J. Phys. Chem. 1996, 100, 8499-8507
8499
Solute-Fluid Coupling and Energy Dissipation in Supercritical Fluids: 9-Cyanoanthracene in C2H6, CO2, and CF3H Jeanette K. Rice,† Emily D. Niemeyer, and Frank V. Bright* Department of Chemistry, Natural Sciences and Mathematics Complex, State UniVersity of New York at Buffalo, Buffalo, New York 14260-3000 ReceiVed: June 6, 1995; In Final Form: January 10, 1996X
We report on the coupling and dissipation of energy between a model fluorescent solute, 9-cyanoanthracene (9CA), and several supercritical fluid solvents. To this end, we have determined experimentally the fluorescence quantum yields and excited-state fluorescence lifetimes for dilute solutions of 9CA in supercritical C2H6, CO2, and CF3H. The 9CA quantum yield is substantially less than unity at lower fluid densities; it approaches unity only at the high-density, liquid-like region. The 9CA excited-state lifetime is also shortened significantly in the low-density region. The radiative (kr) and nonradiative (knr) decay rates for 9CA are found to be strongly density dependent. In the low-density region, the nonradiative rate dominates; however, in the highdensity region the 9CA deexcitation follows the radiative pathway. The Strickler-Berg relationship (kr ∝ n2; n ) solvent refractive index) holds for 9CA in many normal liquid solvents. However, in supercritical fluids in the low-density regime, the simple Strickler-Berg expression cannot account fully for the observed kr results. Additional corrections, accounting for the shifts in the 9CA absorbance spectra, also cannot compensate completely for deviations from the predicted Strickler-Berg behavior. To yield agreement between the experimental kr data and the Strickler-Berg predictions, we require there to be changes in the total 9CA molar absorptivity with density. Recent experiments on anthracene and pyrene in supercritical CO2 (Rice, J. K.; Niemeyer, E. D.; Bright, F. V. Anal. Chem. 1995, 67, 4354) demonstrate that the average solute molar absorptivity is indeed a function of fluid density. The strong density dependence of the nonradiative decay rate is interpreted in terms of an increase in fluid density leading to an increase in the energy gap (∆E) between T2 and S1 states. Specifically, at the lower fluid densities the S1-T2 intersystem crossing (ISC) rate increases because (1) ∆E is small and the fraction of 9CA molecules that occupy states within the S1 manifold above the lowest vibrational level of the T2 envelope is increased and (2) the number of effective ISC crossing pathways from S1 to T2 is increased because the Franck-Condon factor depends strongly on ∆E. Finally, our data demonstrate that the extent of solute-fluid coupling to/with the fluid bath (i.e., the 9CA radiative or nonradiative decay rates) can be tuned over more than an order of magnitude by simply adjusting the density of the supercritical fluid.
Introduction Supercritical fluids (SFs), substances raised above their critical temperature, represent an area of significant active research.1-7 Much of this interest arises because SFs exhibit liquid-like densities and gas-like mass transport properties, which make them attractive solvents for effecting chemical reactions and separations. In addition, it is well-known that the physicochemical properties of all SFs are a strong function of pressure.1-7 Thus, SFs represent truly tunable solvents because one can continuously adjust solvent strength, dielectric constant, refractive index, density, etc. by simply controlling system pressure and temperature. It is now well-established (experimentally and theoretically) that there are unique interactions between SFs and dissolved solutes that can result in increases in density and/or composition in the region immediately surrounding the solute (i.e., fluid “clustering”, “augmentation”, or “charisma”).8-18 These clusters are dynamic in nature,11 and their effects are generally greatest in the near-critical region.18 It is also known that solute-fluid clustering can affect the rate and outcome of chemical * Author to whom all correspondence should be addressed. Telephone: (716) 645-6800 ext. 2162 (office). FAX: (716) 645-6963. E-mail:
[email protected]. † Current address: Department of Chemistry, Georgia Southern University, Landrum Box 8064, Statesboro, GA 30460. X Abstract published in AdVance ACS Abstracts, April 15, 1996.
S0022-3654(95)01568-1 CCC: $12.00
reactions.19-25 However, although we know neat and cosolventmodified SFs can be used to influence reactions and separations, our understanding is incomplete regarding how solute-fluid clustering affects the coupling of the solute to the SF bath and how one can use SFs to control the reaction pathways. In this study, we aim to address this issue by determining how energy (deposited into a solute by a photon) is dissipated to the SF bath and how the density and SF structure affect the dissipation efficiency and relaxation pathways. Toward this end, we determine experimentally the solute fluorescence lifetime and quantum yield, compute the radiative and nonradiative decay rates of the fluorophore, and follow how these rates are influenced by fluid density and structure. We then determine how the recovered rate terms compare to values predicted by established models (e.g., the Strickler-Berg relationship or the energy-gap law). The fluids used in this work are C2H6, CO2, and CF3H. These were chosen because they are most commonly used in SF science and technology, they cover a broad range of properties (e.g., polarities, polarizabilities), and their critical regions are relatively easy to access experimentally. The solute used in this work is 9-cyanoanthracene (9CA). 9CA was chosen for several reasons. First, it is strongly fluorescent. Thus, we can work under infinitely dilute conditions where solute-solute interactions are minimal. Further, the strong fluorescence from 9CA allows us to carry out experiments well below the critical © 1996 American Chemical Society
8500 J. Phys. Chem., Vol. 100, No. 20, 1996
Rice et al.
