) and 50 "C (5.9 x
concentration of 6 x l W 5 M are smaller than those at a much lower pyrene concentration of 2 x M (Figure 4). However, the density dependencies of the yields at the two pyrene concentrations are similar. As shown in Figure 4,the excimer emission yields @m decrease more rapidly with increasing C02 density. Relative fluorescence yields of the monomer and excimer @FD/@'FMare also obtained as a function of C02 density at different temperatures (Figure 5). The ratios @&@)M decrease with increasing C02 density in the region of reduced density larger than -0.9 at 35 "C and -0.7 at 50 "C, respectively. There is a clear difference in the density dependencies of the relative yields at the two temperatures. At 35 "C, a temperature closer to the critical temperature of C02 (31 "C), the decrease in the ratio @'FD/@m with increasing C02 density is more significant than that at 50 "C. Similar observations have also been reported p r e v i o ~ s l y . ~However, ~~~* with the use of the chemometric method, the results presented here are more quantitative and amenable to further treatments in terms of mechanistic models. At low densities, the added pyrene is not completely dissolved due to saturation of the supercritical fluid solution. The ratio appears to increase with increasing C02 density at 35 "C as a result of increasing pyrene solubility (Figure 5). At 50 "C, the added pyrene sample becomes completely soluble at a lower C02 density. Solubility. Solubilities of pyrene in C02 are determined as a function of density at 40 "C using observed absorbances. The molar absorptivities at different vibrational bands of the pyrene
Sun and Bunker
13782 J. Phys. Chem., Vol. 99, No. 38, 1995
O"O
r-----. 1.2
0
5E 0.8 Ls
0
0
8 0.00 0 . 2 0.4 0.6 0.8 1.0 1.2 1.4 1 . 6 REDUCED D E N S I T Y Figure 6. Pyrene solubilities as a function of CO2 reduced densities at 40 "C. The dashed line represents the concentration corresponding to the amount of pyrene sample added to the optical cell.
0.4
0.0 0.00 0.02 0.04 0.06 0.08 0.10 CONCENTRATION (mM) Figure 8. Ratios of the excimer and monomer fluorescence quantum yields as a function of pyrene concentrations at 35 "C and COz reduced The lines are from linear least-squares densities of 1.1 (0)and 1.4 (0). regressions. The ratio of slopes is 3.25. 2.0
1.5
i
0
oAoo
I
I
w
2
2
0.4
0.5
no 0.4
0.8
1.2
1.6
2.0
REDUCED DENSITY
CONCENTRATION ( m M ) Figure 7. Fluorescence quantum yields (total, 0; monomer, 0; and excimer, A ) as a function of pyrene concentrations in supercritical COZ at 35 "C and reduced densities of 1.1 (A) and 1.4 (B).
Figure 9. Ratios of excimer and monomer fluorescence quantum yields as a function of COz reduced densities at pyrene concentrations of 2.2 x M (35 M (40 "C, A), 2.8 x IO+ M (35 O C , 0), and 6.2 x "C, 0). The dashed line represents the solubility curve of pyrene in CO2 obtained from Figure 6.
As shown in Figure 8, the increase of @m/@mwith increasing pyrene concentration is much more significant at the reduced density 1.1 than at 1.4. A systematic comparison of pyrene concentration dependencies of the fluorescence quantum yield ratios @FD/@FM at different C02 densities is shown in Figure 9. At a pyrene concentration of 6.2 x M, the increase of the ratio @FD/ @FM with increasing C02 density in the region of reduced density less than -0.9 is due to solubility changes.
absorption spectrum are slightly C02 density dependent. The dependencies are characterized by using a dilute pyrene solution, in which the added pyrene sample becomes completely soluble at a low C02 density. Therefore, density dependencies of the molar absorptivities are determined from density dependencies of the observed absorbances upon the sample being completely soluble. The results are then used in the determination of pyrene solubilities at different C02 reduced densities. In the absorbance measurements, the first intense absorption band (327 nm) was Discussion used at low COz densities where the solution is dilute, and the The dependence of pyrene excimer formation on CO:! density fourth band (290 nm) was used at high C02 densities where is characteristic. At low C02 densities, the increase of relative the solution becomes much more concentrated. The solubility fluorescence yields @ ~ / @ F M with increasing fluid densities is results thus obtained are shown in Figure 6 (the plateau at due to changes in pyrene solubility. As shown in Figure 9, the reduced densities of -1 and higher are due to the fact that the density dependence of the ratio @FDJ(D.FM at low C02 densities added amount of pyrene sample becomes completely soluble), with the solubility curve of pyrene in supercritical which are in general agreement with those in the l i t e r a t ~ r e . ~ ~ , ~coincides ~ C02. A higher pyrene concentration due to increasing solubility Concentration Dependence. Fluorescence quantum yields shifts the excited state equilibrium toward the excimer (Figure are also determined as a function of pyrene concentration at 10). With the amount of pyrene added to the optical cell constant COz reduced densities of 1.1 and 1.4 (35 "C). While M, the sample corresponding to a concentration of 6.2 x the total fluorescence yields are insensitive to changes in the becomes completely soluble at a C02 reduced density of -0.9 pyrene concentration, the monomer fluorescence yields decrease at 35 O C . The fluorescence quantum yield ratio @ m / @then ~ and excimer fluorescence yields increase with increasing pyrene decreases rapidly with increasing C02 density under the concentration (Figure 7). Consequently, the quantum yield condition of constant temperature (Figure 5). ratios @FD/@FM are strongly pyrene concentration dependent.
