Photophysics of Phenanthrene in Supercritical Carbon Dioxide

J. Phys. Chem. 1996, 100, 17931-17939

17931

Photophysics of Phenanthrene in Supercritical Carbon Dioxide. Solvent-Solute and Solute-Solute Interactions Revealed by Lifetime Distribution Analysis Timothy A. Rhodes and Marye Anne Fox* Departments of Chemistry and Biochemistry, The UniVersity of Texas at Austin, Austin, Texas 78712-1167 ReceiVed: April 17, 1996; In Final Form: August 30, 1996X

The exponential series method of analysis is applied to single photon counting measurements of phenanthrene fluorescence decay in supercritical carbon dioxide at 32 and 35 °C and at pressures ranging from 76 to 207 bar for chromophore concentrations between 5 × 10-5 and 5 × 10-6 M. The analysis revealed trimodal fluorescence lifetime distributions near the critical temperature which can be explained by the presence of solvent-solute and solute-solute clustering. This local aggregation causes an increase in nonradiative relaxations and, therefore, a decrease in the observed fluorescence lifetimes. Concentration and density gradients are responsible for these three unique lifetimes (trimodal) in the supercritical fluid, as contrasted with the single lifetime observed in a typical organic solvent. An increase in temperature to 35 °C induces no change in lifetime distributions at high chromophore concentration, but the trimodal distribution collapses to a single mode at lower concentrations, indicating that the disappearance of solvent-solute and solutesolute clustering with an increase in temperature is dependent on local chromophore concentration. Furthermore, the pressure has little or no effect on the clustering over the pressure range studied along an isotherm.

Introduction Investigations of supercritical fluids at the molecular level have been fueled by their increased importance in industry as solvents for extraction and chromatography and because their unique “tunability” makes them an attractive alternative to organic solvents as a controllable reaction medium.1-3 Supercritical fluids’ unique behavior stems from the ability to alter their physical properties (e.g., density, viscosity, dielectric constant, and diffusivity) by varying the pressure and temperature, most notably near the critical point. The variable nature of supercritical fluids makes them useful for chromatography and for controlling selectivity among competing reactions. The specific noncovalent associations of a solute with its surrounding medium make up a microscopically heterogeneous environment responsible for the reactivity of the solute. Local solvent structure plays an important role in determining the structure and reactivity of a solute, and both theory and experiment suggest that solvent structure plays an even larger role in supercritical fluids.3-9 Spectroscopic transitions and reaction dynamics are affected by solvent structure, and studies using absorbance, fluorescence, NMR, ESR, and FTIR spectroscopies have been done to investigate the microscopic structure of supercritical fluids.2,10-15 The importance of intermolecular interactions between solvent-solute and solutesolute pairs is supported by these spectral data. Steady state absorbance measurements of solvatochromic probes have demonstrated that fluid density about an infinitely dilute solute molecule is greater than the bulk density.16,17 The shift in absorption maxima of p-(N,N-dimethylamino)benzonitrile and ethyl p-(N,N-dimethylamino)benzoate11,18 were similarly reported to display solvent-solute clustering. The observed pressure effects on the stereochemistry and regiochemistry of the photodimerization of isophorone19 and cyclohexenone20 similarly require such association. The kinetics of a Michael addition in supercritical fluoroform also show a density dependence consistent with enhanced solvent-solute clustering near X

Abstract published in AdVance ACS Abstracts, October 15, 1996.

S0022-3654(96)01124-0 CCC: $12.00

the critical point.21 Furthermore, it was concluded that the nonlinear kinetics of this reaction in supercritical ethane were consistent with enhanced solute-solute clustering, wherein the assumption of infinite dilution is necessarily invalid. Recent work on the methanol esterification of phthalic anhydride in supercritical carbon dioxide also shows evidence for solutesolute clustering,22 and time-resolved fluorescence measurements have demonstrated the unique density dependence of fluorescence kinetics in supercritical fluids.23 The reaction kinetic models applied in these studies were, in all cases, standard solution phase kinetic scenarios, the critical assumption being that the solute distribution is homogeneous. The presence of solvent-solute clustering does not necessarily negate the assumption of macroscopic homogeneity, but it does necessitate local heterogeneity. Heterogeneous solutions require the application of a different, more complex kinetic model. A traditional method for dealing with nonexponential kinetics is to fit the data with two or three exponential terms. These terms do not necessarily possess intrinsic physical meaning, because the same decay curve can often be fit equally well with other sets of terms. A recently developed technique treats the observed decay as a distribution of lifetimes without arbitrarily assuming the existence of two or three exponential terms. Lifetime distribution analyses employing this approach have been performed for micelles,24,25 fluorophores in viscous media,26,27 and surface kinetics28 using Gaussian or Lorentzian distributions as the relevant basis set. The use of an a priori model greatly simplifies the mathematical solution to these systems, but a unique theoretical justification is not always available. As a result, the simple lifetime distribution analysis is sometimes inapplicable. A general means of analysis that assumes no a priori knowledge about a system and that could be applied equally well to any system can offer an additional check when a theoretical model is available. This study investigates the density dependence of the multiexponential fluorescence decay rate constant of phenanthrene in supercritical carbon dioxide using time-resolved fluorescence © 1996 American Chemical Society