density. Second, 9CA has been studied extensively as isolated molecules in supersonic jets, in condensed phase liquids, and most recently in SFs, and its photophysics are well understood.26-34 For example, in a supersonic jet expansion, the 9CA fluorescence quantum yield is unity, and no intersystem crossing to a triplet state is observed when excited at the 0-0 transition.27 The excited-state fluorescence lifetime (τ) of the 0-0 transition in a jet expansion is 28.0 ( 0.2 ns.27,28 Hirayama and co-workers30,31 have also demonstrated that a plot of 1/τ vs n2 for 9CA in a jet expansion, in liquid n-hexane and in liquid methylcyclohexane at high pressure, is linear. These facts establish that 9CA obeys the well-known Strickler-Berg35 relationship (Vide infra) in these liquid solvents. More recently, Sun and Fox34 showed that 1/τ vs n2 for 9CA in supercritical C2H6 did not obey the Strickler-Berg relationship at low fluid densities; the linear dependence was only approached at higher fluid densities (i.e., when 9CA was in a more liquid-like environment). However, the implicit assumption in these particular experiments was that the 9CA quantum yield (Φ) remained unity in SFs. Clearly, the 9CA quantum yield is unity in n-hexane and methylcyclohexane,30,31 but Melhuish’s36 classic work demonstrates that the 9CA quantum yield can be significantly less than unity even in neat liquids (e.g., 0.885 in benzene, 0.755 in petroleum ether, 0.845 in ethanol). Thus, the issue of deviation from the Strickler-Berg model in SFs is far from closed especially when one bases conclusions on excited-state lifetime measurements alone. The remainder of this paper is structured as follows. In the Theory section we present the necessary mathematical relationships between the experimental measurables (τ and Φ) and the rate terms describing the deexcitation of any fluorescent solute. We also provide a mathematical expression for determining fluorescent quantum yields from measured absorbance and fluorescence spectra that uses a reference fluorophore for calibration, and we present the Strickler-Berg relationship and establish how the radiative rate is predicted to depend on the physicochemical properties of the solvent/fluid. The Experimental Section follows, and we discuss the protocols used to obtain all the measurables and discuss how the physicochemical properties of the SF are determined. In the Results and Discussion section we report new fluorescence lifetime and quantum yield data for 9CA in C2H6, CO2, and CF3H over a wide density range, as well as how the actual radiative and nonradiative decay rates vary with fluid density. We next determine the density dependence of the 9CA fluid-clustering process, compare our experimental kr values to those predicted by the Strickler-Berg model, and illustrate how densitydependent changes in the 9CA molar absorptivity may be responsible for deviations from Strickler-Berg predictions. Finally, we offer an explanation for the density dependence of knr in terms of an increase in fluid density increasing the energy gap (∆E) between T2 and S1 states which in turn alters the fraction of 9CA molecules that occupy states within the S1 manifold aboVe the lowest vibrational level of the T2 envelope and the number of effective ISC pathways from S1 to T2 changing because the Franck-Condon factor too depends on ∆E. Theory For any fluorophore, the radiative (kr) and nonradiative (knr) decay rates characterize the fluorescence decay process following electronic (optical) excitation:37
Φ kr ) τ
(1)
knr )
(1 - Φ) τ
(2)
In eqs 1 and 2, Φ is the fluorescence quantum yield and τ is the excited-state fluorescence lifetime. Thus, one can effectively access kr and knr by simply determining the quantum yield and excited-state lifetime. Of course, if Φ ) 1, 1/τ ) kr. Fluorescence lifetimes are routinely measured in supercritical fluids.16,38-40 However, to date, fluorophore quantum yields41 have not been reported in SFs. Modern fluorescence quantum yield determinations are generally now made relative to a dilute standard solution containing a fluorophore whose quantum yield (Φs) is accurately known.42 In this scheme one need only make four spectroscopic measurements: (1) the absorbance of the unknown at the excitation wavelength (Absu), (2) the absorbance of the standard at the same excitation wavelength (Abss), (3) the integrated area under the emission profile for the unknown when excited at the excitation/absorbance wavelength (Emu), and (4) the integrated area under the emission profile for the standard when excited at the excitation/absorbance wavelength (Ems) and apply42
Φu ) Φs
( )( )( ) Abss Emu nu2 Ems Absu n 2 s
(3)
In this expression, ns and nu denote the refractive index of the solvents in which the standard and unknown, respectively, are prepared. The ideal quantum yield standard should meet several criteria: (1) there should be no overlap of the absorbance and emission spectra, (2) it should be soluble in the same solvents as the unknown, (3) it should be impervious to O2 quenching, (4) its quantum yield should not depend on excitation wavelength, and (5) the quantum yield must be accurately known.42 Few fluorophores actually meet all of these requirements, but there are several that are suitable standards.42 In the current work we use perylene in 95% ethanol because its quantum yield (0.92 ( 0.09)42 has been confirmed by several researchers.36,43 Unfortunately, perylene is susceptible to O2 quenching and we are required to purge all perylene samples with N2 prior to use. The Strickler-Berg relationship30,31,35,42-51 (eq 4) establishes a link between kr (eq 1) and the properties of the solvent and the fluorophore:
kr ) 2900n2νo2∫ dν
(4)
In this expression n is the solvent/fluid refractive index, νo is the peak frequency of the fluorophore absorbance spectrum, and ∫ dν represents the integrated area under a curve of the molecular extinction coefficient vs wavenumber. Equation 4 predicts a linear dependence of the radiative rate on the square of the solvent refractive index. While several authors have questioned this dependence,50,51 Lampert et al.45 have done a careful study on the relationship between refractive index and radiative rate and report that, while it can be difficult to distinguish between an n2 and n3 dependence in some cases, an n2 dependence is generally valid. This is supported by work from Hirayama et al.30,31 who have investigated the dependence of the radiative rate of several anthracene derivatives on n2 in jet expansions and in liquid solvents at ambient conditions and under high pressure. Experimental Section Materials and Reagents. 9-cyanoanthracene (99+%), perylene (99.5%), anthracene (99.9%), 9,10-diphenylanthracene