Complex Formation in Supercritical Carbon Dioxide
J. Phys. Chem., Vol. 99, No. 38, 1995 13783 slope in eq 9, the term k'FD/km is most likely the same at the two reduced densities. The fluorescence radiative rate constants are typically insensitive to changes in solvent environment, except for a correction due to the difference in solvent refractive i n d e ~ . The ~ ~ correction ~ , ~ ~ should be made to both km and ~ F D and is therefore canceled in the ratio. For pyrene monomer, one may argue that the lowest electronic transition is only weakly allowed, subject to solvent effects.44 The effects are reflected in the Py solvation scale. However, it is known that the Py values in COZ (Figure 2) and other supercritical fluids are insensitive to density changes in the near-critical density region.I4 Therefore, the transition probability should remain unchanged from the reduced density of 1.1 to 1.4. The other term in the slope of eq 9 can be rearranged as
ko = kFD + kiD K = (kDMhlD) = [D'Y[M'I[Ml
kM = ~ F M +k i ~
I E
MFigure 10. Photophysical mechanism commonly used for pyrene in ~ k i ~are overall nonradiative normal liquid ~ o l v e n t s , 4where ~ ~ ~ k~ i and rate constants (intemal conversion and intersystem crossing) of the excited monomer and excimer, respectively. The contribution of pyrene excimer emission is more significant at a density closer to the critical density. As shown in Figure 8, dependencies of the relative fluorescence quantum yields @'FD/@m on pyrene concentration are extremely different at the two COZreduced densities of 1.1 and 1.4. Although an increase in viscosity at a higher reduced density could affect the excimer formation, as indicated in the literature?8 the change in the diffusion rate constant from the COZreduced density of 1.1 to 1.4 is too small to account for the different dependencies of the @'FD/@m values on pyrene concentration (Figure 8). The photophysics of pyrene excimer formation and decay in normal liquid solvents is commonly described by the classical mechanism shown in Figure 10!7948 For pyrene in supercritical fluids, it was shownz8 that such a classical photophysical mechanism, along with a hydrodynamic expression of the diffusion rate constant (Debye equation), can also be used to explain the time-resolved fluorescence results in COz. It impliedz8 that the pyrene excimer formation in COZ and in normal liquid solvents are basically the same, except for the fact that the rate constants ~ M and D DM are nearly 2 orders of magnitude larger in CO2 than in normal liquid solvents. The conclusion based on these results left an impression that there is hardly anything unusual in the photophysical behavior of pyrene in supercritical COz when it is compared to that in normal liquid solvents. If the conclusion were correct, both fluorescence lifetime and quantum yield results should follow a single photophysical model. It is thus logical to examine the validity of the classical mechanism (Figure 10) in an explanation of the fluorescence quantum yield results presented here. By using the symbols in Figure 10, fluorescence quhtum yields of the are as follows$7 monomer @ p ~ h . ~and excimer
+
where ch = ( k ~ / k ~ ) [ ( kkp,f~)/kDM]. ~ The fluorescence quantum yield ratio is
= (kFD/kFM)[kDM/(kD+ kMD)lc
(9)
At constant temperature and COz density, eq 9 predicts that the fluorescence quantum yield ratio (PFD/@mlinearly depends on pyrene concentration, with slope of ( k F D / k w ) [ k ~ ~ l+ ( k~~M D ) ] . For the results shown in Figure 8, linear least-squares regressions yield slopes of 16 x lo3 and 4.9 x lo3 M-' at COZ reduced densities of 1.1 and 1.4, respectively. In the expression of the
kDMl(kD + kMD) = (kDM/kMD)/[l
=
+ K/[l
+ (kdkMD)l (lo)
In normal liquid solvents, the constant K for pyrene excited state equilibrium is virtually unchanged in very different solvents such as cyclohexane and ethan~l!~-~~ It is also k n o ~ n " 3 ~that ' in other excited state equilibria the density dependence of the equilibrium constants is nearly a plateau at reduced densities larger than 0.5 or so, even when the equilibria are strongly solvent dependent in normal liquid solvents. Thus, it can be concluded that the pyrene excited state equilibrium constant K remains essentially the same when the COZreduced density is changed from 1.1 to 1.4. The ratio of the slopes at the two reduced densities becomes
= [1 + (kdkMD)i.41/[1 + (kdkM~)i.il (1 1) where the subscript pred denotes the predicted ratio of slopes by the mechanism shown in Figure 10. In normal liquid solvents, k~ is comparable to kMD.47348However, ~ M becomes D much larger in supercritical fluids as a result of low viscosities.28 With kdkMD < 1 at both reduced densities of 1.1 and 1.4, we have (slo~ei.,/slo~ei,4)pre, = I1 + (k&~,)1,4I/[l
+ (kdkMD)l,ll