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Rhodes and Fox

spectroscopy. Recent progess in developing the utility of the exponential series method (ESM) allows for the analysis of nonexponential fluorescence decay curves without a welldefined knowledge of the mechanism of relaxation.29-33 This method is applied to our single photon counting measurements to yield fluorescence lifetime distributions of phenanthrene clusters near the critical point of carbon dioxide. The observed lifetime distributions reveal the importance of clustering in controlling excited-state dynamics. The Exponential Series Method The expression used to describe a continuous distribution of lifetimes is

I(t) ) ∫0 A(τ)e-t/τ dτ ∞

(1)

where I(t) is the fluorescence intensity at time t and A(τ) is the distribution of lifetimes τ. The solution to eq 1 can be approximated using a discrete function, as in eq 2 N

I(t) ) ∑aie-t/τi

(2)

i)1

where N is the number of exponential terms and ai are the preexponential factors for the observed lifetimes τi. A large sampling of lifetimes is essential to ensure that eq 2 approximates the continuous distribution of eq 1. In actuality, the observed fluorescence decay signal is described by neither eq 1 nor 2, but rather by the convolution of the instrument response function, L(t), with the decay of the system, I(t).

e(t) ) ∫0 L(t-t′) I(t) dt′ t

(3)

When the measurement is performed using the single photon counting technique,34 as is the case here, the detection is a series of discrete measurements at equally spaced time intervals described by eq 4 t

e(t) ) (∆t)∑L(t-i∆t) I(i∆t)

(4)

i)0

where the time interval, ∆t, can be scaled to ∆t ) 1. Equation 4 is equivalent to the general matrix equation

A‚x ) b

(5)

where A is the convolution matrix of the instrument response function, b is the observed decay, and x is the solution vector of preexponential terms to be obtained. A matrix equation of this type can be solved using the method of conjugate gradients,35 which minimizes the function g(x + Rr), where g(x) is

g(x) ) 1/2|A‚x - b|2

(6)

This function is minimized by iterative approximations of x using the equations for ∇g, the gradient of eq 6, and R, a step value for improving the solution vector, defined as

∇g(x) ) AT‚(A‚x - b) and

(7)

R)

-r‚∇g |A‚r|2

(8)

where AT is the transpose matrix of A and r is the residual of A‚x - b. The conjugate gradient method is applied to single photon counting measurements of fluorescence decays using 80-200 lifetime terms fixed at even intervals in log τ space,36 while varying the preexponential terms, ai in eq 2 or the solution vector x in eqs 5-8. The initial values for the preexponential terms are all the same: thus, no a priori knowledge is assumed. The iterative method inherently allows the preexponential terms to explore all real space. However, negative preexponential terms can be disallowed by setting them to zero as long as each additional iteration causes ai < 0. In addition, very long and very short lifetimes can be included in the fitting process to account for large dark currents and/or laser scattering, respectively. The exponential series method is the solution to eq 4 where a sum of exponential terms with fixed lifetimes can be fit to real data. It is essentially an iterative linear least-squares method of analysis, and in this case, the conjugate gradient method is employed to obtain the solution. Experimental Section High-Pressure Equipment. The time-resolved fluorescence measurements were made with two different high-pressure cells. One cell uses fiber optics for the excitation and detection and is constructed from a seven-port manifold (Valco Instruments Co., Inc.) with 1/8 in. fittings. The ports are used for fiber optics, inlet and outlet port, and temperature probe. The fiber optic is held in place using a 1/16 in. Valco stainless steel nut and 1/16 in. graphite ferrule in a 1/8 to 1/16 in. adapter. A heating cartridge mounted in a heating jacket surrounds the cell for even heating. A more detailed description of this high-pressure fiber-optic cell can be found elsewhere.37 The second high-pressure cell for fluorescence and absorbance measurements was constructed in-house from 316 stainless steel (Figure 1). It contains four sapphire windows (Insaco, 0.5 in. thick and 1.0 in. diameter) with an absorbance cutoff of 200 nm. The Teflon O-ring provides a pressure seal when the threaded cap is tightened. The cell contains four inlets for highpressure connections made by welding Valco 1/8 in. female plugs into place before drilling the clearance holes. This method provides the best leakproof method for making connections because the critical pressure seal components (nut, ferrule, and plug) are available commericially from the same source (Valco). This replaces a time-consuming and error-prone method in which the taper seals were machined to match the commercial nut and ferrules. The high-pressure connections allow for a temperature probe, inlet, and outlet using either 1/8 or 1/16 in. components (making use of an 1/8 to 1/16 in. adapter). The cell contains two fluid compartments. The inner compartment is the 15.0 mL sample chamber (4.0 cm path length) surrounded by a separate internal flow loop used for water bath temperature control. The pressure is measured using a Heise Model 901A pressure indicator with a range of 0-345 bar. The temperature is monitored and controlled in the cell with an Omega temperature controller and a temperature probe mounted in one of the highpressure ports. Heating is accomplished in the fiber-optic cell by a heating cartridge mounted in an aluminum heat distributor which surrounds the cell or by an external temperaturecontrolled water bath attached to the internal flow loop of the