9-Cyanoanthracene in C2H6, CO2, and CF3H (99%), pyrene (99.9%), 1,4-bis(4-methyl-5-phenyl-2-oxazolyl)benzene (Me2POPOP), and n-hexane (99+%) were purchased from Aldrich and used as received. Acetonitrile (J.T. Baker; HPLC Grade), dimethylformamide (Fisher, ACS Certified), and ethanol (200 Proof; Pharmco) were also used as received. Ethane (99%), CO2 (SFC Grade), and CF3H (98%) were purchased from Scott Specialty Gases (Plumsteadville, PA) and were further purified by passage through an oxygen trap (Matheson Gas Products, Montgomeryville, PA). Instrumentation. All absorbance measurements were carried out on a Spectronic 1201 UV-vis spectrophotometer (Milton Roy, Rochester, NY) with a spectral bandpass of (0.5 nm. The scan rate was typically 200 nm/min, and all spectra were blank corrected. Steady-state emission spectra were acquired on an SLM-AMINCO 48000 MHF spectrofluorometer in the standard ratiometric mode. Excitation was achieved by using the 351.1 and 363.8 nm lines of an argon-ion laser (Coherent Innova 40010). Laser power was generally maintained at 50 mW, and no sample photodecomposition was observed over the course of an experiment. An interference filter (10 nm fwhm, Oriel) was used to remove extraneous plasma discharge. Integrated areas under the entire fluorescence profile (370-525 nm) were obtained by using the SLM software. In all cases, the blank contribution to the total emission was less than 0.5%. Raman from the SF did not contribute under our experimental conditions. Excited-state fluorescence lifetime measurements were made using frequency-domain fluorometry.52-56 Excitation was again from an argon-ion laser (351.1 nm), and extraneous plasma discharge was removed with an interference filter. The entire emission was monitored using a 385-nm longpass filter (Oriel). Under these particular conditions, the blank contribution was always less than 1% of the total emission. Magic angle polarization was used for all excited-state intensity decay experiments.57 Me2POPOP in ethanol served as the reference lifetime standard; its lifetime was assigned a value of 1.45 ns.58 For all experiments, the Pockels cell was operated at a repetition rate of 5 MHz. Typically data was collected for 60-90 s over a frequency range of 5-125 MHz (25 frequencies). At least 10-15 multifrequency data sets were acquired at each set of experimental conditions. All multifrequency phase and modulation data were analyzed by the global analysis method as described elsewhere.59 The high-pressure optical cells used in these experiments were constructed in-house and described in detail elsewhere.60 The optical path length of the cell is approximately 1 cm. Quartz optical windows were used (Behm Quartz Industries, Dayton, OH), and the position and orientation of the individual windows within the cell were kept constant for all experiments. Pressure was generated from a syringe pump (Isco Model 260D, Lincoln, NE) and monitored ((1 psi) with a calibrated Heise gauge. Temperature control was maintained with a Haake A80 temperature bath by circulating water through the high-pressure cell body. Temperature was monitored (( 0.1 °C) using a solidstate thermocouple (Cole-Parmer, Chicago, IL) inserted directly into the cell body. All pressure changes were made from low to high pressure, with a minimum of 1 h equilibration between pressure change and data acquisition. Sample Preparation. A perylene stock solution was prepared by dissolving the appropriate amount of perylene in 95% ethanol such that the final concentration was 10-6 M. An aliquot of this stock solution was placed into an optical cell that is identical to the one used at high pressure. This particular step is important to ensure that the spatial character of the absorbance and emission and overall collection efficiency of
J. Phys. Chem., Vol. 100, No. 20, 1996 8501 the optical system are identical for the reference and samples. All perylene solutions were purged with N2 for at least 1.5 h. 9CA samples for study were prepared as follows. A small (microliter) aliquot of a 9CA stock solution (in ethanol) was micropipetted directly into a clean, dry high-pressure optical cell (internal volume ) 5.0 mL), such that the final concentration of 9CA was 5 µM. The solvent was then slowly removed using a gentle N2 stream, and a metal stir bar (Teflon coating removed) was added to the cell. The high-pressure valve assembly was connected, joining the cell to the high-pressure pump. A 30 µm vacuum was then maintained over the entire system for a minimum of 6 h to minimize O2 in the cell. The cell was subsequently heated to the experimental temperature, allowed to equilibrate, and then charged to the initial fluid pressure. The cell contents were stirred overnight prior to each experiment. Stirring continued throughout the experiment. Experiments were carried out over a reduced density (Fr; )Fe/ Fc; Fe ) experimental density; Fc ) critical density) range of Fr ) 0.3-2.0. The reduced temperature (Tr; ) Te/Tc; Te ) experimental temperature; Tc ) critical temperature) was maintained at 1.10. Calculation of Fluid Refractive Index. Equation 3 demonstrates that it is generally necessary to correct quantum yield values if the solvent used for the standard and sample is not identical. In a SF this problem is exacerbated further because the SF refractive index is a function of fluid density; therefore, we must compensate for the effects of SF density on n at all pressures and temperatures. To address this issue we estimated the SF density at a given P and T using commercially available software (SFSolver, Isco, Inc., Lincoln, NE). Refractive indices for C2H6 and CO2 were subsequently calculated from the Lorentz-Lorenz relationship:61
R)
[ ]
3 n2 - 1 4πN n2 + 2
(5)
In this expression, R is the molecular polarizability (cm3), N is the fluid number density (density (g/cm3)Nav (moles-1)/MW (g/ mol)), and n is the refractive index. The refractive index for CF3H was computed using computer software developed inhouse and based on the Debye equation:61
R+
[ ]
d2 3 n2 - 1 ) 3kT 4πN n2 + 2
(6)
where d is the solvent dipole moment (esu‚cm, 1 esu ) 1 g1/2 cm3/2 s-1), k is the Boltzmann constant (J/K), T is the temperature (K), and all other terms are as described above. The actual polarizabilities used for each fluid are as follows: C2H6, 4.47 × 10-24; CO2, 2.91 × 10-24; and 3.57 × 10-24 cm3 and the CF3H dipole moment is 1.65 D () 1.65 × 10-18 esu‚cm).62 Results and Discussion Excited-State Fluorescence Lifetimes. In order to access kr and knr, we require excited-state fluorescence lifetimes and fluorescence quantum yields (eqs 1 and 2). Figure 1 presents the experimentally determined fluorescence lifetime of 9CA in C2H6, CO2, and CF3H as a function of fluid density at Tr ) 1.10. In all cases, the intensity decay was best described by a monoexponential decay law and excitation between 337 and 381 nm did not lead to an appreciable ((1 ns) change in the fluorescence lifetime. Inspection of these results shows that
8502 J. Phys. Chem., Vol. 100, No. 20, 1996
Rice et al. TABLE 1: Quantum Yields of Various Fluorescence Solutes Determined in Dilute Liquid Solutions Relative to a Perylene in 95% EtOH Standard Solution solute
solvent
quantum yield literaturea
this work
anthracene 9-cyanoanthracene 9-cyanoanthracene 9,10-diphenylanthracene
ethanol hexane ethanol hexane
0.27b 1.00c 0.85d 0.95e
0.26((0.05) 0.97((0.10) 0.83((0.10) 0.85((0.18)
a
Figure 1. Recovered excited-state fluorescence lifetimes of 9CA in supercritical ethane (1), carbon dioxide (0), and fluoroform (9) as a function of reduced fluid density. Tr ) 1.10.
the lifetime is generally shortest in the low-density regime, increases with increasing density to a point in the near-critical regime, and then decreases slightly with density. It is also interesting to note that the 9CA fluorescence lifetime is shortest in the least polar fluid (C2H6) and that it increases with increasing fluid polarity. The 9CA dipole moment in the S0 and S1 states has been calculated (in vacuo) to be 3.8 D.63 This demonstrates that 9CA is moderately polar but that there is no appreciable change in dipole moment on photoexcitation. However, the observed lengthening of the lifetime in CO2 and CF3H relative to C2H6 can be explained partially in terms of favorable solute-fluid interactions. For example, Parker64 argues that a molecule is solvated through electrostatic interactions and that even if there is no net change in the dipole moment magnitude, there is generally a change in electron distribution on going from the ground to excited state. As a result, there is a change is the solvation structure between the ground and excited states. An increase in solvation generally serves to stabilize the excited state, and this effect should be greatest (1) for molecules exhibiting a large change in dipole moment between the two states, (2) in more polar solvents for a given molecule, or (3) in solvents where specific interactions between the solute and fluid (e.g., acid-base, hydrogen bonding) are possible. Parker further asserts that an excited-state electron will invariably occupy a “more extended orbital” and is therefore more polarizable. As a result, the extent of solvation is expected to increase in the excited state, even if no change in dipole moment occurs during excitation.64 Together these arguments help to explain in part the relative magnitudes of the excited-state lifetimes seen in Figure 1. In effect, there are no strong interactions between C2H6 and 9CA but stronger interactions are possible between CO2 (Lewis acid) and CF3H with 9CA. Fluorescence Quantum Yields. Liquids. There are several aspects to performing accurate quantum yield measurements in SFs that present special challenges. As a result, prior to carrying out any quantum yield determinations in SFs, we performed a series of control experiments in normal liquids to ensure that our protocol and methodology yielded accurate quantum yield values. Quantum yields are typically determined by acquiring the absorbance and fluorescence data on the exact same sample. This presents a bit of a problem in the current work because we are forced to acquire all the absorbance spectra in a stepwise fashion from low to high density, clean the entire high-pressure
(10%. b From ref 42. c From ref 30. d From ref 36. e From ref 50.
cell, reprepare the sample, and then acquire the emission spectra at the same fluid densities. In concept this is not necessarily a challenge, but the fact of the matter is that we are forced to make the absorbance and emission measurements on different days and on different samples that are prepared identically. Thus, our protocol deviates somewhat from traditional methods and it is necessary to check the validity of our approach. A second problem arises in SFs because all the solute placed in the cell is not necessarily completely solubilized at the lower fluid densities. As a result, the actual analytical concentration of dissolVed 9CA can be below the micromolar level. Thus, one must ask if our methodology can accurately determine quantum yields on dilute solutions. To this end, we used 10-7 M solutions of several fluorophores in liquids to mimic the conditions expected in SFs. The compounds used in these control experiments and their solvents are: anthracene (ethanol); 9,10-diphenylanthracene (ethanol) and 9-cyanoanthracene (hexane and ethanol). Table 1 collects and summarizes the results of our liquid-phase experiments and compares our recovered quantum yields to those previously reported in the literature. All experiments were performed relative to a perylene standard. The actual SF high-pressure cells were used for these experiments, and the cells were processed and cleaned accordingly. Inspection of Table 1 clearly demonstrates that our measurement protocol and experimental methodology yield accurate quantum yield values even for relatively dilute solutions. Supercritical Fluids. The results from the previous section demonstrate that we can indeed obtain accurate quantum yield values in dilute liquids. We next determined the 9CA quantum yield in supercritical C2H6, CO2, and CF3H at Tr ) 1.10 as a function of fluid density. The results of these experiments, the average of three replicate runs, are presented in Figure 2. Several aspects of these results merit special mention. First, the 9CA quantum yield is not constant over the entire density range investigated. Second, the 9CA quantum yield vs density profiles are not the same in each SF. Third, the 9CA quantum yield is substantially less than unity below a reduced density of about 0.4. Fourth, above a reduced density of 0.4, in supercritical CO2 (panel B) and CF3H (panel C), we observe that the 9CA quantum yield levels off at unity. Finally, in supercritical C2H6 (panel A), the 9CA quantum yield also levels off, but at a value of only 0.65. This is a somewhat surprising result when compared to the aforementioned n-hexane and methylcyclohexane liquid work.30,31 For example, in liquid n-hexane Φ is unity, however, in liquid ethanol the value decreases to 0.83. In the SFs studied here Φ is unity in supercritical CF3H and CO2 and Φ is only 0.65 in supercritical C2H6. This issue will be discussed in more detail in the following section. Radiative and Nonradiative Decay Rates. From our Φ and τ data, we compute the actual kr and knr for 9CA in supercritical C2H6, CO2, and CF3H at Tr ) 1.10 as a function of density. Figure 3 summarizes the effects of fluid density and structure
9-Cyanoanthracene in C2H6, CO2, and CF3H
J. Phys. Chem., Vol. 100, No. 20, 1996 8503
Figure 2. Experimentally determined fluorescence quantum yields for 9CA in supercritical ethane (panel A), carbon dioxide (panel B) and fluoroform (panel C) as a function of reduced fluid density. Tr ) 1.10. The horizontal dashed line represents the value of the 9CA quantum yield in liquid n-hexane.