Photophysics of Phenanthrene in Supercritical CO2

Figure 1. Side view and internal structural view of a high-pressure absorbance/fluorescence cell: (A) high-pressure inlets, (B) stainless steel cell body, (C) threaded cap for holding a sapphire window, (D) sapphire window, (E) flow loop for water bath temperature control, (F) Delran O-ring, (G) Teflon O-ring, and (H) sample compartment.

high-pressure cell (Figure 1). Pressure is generated using a High Pressure Equipment Co. pressure generator Model 87-6-5. Sample Preparation. Up to 80 µL of a 1 × 10-3 M solution of phenanthrene is injected with a syringe into the top port on the cell. After the solvent is allowed to evaporate (15 min), the cell is sealed, and oxygen and any remaining solvent are evacuated for 30 min using a high-vacuum pump inline. Carbon dioxide is then introduced to pressurize the cell. Pressure and temperature are maintained to within (0.25 bar and (0.1 °C, respectively. Experiments are performed along a particular isotherm and at constant molarity by starting at low pressure and increasing to high pressure. The cell is cleaned before each experiment by flushing with spectroscopic grade methanol several times, followed by a carbon dioxide purge and evacuation for 15 min. Materials. The carbon dioxide (Wilson Oxygen, Precision Aquaratic Grade, g99.99% purity) is used as received. Further purification by passing through an oxygen scrubber and activated carbon filter produced no change in the solvent absorbance or the fluorescence decay kinetics. Phenanthrene is recrystallized from hexanes (mp 97-97.5 °C). Phenanthrene (17.82 mg, Aldrich) is dissolved in acetonitrile (Mallinckrodt Spectral Grade) in a 10 mL volumetric flask to make a 1.00 × 10-2 M solution. The phenanthrene solution is diluted in a 10 mL volumetric flask to yield a 1.00 × 10-3 M solution. Measurements. Collection of Time-ResolVed Data. Timeresolved emission decay curves were obtained by single photon counting. Sample excitation was achieved with a 290 nm pulse (∼70 ps) generated using a 10 MHz cavity-dumped dye laser (Coherent) pumped by a frequency-doubled mode-locked Nd: YAG laser (Quanta Ray). Sample emission was collected over a 222 ns time scale with a monochromator and multichannel plate detector linked to a counter with 8192 bins. Analysis of Time-ResolVed Data. The single photon counting data were analyzed with software written in-house which uses the least-squares method and iterative reconvolution to account for the instrument response. Each decay trace was fit with 1, 2, and 3 exponentials. The goodness-of-fit is judged by the chi-squared value, the randomness of the weighted residuals, and the autocorrelation function. Preference is always given to the least number of exponentials required to obtain an acceptable fit. The exponential series method (ESM) was applied to the single photon counting data with Poisson statistics using software written in-house based on the above algorithm. It also

J. Phys. Chem., Vol. 100, No. 45, 1996 17933

Figure 2. Dependence of density of supercritical carbon dioxide on pressure at 32, 35, 40, and 50 °C.

uses the least-squares method and iterative reconvolution. The number of exponentials (2-300) and their spacing (normal or logarithmic) were used to generate a fitting matrix with preset fixed exponentials, allowing for a linear fitting algorithm. The starting distribution is set arbitrarily to ai ) 1/n, where ai is the preexponential for τi and n is the number of exponentials. Negative preexponentials are disallowed in all calculations. Physical Parameters of CO2. The critical parameters for carbon dioxide are Tc ) 31.0 °C, Pc ) 73.7 bar, and Fc ) 10.63 mol/L. The pressure-dependent densities can be calculated using an empirical equation developed for carbon dioxide in the critical region.10,38 An iterative method was used to calculate the density at each pressure. All density-dependent data are represented as Fr, the reduced density, defined as Fr ) F/Fc, where F is the calculated density and Fc is the critical density. Figure 2 depicts the pressure dependence of the density at the four isotherms investigated. Results Time-resolved fluorescence decay traces were measured for dilute solutions of phenanthrene in supercritical carbon dioxide at pressures ranging from 76 to 207 bar and from 32 to 50 °C at two concentrations, 5 × 10-6 and 5 × 10-5 M. The measurements taken at higher concentration were obtained using the high-pressure fiber-optic cell, whereas those at the lower concentration were made in the larger volume high-pressure cell. The second cell was employed in order to ensure that the experimental observations were real and not some artifact created by the experimental setup. Furthermore, the small volume and short path length of the fiber-optic cell made low concentration measurements difficult because of the decreased signal/noise ratio and long collection times. Measurements made in the fiber-optic cell had maximum signals from 1000 to 3000 counts in the peak channel with collection times ranging from 15 min to more than 1 h. All measurements in the large volume cell had maximum signals greater than 5000 counts in the peak channel. A typical fluorescence decay trace is shown in Figure 3. Figure 3a depicts the photon counting data (‚‚‚) along with the instrument response (-‚-) and the data fit using the exponential series method (s). Figure 3b-d depicts the residuals from the fits of the data using two exponentials, three exponentials, and the ESM, respectively. On the basis of the randomness of the residuals, it is clear that the two-exponential fit does not

17934 J. Phys. Chem., Vol. 100, No. 45, 1996

Figure 3. Fit of a typical decay of phenanthrene in supercritical carbon dioxide. (a) (‚‚‚) decay curve, (-‚-) laser profile, (s) ESM fit; (b) residuals for two-exponential fit; (c) residuals for three-exponential fit; (d) residuals for ESM fit.

sufficiently describe the decay process. However, a visual difference between the three-exponential and ESM fits is less apparent. It is important to remember that a visual inspection of the fit residuals is never sufficient to indicate the better of two fitting functions. Nor is the minimum chi-squared a sufficient selection criterion by itself. These factors must be considered together, especially since the large number of exponentials (three or more) precludes any real difference in either the residuals or the chisquared values. The assumption that a continuous distribution of lifetimes has more physical meaning than several discrete lifetimes must be invoked in order to select the “better” fitting routine, i.e., ESM instead of the triexponential fit. The reproducibility and reliability of the ESM results must be determined in order to establish the limitations of the method. Understanding these limitations is essential to avoiding overinterpretation of any obtained results. The limiting cases of the ESM method are best illustrated by the analysis results obtained from two different data sets (Figures 4 and 5). The distributions shown in Figure 4 were obtained for a solution near the critical point from data with 1 × 104 counts in the peak channel (1500 channels at 108 ps/channel). The ESM analysis was performed with 200 exponentials (Figure 4a) and 80 exponentials (Figure 4b) logarithmically spaced from 0.01 to 70 ns. Figure 4c is the result of a three-exponential fit of the same data using chi-squared minimization and unconstrained parameters (three lifetimes and three preexponential factors). The undeniable agreement between the three fitting methods suggests that the ESM fitting routine can handle data with an accuracy and quality comparable to that used in Figure 4. The

Rhodes and Fox

Figure 4. Lifetime distribution analysis of a phenanthrene fluorescence decay in supercritical CO2 (32 °C, 79.3 bar, 5 × 10-5 M, 1 × 104 counts, 1500 channels, 108 ps/channel) using ESM analysis with (a) 200 exponentials and (b) 80 exponentials and (c) using least-squares minimization with three exponential terms.

validity of these results is further warranted by the consistent regularity of the distributions. In order to ensure that the ESM method can distinguish between a distribution and two or more discrete lifetimes, the ESM analysis is applied to an artificial decay curve generated from three discrete lifetimes. The artificial decay curve is generated by the convolution of the three-exponential experimental fitting parameters in Figure 4c and the instrument response function, with Poisson noise added. ESM analysis is applied to this artificial curve to produce a distribution very close to the three discrete lifetimes corresponding to the parameters used in generating the decay and is easily distinguished from the distributions (Figure 4a,b). The distributions shown in Figure 5 were obtained from data with 3 × 103 counts in the peak channel (400 channels at 108 ps/channel) at conditions under which a supercritical fluid is formed. As before, the ESM analysis was performed with 200 exponentials (Figure 5a) and 80 exponentials (Figure 5b) logarithmically spaced from 0.01 to 70 ns. Figure 5c is the result of an unconstrained three-exponential fit. Clearly, the ESM routine had difficulty fitting the decay data. The lack of consistency and regularity suggests that the routine cannot resolve a distribution from low-quality data similar to that in Figure 5. Based on the quality limitations established for the exponential series method of analysis, the distributions presented in the remainder of the paper are derived from measurements that yield data of equal or higher quality than that found in Figure 4. Emission decay data were collected at four isotherms (32, 35, 40, and 50 °C) using 5 × 10-5 M concentration in the fiberoptic cell. This concentration exceeded solubility limits at 40


Figure 5. Lifetime distribution analysis of a phenanthrene fluorescence decay in supercritical CO2 (35 °C, 91.7 bar, 5 × 10-5 M, 3 × 103 counts, 400 channels, 108 ps/channel) using ESM analysis with (a) 200 exponentials and (b) 80 exponentials and (c) using least-squares minimization with three exponential terms.

and 50 °C over the pressure range studied, so those data were discarded. The fluorescence decay was measured at 32 °C, just above the critical temperature, and at several different pressures. Figure 6a-c represents the ESM analysis of data taken at 79.3, 89.7, and 160.0 bar, respectively. The trimodal (three centers) distributions are apparent over the entire pressure range as well as the decrease in the lifetime with increasing pressure. Increasing the temperature to 35 °C shows a somewhat similar trend. The ESM analysis of decays measured at 35 °C and 80.7, 94.5, and 164.8 bar is illustrated in Figure 7a-c. The trimodal distribution is clear at the lowest pressure, near the critical point, but a change to a bimodal distribution is observed upon increasing the pressure. The overall decrease in lifetime with an increase in pressure is again apparent. The measurements at lower concentration, 5 × 10-6 M, were done to demonstrate the generality of the distributions over a range of conditions. Figure 8a-c shows the ESM analyses of data collected at 32 °C and 77.7, 103.4, and 206.9 bar, respectively. Again, the trimodal distributions can be seen over the entire pressure range. The decrease in lifetimes with increasing pressure is less obvious than at the higher solute concentration. Figure 9a-c represents the ESM analyses of fluorescence decays measured at 35 °C and 75.9, 103.4, and 206.9 bar, respectively. Although the analyses yielded trimodal distributions, the distributions were dominated by a long lifetime component, with relatively small contributions from shorter lifetime components. Furthermore, the distributions are very similar over the entire pressure range studied.