on kr and knr. Again, several points require special mention. First, in all SFs studied, knr clearly dominates the 9CA decay/ relaxation process in the low-density region, although the magnitude of this term varies with the actual fluid. For example, in C2H6 (panel A) and CO2 (panel B) at the lowest density investigated, knr is (8.25 ( 0.01) × 107 and (12.1 ( 0.1) × 107 s-1, respectively, compared to (5.70 ( 0.02) × 107 s-1 for 9CA in CF3H (panel C). This is most likely a result of the extra stabilization (Vide supra) offered by CF3H compared to the other SFs. Second, knr decreases with an increase in fluid density. Third, the reduced density value at which knr levels off is fluid dependent. For example, at the higher densities (above Fr ) 0.5), in CO2 and CF3H, knr is essentially zero. However, in C2H6, knr levels off at a value of (2.05 ( 0.05) × 107 s-1, indicating that nonradiative decay processes still contribute significantly to the 9CA decay even under high-density liquidlike conditions. What makes this particular result most intriguing is that, in a nonpolar liquid solvent like n-hexane, the 9CA quantum yield is unity, and knr is for all practical purposes zero. Inspection of the kr results shows that they complement the knr results. For example, kr generally increases with increasing fluid density in the near-critical region, followed by a leveling off. In addition, despite the fact that the high-density value of kr in CO2 (panel B) and CF3H (panel C) differ ((5.10 ( 0.02) × 107 and (3.89 ( 0.02) × 107 s-1, respectively), the reduced density at which the values of kr (and knr) begin to level off (ca. 0.5) is essentially the same. We speculate that the radiative decay rate is less in CF3H because of the favorable electrostatic interactions (Vide supra). In C2H6 (panel A), we do not see a leveling off in kr until we reach a reduced density well over 0.5 (close to 1.0). A possible explanation for this follows.
Figure 3. Calculated radiative and nonradiative decay rates for 9CA in supercritical ethane (panel A), carbon dioxide (panel B), and fluoroform (panel C) as a function of reduced fluid density. Tr ) 1.10.
Our lifetime data suggest an increase in the interaction between 9CA and CO2 and CF3H, which has been explained in part in terms of solvation theory. It seems reasonable to propose that the more favorable the electrostatic interactions between the solute and the fluid, the more pronounced these short-range interactions would be, resulting in greater local density augmentation about the solute. If this scenario were to continue, one could envision these fluid clusters acting to insulate the solute from nonradiative decay pathways. In other words, if there are solute-fluid clusters they may actually further stabilize the excited state and minimize the availability of nonradiative decay pathways. If this were the case, it would manifest itself as follows. The excited-state lifetime would show a maximum where the relative density augmentation is greatest. Additionally, the nonradiative decay rates would decrease most in the density region where the clustering is greatest as well as in the SF where the clustering process is greatest. Inspection of Figure 1 shows a clear maximum in the τ vs Fr plots near a reduced density of 0.5 for 9CA in CO2 and CF3H, with the maxima being most evident in CF3H. In C2H6, such a maxima is not at all evident over the density range investigated. Also, on inspecting Figure 3 carefully we see that the reduced density at which the rates cross over is significantly higher in C2H6 than in CO2 and CF3H (Fr ) 0.6 vs Fr ) 0.4). Together these observations suggest that the 9CA excited state is not as well stabilized or solvated in C2H6 as it is in CO2 and CF3H. Further, they imply less solute-fluid clustering in C2H6 and that the lack of clustering allows the nonradiative decay pathways to remain active in C2H6 over a greater density range.
8504 J. Phys. Chem., Vol. 100, No. 20, 1996
Figure 4. Effects of density on the extent of density augmentation (Flocal/Fbulk) for 9CA in ethane (1), carbon dioxide (0), and fluoroform (9). Tr ) 1.10.
Local Density Surrounding 9CA. From the shifts in the 9CA electronic absorption spectra (cf. Figure 2 in ref 34), one can estimate the extent and magnitude of solute-fluid clustering relative to the bulk fluid density.65 Further, because the groundand excited-state dipole moments of 9CA are the same magnitude,63 the results from the absorbance should not be significantly different for ground- and excited-state 9CA. In Figure 4 we present the extent of local density augmentation (Flocal/Fbulk) as a function of fluid density for 9CA in supercritical C2H6, CO2, and CF3H at Tr ) 1.10. Details on the methodology used to extract these results from the experimental measurables have been reported elsewhere.65 These results show that local density augmentation is greatest in CF3H and CO2, with the value reaching a maximum over 2.0 at reduced densities of 0.75 and 0.60, respectively. The magnitude of solute-fluid clustering is clearly diminished (1.5 vs 2.0) in C2H6, and the maximum augmentation occurs more near a reduced density of 0.9. We also note that the C2H6 profile is considerably more broad compared to the CF3H and CO2 results, suggesting that the solute-fluid clustering, while less in magnitude in C2H6, is more persistent over the entire density range investigated. Refractive Index Dependence of kr. The Strickler-Berg relationship (eq 4) predicts that the radiative decay rate of a fluorescent molecule will scale linearly with solvent refractive index.35 For 9CA, this relationship is obeyed in the gas and liquid phases;30,31 however, deviations have been observed for 9CA in supercritical C2H634 (Vide supra). In investigating the refractive index dependence of kr, our initial efforts centered on reproducing previous work on 9CA in C2H6.34 Figure 5 presents the reciprocal of the fluorescence lifetime vs fluid refractive index for 9CA in C2H6, CO2, and CF3H over a broad density range. In general the agreement between our new C2H6 data with those from Sun and Fox34 is very good (i.e., upward deviation from the Strickler-Berg prediction is evident at low densities) and the other fluids exhibit a similar trend. Of course, the 1/τ representation for kr is inaccurate if the quantum yield is not unity (cf. eqs 1 and 2). Thus, the Figure 5 format is not applicable nor accurate for 9CA in the current SFs studied. On incorporating Φ into our calculation of kr (eq 1), we observe an improvement (Figure 6) between the Strickler-Berg predictions and the experimental kr (compare Figures 5 and 6) and a downward deviation from the expected behavior at the lower fluid densities. Clearly, while Φ is density dependent in the region where Strickler-Berg is not obeyed, this fact alone is apparently not entirely sufficient to account completely for deviations from the Strickler-Berg predictions.
Rice et al.
Figure 5. Reciprocal of excited-state fluorescence lifetime (1/τ) as a function of the square of the solvent refractive index (n2) for 9CA in ethane (1), carbon dioxide (0), and fluoroform (9). The solid line represents behavior predicted by the Strickler-Berg relationship based on 9CA in jet expansion (O), room temperature and pressure n-hexane (b), and methylcyclohexane under high pressure (3).30,31 Tr ) 1.10.
Figure 6. Actual radiative decay rate (kr) calculated from experimentally determined fluorescence quantum yields and excited-state lifetimes as a function of the square of the solvent refractive index for 9CA in ethane (1), carbon dioxide (0), and fluoroform (9). See Figure 5 for description of other symbolism.
If we re-examine eq 4 more closely, we see that kr scales linearly with n2 if and only if the other terms are density independent. Of course, we know from this work and that of Sun and Fox34 that νo, the peak absorbance maximum, is actually density dependent. In fact, the 0-0 S1 transition shifts several hundred wavenumbers in C2H6 (cf. Figure 2 in ref 34). When we take the νo shifts into consideration (Figure 7) in a plot of kr vs n2νo2 we see slight changes in agreement between the predictions and the experimental data, but generally the improvement (if any) is minimal. The final factor in the Strickler-Berg relationship (eq 4) that could affect the agreement between our experimental data (kr) and the predicted rates is the integral term, ∫ dν. In Figure 8 we illustrate the behavior needed to produce agreement between our experimental data and the Strickler-Berg model. The basic result of this exercise shows that the aVerage molar absorptivity would need to be low in the low-density regime and increase by about a factor of 3-5 as the fluid density increases. The best way to address this issue is, of course, to actually measure ∫ dν for 9CA in each fluid as a function of fluid density. Although conceptually simple, this becomes problematic for
9-Cyanoanthracene in C2H6, CO2, and CF3H
Figure 7. Actual radiative decay rate calculated from experimentally determined fluorescence quantum yields and excited-state lifetimes as a function of the product of the square of the solvent refractive index and the wavenumber of the absorbance peak maximum (n2νo2) for 9CA in ethane (1), carbon dioxide (0), and fluoroform (9). See Figure 5 for description of other symbolism.
J. Phys. Chem., Vol. 100, No. 20, 1996 8505
Figure 9. Hypothetical representation of the S1-T2 energy gap dependence on the ISC Franck-Condon factor between S1 and T2 manifolds of 9CA in supercritical C2H6, CO2, CF3H. Points A, B, and C denote low-, intermediate-, and high-density SFs, respectively. No specific shape is implied by the FC profile.
is below T2(0) (the lowest vibrational level in the T2 manifold). That is, the energy gap (∆E ) T2(0) - S1(0)) is positive and nonzero. Further, in liquids when pressure is increased one sees that S1 drops in energy with respect T2.67 As a result, ∆E increases and the ISC rate (kisc) decreases. That is, one can write an expression for kisc of the form:
kisc ) (2πh)V2Fδ
Figure 8. Predicted trend in ∫ dν as a function of reduced fluid density for 9CA in ethane (1), carbon dioxide (0), and fluoroform (9).