J. Phys. Chem., Vol. 100, No. 45, 1996 17935

Figure 6. Lifetime distributions of phenanthrene fluorescence decays (5 × 10-5 M) in supercritical CO2 at 32 °C. ESM analysis using 150 exponentials (0.01-70 ns) at (a) 79.3 bar, Fr ) 1.2; (b) 89.7 bar, Fr ) 1.39; and (c) 160.0 bar, Fr ) 1.77.

Discussion The average fluorescence lifetime is defined as in eq 9:

τf )

1 kf + kIC + kISC + kq[Q]

(9)

where kf is the intrinsic radiative rate constant, kIC is the rate constant for internal conversion, kISC is the rate constant for intersystem crossing, kq is the fluorescence quenching rate constant, and [Q] is the quencher concentration.39 The intrinsic radiative rate constant is determined by the properties of the molecule, in this case phenanthrene, and is not affected significantly by changes in pressure or temperature. However, the nonradiative relaxation of the excited state can be affected by these changes in the environment. Altering the coupling coefficients induces the transitions and/or causes a change in the collisional frequency, which in turn affects the observed quenching efficiency. In order to explain the changes in the nonradiative rate constants observed for phenanthrene in carbon dioxide, several properties of supercritical fluids must be considered. The effect of pressure, local density, and local composition must all be considered to shed light on the observed kinetics. The fluorescence decay of phenanthrene is treated as a reactant, the S1 state of phenanthrene, undergoing competing reactions to form triplet phenanthrene and ground state phenanthrene, eq 10. The singlet excited state of phenanthrene, S1, decays by several competing processes to yield triplet phenanthrene and ground state phenanthrene, eq 10.

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Figure 7. Lifetime distributions of phenanthrene fluorescence decays (5 × 10-5 M) in supercritical CO2 at 35 °C. ESM analysis using 150 exponentials (0.01-70 ns) at (a) 80.7 bar, Fr ) 0.93; (b) 94.5 bar, Fr ) 1.33; and (c) 164.8 bar, Fr ) 1.74. kIC

S1 Df S0 + heat

internal conversion

kISC

S1 Df T1 + heat kf

S1 98 S0 + hν

intersystem crossing fluorescence

kq

S1 + Q Df S0 + heat

fluorescence quenching

(10)

Although no quencher was explicitly added, fluorescence quenching has been included to account for the possibility of phenanthrene, the cell walls, and/or carbon dioxide acting as an excited state quencher.40 Thermodynamic Pressure Effect. The effect that pressure has on the processes outlined in eq 10 can be explained as a thermodynamic pressure effect. In essence, any increase in pressure will favor the species with the smaller volume (Le Chatelier’s principle applied to pressure). Any change in volume between reactants and a transition state, eq 11, will result in a pressure-dependent response. Here, the transition state can be thought of as a collision (with strong short-lived orbital interactions) that leads to the triplet state or ground state.

S1 + Q h [S1‚Q]‡ f T1 + S0

(11)

If the encounter complex (transition state) in eq 11 has a smaller volume than the reactants, then an increase in pressure will cause a corresponding increase in the reaction rate constant. Such pressure effects caused by large volume changes (partial molar volume) have been reported previously in supercritical fluids.41,42 The fluorescence measurements illustrated in Figures 6 and 7 show a decrease in the observed singlet excited state lifetime


with increasing pressure corresponding to an increase in the nonradiative rate constants. If this were the sole consideration, then such an increase would be consistent with a thermodynamic pressure effect. However, several factors suggest that the thermodynamic pressure effect is playing little or no role in the observed pressure dependence of the fluorescence lifetimes. A pressure effect cannot explain the trimodal distributions observed in Figures 6-9. A single chromophore in a uniform environment (homogeneous) has a single-exponential (unimodal) fluorescence decay, not the trimodal decays observed. Furthermore, an increase in pressure would uniformly increase the collisional frequency (as would a change in temperature) and would therefore cause a similar (albeit slightly faster) singleexponential decay. Lowering the concentration of phenanthrene from 5 × 10-5 to 5 × 10-6 M caused a significant change in the observed pressure dependence of the fluorescence lifetimes. In contrast to the large observable decrease in fluorescence lifetimes at 5 × 10-5 M, the pressure effect at 5 × 10-6 M is almost nonobservable. A pressure change over a wide range (from 80 to 200 bar) causes no appreciable decrease in the observed fluorescence lifetimes. Local Density Effect. Spectroscopic and theoretical evidence suggest that the local density of supercritical fluids around a solute molecule can be larger than the bulk density, especially in the highly compressible region near the critical point. The presence of these density gradients makes the system inhomogeneous and can affect chemical reactivity in a way not anticipated by homogeneous solution kinetics. The presence of the enhanced local densities is supported by studies of solvatochromic probes using absorption and fluorescence measurements in various supercritical solvents, as well