9CA because one must know the analytical concentration of 9CA dissolVed at a given density. That is, one must prepare working curves under conditions where all the 9CA in the cell is actually completely soluble at each C2H6, CO2, and CF3H density. Unfortunately, solubility data on 9CA in these SFs is not available and we do not have access to equipment for measuring such. However, in a recent publication from this group, Rice et al. reported on the wavelength-dependent molar absorptivity of the related compound anthracene and pyrene in supercritical CO2.66 The results of these experiments (cf. Figures 2-5 in ref 66) illustrate that there is indeed a strong dependence of ∫ dν on density and that the general form of this dependence is remarkably similar to Figure 8. Interpretation of knr. Figure 3 shows that knr is generally large at low densities and decreases at higher densities. This result is strongly reminiscent of the behavior of other 9-substituted anthracenes in liquids as a function of pressure.67 For example, it is well-known that the medium can affect the nonradiative rate by influencing the S1-T2 intersystem crossing (ISC) process. Specifically, in the 9-substituted anthracene systems S1(0) (the lowest vibrational level in the S1 manifold)
(7)
where V, F, and δ are the electronic matrix element, the FranckCondon (FC) factor, and the density of the final states, respectively. For the ISC process, δ is the density of states within the T1 manifold coupled to T2 and V corresponds to the matrix element for spin-orbit coupling between S1 and T2. Both these factors are considered independent of pressure67 and in turn ∆E. Thus, the changes in kisc are generally thought to arise from drastic changes in the FC factor between S1 and T2.67 Further, because the T2 vibrational levels, ν’, are sparse when compared to S1,67 the number of active modes that can contribute in the S1-T2 ISC is minimized as S1 drops relative to T2. Moreover, on assuming a Boltzmann distribution for the vibrational levels of each manifold and recognizing that the individual vibrational levels in the S1 manifold (i.e., S1(ν)) are populated thermally one can write67 ∞
∑
kisc )
kisc(ν) e-E(ν)/RT
E(ν))E ∞
∑
(8) -E(ν)/RT
e
E(ν))0
In this expression, kisc(ν) and E(ν) are the ISC rate constant and excess vibrational energy at a given S1 vibrational level, ν, respectively. The effects of fluid density on the 9CA S1-T2 ISC (i.e., knr) process are illustrated in Figures 9 and 10. First, at low fluid densities the FC factor from the S1 to T2 manifold is significant (Figure 9 point A) and there is an appreciable degree of S1-T2 ISC because ∆E (Figure 10, top panel) is small enough such that several vibrational levels, S1(ν), are populated at the experimental temperature. As the fluid density is increased (Figure 9, point B), ∆E increases further as the S1 shifts to lower energy to a greater extent than T2.67 Hence, the FC factor in eq 7 decreases, the number of individual vibrational modes
8506 J. Phys. Chem., Vol. 100, No. 20, 1996
Rice et al. 1950-3100 cm-1 regions68 and the local density profiles (Figure 4). Such a degree of vibrational overlap is significantly less between CF3H and CO2 and 9CA most especially in the lowfrequency regions. The issue of vibrational coupling and microstructure is the subject of related work from the Blanchard and Bright groups.69 Conclusions
Figure 10. Schematic diagram describing the fluid density dependence of ∆E and hence kisc in SF. (upper panel) Low-density region. (center panel) Intermediate-density region. (lower panel) High-density region. Symbols: S1(ν), vibrational level ν, within the S1 manifold; kisc(ν), vibrational level-dependent ISC rate between S1(ν) and T2(ν′) (eq 7); T2(ν′), vibrational level ν′, within the T2 manifold. Note: ν and ν′ are generally not the the same vibrational level numbers.
within the S1 manifold that are thermally populated and can couple to the T2 manifold decreases (Figure 10, center panel), and kisc decreases. Finally, at the highest densities (Figure 9, point C), ∆E increases further because the fluid better solvates the S1 state and the number of individual vibrational modes within S1 that can couple to (i.e., are thermally populated) T2 declines (Figure 10, lower panel) and the FC factor for ISC again decreases. In the CO2 and CF3H fluids the FC factor that governs ISC essentially approaches zero at high fluid densities. However, in C2H6, kisc is still significant even at the highest densities investigated. It is unlikely that such arises because of a difference in the thermal population of the S1 states between the individual solvents. A more likely explanation is that ∆E is not as large in C2H6 compared to the other fluids, there is stronger vibrational coupling between 9CA and C2H6, and/or there are differences in the local solute-fluid microstructure surrounding the 9CA in C2H6. The first scenario can be ruled out because the 9CA absorbance maxima vs fluid density (not shown) are not consistent with such. The final two scenarios are possibilities due to the strong overlap in the vibrational spectra of 9CA and C2H6 in the 750-900, 1350-1600, and
We have carried out a detailed set of experiments to determine the nature of energy dissipation between a model solute, 9CA, in supercritical C2H6, CO2, and CF3H over a broad density range. We have demonstrated for the first time that the 9CA fluorescence quantum yield in SFs is not constant with fluid density. In the near-critical region, the 9CA quantum yield depends strongly on density and fluid structure but levels off at a value near unity at moderate to high fluid densities in CO2 and CF3H. The 9CA quantum yield does not, however, level off to unity in C2H6; it approaches 0.65 at the highest density investigated. Experimental estimates of the local fluid density augmentation surrounding 9CA over the same density range parallel the quantum yield and lifetime results and suggest that the coupling between 9CA and the individual fluids is actually quite different from one another. When used in concert with fluorescence lifetime data, the quantum yields provide direct access to the actual radiative and nonradiative decay rates that describe the 9CA deexcitation kinetics. In the low-density region, the nonradiative decay rate/ pathway dominates in all fluids investigated. The radiative pathway only dominates above a reduced density of 0.4 in CO2 and CF3H and above 0.6 in C2H6. Thus, one can control, over a fairly broad range, the actual rate terms and the relative efficiency of the individual pathways by tuning the SF density and structure. As an example, we can effectively “shut down” 9CA photoemission (kr) and force energy into nonradiative relaxation (S1-T2) pathways at low densities in any of the SFs studied. Furthermore, we can adjust the relative magnitude of the individual relaxation processes by tuning the fluid density over a modest range. Deviation from the Strickler-Berg relationship, which predicts a linear dependence of kr with n2, and which is well established to hold in liquid solvents, has been verified for 9CA in the low-density region in SFs. This deviation cannot be accounted for entirely on the basis of changes in the 9CA fluorescence quantum yield nor on bathochromic shifts of the 9CA absorbance spectra. Calculations demonstrate that adherence to the Strickler-Berg predictions can result only if there is a density dependence in the 9CA molar absorptivity. Recent experiments on anthracene and pyrene66 demonstrate that the average solute molar absorptivity is indeed a function of fluid density and such may indeed account for the observed “deviation” from the Strickler-Berg predictions. The strong density dependence of the 9CA nonradiative decay rate is interpreted in terms of an increase in fluid density leading to an increase in the energy gap (∆E) between T2 and S1 states. Specifically, at the lower fluid densities the S1-T2 intersystem crossing (ISC) rate increases because ∆E is small, the fraction of 9CA molecules that occupy states within the S1 manifold above the lowest vibrational level of the T2 envelope is increased, and the number of thermally populated vibrational levels in the S1 manifold that can facilitate ISC crossing from S1 to T2 is increased because the Franck-Condon factor depends strongly on ∆E (Figures 9 and 10). However, as density is increased, ∆E increases, the Franck-Condon factor decreases (Figure 9), the number of thermally populated vibrational modes within the S1 manifold decreases (Figure 10), and kisc decreases.
9-Cyanoanthracene in C2H6, CO2, and CF3H Together these results demonstrate that one can use SFs to control the distribution of energy between radiative and nonradiative states simply by modulating the local microenvironment surrounding the solute which in turn controls the S1-T2 energy gap. Acknowledgment. Financial support for this research was provided by the Division of Chemical Sciences, Office of Basic Energy Sciences, Office of Energy Research, United States Department of Energy (DE-FG02-ER14143-A002). We thank Professor Ya-Ping Sun for providing preprints of his work prior to publication and also thank Professor Gary J. Blanchard for his computational help on the 9CA ground- and excited-state dipole moments. References and Notes (1) Brennecke, J. F.; Eckert, C. A. AIChE J. 1989, 35, 1409. (2) Eckert, C. A.; Knutson, B. L. Fluid Phase Equilib. 1993, 83, 93. (3) Supercritical Fluid Engineering Science. Fundamentals and Applications; Kiran, E., Brennecke, J. F., Eds.; ACS Symposium Series 514; American Chemical Society: Washington, DC, 1993. (4) Supercritical Fluid Technology. Theoretical and Applied Approaches in Analytical Chemistry; ACS Symposium Series 488; Bright, F. V., McNally, M. E. P., Eds.; American Chemical Society: Washington, DC, 1992. (5) Supercritical Fluid Science and Technology; Johnston, K. P., Penninger, J. M. L., Eds.; ACS Symposium Series 406; American Chemical Society: Washington, DC, 1989. (6) Supercritical Fluid Technology-ReViews in Modern Theory and Applications; Bruno, T. J., Ely, J. F., Eds.; CRC Press: Boca Raton, FL, 1991. (7) Eckert, C. A.; Ziger, D. H.; Johnston, K. P.; Kim, S. J. Phys. Chem. 1986, 90, 2738. (8) Eckert, C. A.; Ziger, D. H.; Johnston, K. P.; Ellison, T. K. Fluid Phase Equilib. 1983, 14, 167. (9) Kim, S.; Johnston, K. P. AIChE J. 1987, 33, 1603. (10) Debenedetti, P. G.; Petsche, I. K.; Mohamed, R. S. Fluid Phase Equilib. 1989, 52, 347. (11) Petsche, I. B.; Debenedetti, P. G. J. Chem. Phys. 1989, 91, 7075. (12) Wu, R-S.; Lee, L. L.; Cochran, H. D. Ind. Eng. Chem. Res. 1990, 29, 977. (13) Morita, A.; Kajimoto, O. J. Phys. Chem. 1990, 94, 6420. (14) Chialvo, A. A.; Debenedetti, P. G. Ind. Eng. Chem. Res. 1992, 31, 1391. (15) Sun, Y.-P.; Bennett, G.; Johnston, K. P.; Fox, M. A. J. Phys. Chem. 1992, 96, 10001. (16) Betts, T. A.; Zagrobelny, J.; Bright, F. V. J. Am. Chem. Soc. 1992, 114, 8163. (17) Eckert, C. E.; Knutson, B. L. Fluid Phase Equilib. 1993, 83, 93. (18) Chialvo, A. A.; Cummings, P. T. AIChE J. 1994, 40, 1558. (19) Johnston, K. P.; Haynes, C. AIChE J. 1987, 33, 2017. (20) Kim, S.; Johnston, K. P. Ind. Eng. Chem. Res. 1987, 26, 1206. (21) Randolph, T. W.; Carlier, C. J. Phys. Chem. 1992, 96, 5146. (22) Kaupp, G. Angew. Chem., Int. Ed. Engl. 1994, 33, 1452. (23) (a) Roberts, C. B.; Zhang, J.; Chateauneuf, J. E.; Brennecke, J. F. J. Am. Chem. Soc. 1993, 115, 9576. (b) Robert, C. B.; Zhang, J.; Brennecke, J. F.; Chateauneuf, J. E. J. Phys. Chem. 1993, 97, 5618. (24) DeSimone, J. M.; Maury, E. E.; Menceloglu, Y. Z.; McClain, M. B.; Romack, T. J.; Combes, J. R. Science 1994, 265, 356. (25) Scholsky, K. M. J. Supercrit. Fluids 1993, 6, 103. (26) Sonnenschein, M.; Amariv, A.; Jortner, J. J. Phys. Chem. 1984, 88, 4214. (27) Hirayama, S.; Shobatake, K.; Tabayashi, K. Chem. Phys. Lett. 1985, 121, 228. (28) Hirayama, S. J. Chem. Phys. 1986, 85, 6867. (29) Amirav, A. Chem. Phys. 1988, 124, 163. (30) Hirayama, S.; Iuchi, Y.; Tanaka, F.; Shobatake, K. Chem. Phys. 1990, 144, 401. (31) Hirayama, S.; Yasuda, H.; Okamoto, M.; Tanaka, R. J. J. Phys. Chem. 1991, 95, 2971.
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