as by reaction dynamics studies.11,18-21 The solvatochromic probes showed wavelength shifts in the absorbance and fluorescence bands inconsistent with bulk properties (a dielectric constant derived from calculated bulk densities) near the critical point. Bimolecular reaction rate constants were shown to depend sensitively on density, with the most marked effects being observed near the critical point.15,20,21,43 Some rate constants were dramatically increased upon approaching the critical point, whereas others showed equally significant reductions in the observed rate constants. All of these observations were explained by the enhanced solvent densities around the solute molecules, most notably near the critical point. None of the rate studies of enhanced local densities in supercritical fluids, either experimental or theoretical, make any mention of analogous nonlinear kinetic behavior. Instead, most available literature describes the dynamics of forming and dissociating solvent-solute clusters on a picosecond time scale. Therefore, any observed effects on rates would be time-averaged for kinetics measured at submicrosecond or slower regimes. The high resolution (8192 data channels at 108 ps/channel) and short time frames (70 ps laser pulse) available in our experiment allow for direct elucidation of these nonlinear effects caused by the inhomogeneity of the system. The multimodal distributions depicted in Figures 6-9 can be explained readily as a consequence of local heterogeneity. The distributions of density around phenanthrene in its excited singlet state produce a variety of environments and a range of collision frequencies with solvent. These factors can alter the efficiency of the various radiationless processes, thus affecting their rate constants and the overall fluorescence decays. Some of the chromophores experience the bulk properties of the solvent, while others are better described as the solvent-solute

J. Phys. Chem., Vol. 100, No. 45, 1996 17937 clusters. The phenanthrene molecule dispersed in the bulk phase encounters a very different environment from one trapped in a solvent-solute cluster. The vast difference in these environments results in differences in the radiationless rate constants, which are then observed as multiple fluorescence lifetimes. The higher densities of these solvent-solute clusters results in a distribution of chromophores with faster fluorescence decay rates and, thus, shorter lifetimes. The bulk phase densities do not exhibit so strong an influence over the radiationless processes, and the phenanthrene exhibits longer fluorescence lifetimes. Solvent-solute clustering thus explains the multimodal lifetime distributions observed for phenanthrene fluorescence decays. It remains to be explained why trimodal rather than a bimodal distribution (one for phenanthrene in the bulk phase and one involved in clustering) is observed. Furthermore, a change in temperature from 32 to 35 °C (from Figure 6 to Figure 7) does not show any change in the number of modes for the higher concentrations of phenanthrene, whereas at the lower chromophore concentrations depicted in Figures 8 and 9 a qualitative change (from 3 modes to 1) is observed. Experimental evidence suggests that the density enhancement falls off rapidly as the temperature is increased beyond the critical point. Thus, the changes from 32 to 35 °C at low chromophore concentration (Figures 8 and 9) are consistent with these observations, but those at higher concentrations are not. It is possible that the density distributions are not solely responsible for differential quenching of excited state phenanthrene in supercritical carbon dioxide. The presence of another quenching process which is strongly affected by the inhomogeneity of the supercritical fluid could be responsible for the third lifetime distribution that is observed. A differential local composition would provide for just such an effect. Local Composition Effect. Several research efforts have shown that added cosolvents can aggregate to a greater extent around a solute molecule in a supercritical fluid than in a homogeneous bulk solution.5,21,22,43 These effects are most pronounced near the critical point. The basis for this idea is the assumption that molecular interactions between cosolvent and solute would be stronger than the solvent-solute interactions or solvent-cosolvent interactions. This can be simply visualized by considering a fairly polar cosolvent and solute mixed in a nonpolar solvent. The polar molecules have a higher affinity for one another than toward the nonpolar solvent. In effect, the cosolvent acts as a local solvating agent. The scenario in which the cosolvent is the same as the solute molecule and the concentration is lowered is that which was referred to above as solute-solute clustering. Solute-solute clustering can affect reactivity in two ways. The increased concentration of reactants can affect the overall rate of a bimolecular reaction, and/or the physical properties of the local aggregate can differ from those of the bulk, thus affecting the rate constant of the reaction. The interaction of a phenanthrene excited state singlet with neighboring ground state phenanthrene molecules can enhance nonradiative decay either by alteration of the local “solvent” properties or by direct interaction with the excited state and their consequent effect on various nonradiative processes. Excimer formation is the most likely result arising from an elevated local concentration of phenanthrene: however, no evidence could be observed for excimer formation. Whether it is intersystem crossing or collisional fluorescence quenching (or excimer formation) that is most enhanced by the concentration gradients, the end result is a decrease in the observed fluorescence lifetimes. Furthermore, the interactions between the solute and a ground state phenanthrene will be very

17938 J. Phys. Chem., Vol. 100, No. 45, 1996 different from the interactions between the solute and carbon dioxide. These different associations then produce pronounced differences in fluorescence lifetimes for the two aggregates. If solvent-solute clusters produce substantial density gradients and solute-solute clustering produces concentration gradients, the observation of three (average) environments for excited phenanthrene becomes quite reasonable. The phenanthrene in the bulk phase experiences relatively weak interactions with solvent and essentially no interactions with other phenanthrene molecules: thus, the observed nonradiative rate constants will be small (relatively) and will account for the long lifetime (i.e., 30 ns in Figure 8a). The higher densities loosely associated with solvent-solute clustering would slightly enhance nonradiative decay because of a measurable increase in collisions. This is consistent with the median lifetime (i.e., 8 ns in Figure 8a) deriving from modest increases in the nonradiative rate. The stronger interactions between two planar aromatic chromophores in a solute-solute cluster would increase the efficiency of nonradiative decay even more, leading to the shortest lifetime distributions observed (i.e., 1 ns in Figure 8a). The importance of solvent-solute and solute-solute clustering can be inferred from the lifetime distributions illustrated in Figures 6 and 8. Clustering is observed at 32 °C over the entire range of pressures investigated. This is consistent with previous reports of clustering even up to reduced densities of 2. An increase in pressure along an isotherm does produce a decrease in the fluorescence lifetimes observed (Figure 6), but when the chromophore concentration is also decreased, the decrease in lifetimes is smaller (Figure 8). Increasing the temperature to 35 °C reveals an intriguing trend. At 5 × 10-5 M (Figure 7), the lifetime distributions become narrower but otherwise duplicate those observed at 32 °C (Figure 6). Clustering still contributes significantly to the observed fluorescence decays, but the dramatic change observed with lower chromophore concentrations (Figure 9) suggests that solvent-solute and solute-solute clustering phenomena have all but dissipated under these conditions. Over the entire density range investigated, the lifetime distributions are almost unimodal (one lifetime) with only small contributions from the shorter lifetime components. Again, changes in pressure induce only minimal decreases in the observed lifetimes. The lower concentration (by a factor of 10) requires fewer solvent molecules for solvation and may cause clustering to fall off faster than at higher concentrations. This large decrease in clustering (local density enhancement) observed upon raising the temperature 3 °C is different from clustering approximations determined using steady state fluorescence measurements of pyrene I1/I3 ratios.44,45 Zhang and co-workers have found local density enhancements decreasing with temperature but still exhibit high local densities (up to 1.4 times the bulk density) as high as 50 °C.45 The time-averaged measurements of solvent-sensitive fluorescence suggest that, on average, the local solvent densities decrease with temperature. However, these measurements cannot distinguish between a changing average solvent environment and two distinct environments with changing contributions. It was concluded that I1/I3 ratios represented a local density enhancement which decreased with increasing temperature, but the same data may represent a fixed local density enhancement which has a decreasing contribution with increasing temperature. The fluorescence lifetime distributions reveal features in the dynamic behavior of the clustering phenomenon which can be hidden by steady state measurements. The changes in the distributions from 32 to 35 °C clearly show the decreasing significance of the shorter component lifetimes even though the

Rhodes and Fox lifetimes remain centered around the same average values (1 and 8 ns). This is consistent with a local density enhancement which remains the same with increasing temperature while the number of clusters has decreased. Conclusions The exponential series method of analysis provides a powerful tool for investigating excited state dynamics with no a priori knowledge about details of the mechanisms for relaxation involved. Proper care must be taken to ensure that the results have significance regarding both the data quality and the physical relevance to the particular system. The ESM analysis has been applied to phenanthrene fluorescence decays at 32 and 35 °C and at various pressures at chromophore concentrations of 5 × 10-5 and 5 × 10-6 M. The trimodal lifetime distributions obtained near the critical point can be explained by solvent-solute and solute-solute clustering. The unimodal distribution at 35 °C and 5 × 10-6 M demands a drastic reduction in clustering even upon a modest (4 °C) temperature shift from the critical point. The continued presence of a trimodal distribution at 35 °C and 5 × 10-5 M suggests that chromophore concentration plays an important role in determining the extent of clustering. These results show the importance of considering concentrations when investigating solvation phenomenon in near-critical and supercritical fluids. Furthermore, it is clear that observations at infinite dilution cannot be applied to higher concentrations where bimolecular reactions are likely to be performed. Acknowledgment. We thank Dr. Stephen E. Webber and Andrew Eckert for access to and assistance in using their single photon counting apparatus. This work was supported by the National Science Foundation. References and Notes (1) Bruno, T. J., Ely, J. F., Eds. Supercritical Fluid Technology: ReViews in Modern Theory and Applications; CRC Press: Boston, MA, 1991; p 593. (2) Brennecke, J. F.; Eckert, C. A. In Supercritical Fluid Science and Technology; Johnston, K. P., Penninger, J. M. L., Eds.; American Chemical Society: Washington, DC, 1989; p 14. (3) Savage, P. E.; Gopalan, S.; Mizan, T. I.; Martino, C. J.; Brock, E. E. AIChE J. 1995, 41, 1723. (4) Randolph, T. W.; O’Brien, J. A.; Ganapathy, S. J. Phys. Chem. 1994, 98, 4173. (5) Chialvo, A. A.; Debenedetti, P. G. Ind. Eng. Chem. Res. 1992, 31, 1391. (6) Murray, J. S.; Lane, P.; Brinck, T.; Politzer, P. J. Phys. Chem. 1993, 97, 5144. (7) Debenedetti, P. G.; Chialvo, A. A. J. Chem. Phys. 1992, 97, 504. (8) Tom, J. W.; Debenedetti, P. G. Ind. Eng. Chem. Res. 1993, 32, 2118. (9) Betts, T. A.; Zagrobelny, J.; Bright, F. V. In Supercritical Fluid Technology; Bright, F. V., McNally, M. E., Eds.; American Chemical Society: Washington, DC, 1992; p 48. (10) Sun, Y.-P.; Bennett, G.; Johnston, K. P.; Fox, M. A. J. Phys. Chem. 1992, 96, 10001. (11) Hrnjez, B. J.; Yazdi, P. T.; Fox, M. A.; Johnston, K. P. J. Am. Chem. Soc. 1989, 111, 1915. (12) Blitz, J. P.; Yonker, C. R.; Smith, R. D. J. Phys. Chem. 1989, 93, 6661. (13) McDonald, A. C.; Fan, F. R. F.; Bard, A. J. J. Phys. Chem. 1986, 90, 196. (14) Lamb, D. M.; Vander Velde, D. G.; Jonas, J. J. Magn. Reson. 1987, 73, 345. (15) Betts, T. A.; Zagrobelny, J.; Bright, F. V. J. Am. Chem. Soc. 1992, 114, 8163. (16) Kim, S.; Johnston, K. P. AIChE J. 1987, 33, 1603. (17) Johnston, K. P.; McFann, G. J.; Peck, D. G.; Lemert, R. M. Fluid Phase Equilib. 1989, 52, 337. (18) Sun, Y.-P.; Fox, M. A.; Johnston, K. P. J. Am. Chem. Soc. 1992, 114, 1187.

Photophysics of Phenanthrene in Supercritical CO2 (19) Hrnjez, B. J.; Mehta, A. J.; Fox, M. A.; Johnston, K. P. J. Am. Chem. Soc. 1989, 111, 2662. (20) Combes, J. R.; Johnston, K. P.; O’Shea, K. E.; Fox, M. A. In Supercritical Fluid Technology; Bright, F. V., McNally, M. E., Eds.; American Chemical Society: Washington, DC, 1992; p 31. (21) Rhodes, T. A.; O’Shea, K.; Bennett, G.; Johnston, K. P.; Fox, M. A. J. Phys. Chem. 1995, 99, 9903. (22) Ellington, J. B.; Park, K. M.; Brennecke, J. F. Ind. Eng. Chem. Res. 1994, 33, 965. (23) Zagrobelny, J.; Betts, T. A.; Bright, F. V. J. Am. Chem. Soc. 1992, 114, 5249. (24) Siemiarczuk, A.; Ware, W. R. Chem. Phys. Lett. 1989, 160, 285. (25) Siemiarczuk, A.; Ware, W. R. Chem. Phys. Lett. 1990, 167, 263. (26) Wagner, B. D.; Ware, W. R. J. Phys. Chem. 1990, 94, 3489. (27) Brochon, J. C.; Livesey, A. K.; Pouget, J.; Valeur, B. Chem. Phys. Lett. 1990, 174, 517. (28) Krasnansky, R.; Koike, K.; Thomas, J. K. J. Phys. Chem. 1990, 94, 4521. (29) Ware, W. R. In Photochemistry in Organized and Constrained Media; Ramamurthy, V., Ed.; VCH Publishers: New York, 1991; p 563. (30) James, D. R.; Ware, W. R. Chem. Phys. Lett. 1986, 126, 7. (31) Siemiarczuk, A.; Wagner, B. D.; Ware, W. R. J. Phys. Chem. 1990, 94, 1661. (32) Landl, G.; Langthaler, T.; Engl, H. W.; Kauffmann, H. F. J. Comput. Phys. 1991, 95, 1. (33) Liu, Y. S.; Ware, W. R. J. Phys. Chem. 1993, 97, 5980.

J. Phys. Chem., Vol. 100, No. 45, 1996 17939 (34) Lakowicz, J. R. Principles of Fluorescence Spectroscopy; Plenum Press: New York, 1983; p 496. (35) Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes in C: The Art of Scientific Computing, 2nd ed.; Cambridge University Press: New York, 1992; p 994. (36) Bertero, M.; Brianzi, P.; Pike, E. R. Proc. R. Soc. London, A 1985, 398, 23. (37) Rhodes, T. A.; Fox, M. A. Submitted to Appl. Spectrosc. (38) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987. (39) For a general review of time-resolved fluorescence spectroscopy, see: Lakowicz, J. R. Principles of Fluorescence Spectroscopy; Plenum Press: New York, 1983; p 496. (40) No particular quenching process is implied. (41) Eckert, C. A.; Ziger, D. H.; Johnston, K. P.; Kim, S. J. J. Phys. Chem. 1986, 90, 2738. (42) Johnston, K. P.; Haynes, C. AIChE J. 1987, 33, 2017. (43) Brennecke, J. F. In Supercritical Fluid Engineering Science; Kiran, E., Brennecke, J. F., Eds.; American Chemical Society: Washington, DC, 1993. (44) Knutson, B. L.; Tomasko, D. L.; Eckert, C. A.; Debenedetti, P. G.; Chialvo, A. A. In Supercritical Fluid Technology; Bright, F. V., McNally, M. E., Eds.; American Chemical Society: Washington, DC, 1992. (45) Zhang, J.; Lee, L. L.; Brennecke, J. F. J. Phys. Chem. 1995, 99, 9268.

JP961124U

Photophysics of Phenanthrene in Supercritical Carbon Dioxide

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