A Fluorescence Lifetime and Integral Equation Study of the Quenching

A Fluorescence Lifetime and Integral Equation Study of the Quenching of Naphthalene Fluorescence by Bromoethane in Super- and Subcritical Ethane...
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A Fluorescence Lifetime and Integral Equation Study of the Quenching of Naphthalene Fluorescence by Bromoethane in Superand Subcritical Ethane Daniel P. Roek,† John E. Chateauneuf,‡ and Joan F. Brennecke*,† Department of Chemical Engineering, University of Notre Dame, Notre Dame, Indiana 46556, and Department of Chemistry, Western Michigan University, Kalamazoo, Michigan 49008

We report on the solvent effect on a kinetic-controlled energy-transfer reaction in super- and subcritical ethane. The reaction chosen, the quenching of naphthalene fluorescence by C2H5Br, occurs well below the diffusion-controlled limit in liquid solvents and in ethane. The reaction was studied in ethane over a wide range of pressures, extending from 34.8 to 111.6 bar at 40 °C, which corresponds to reduced densities (Fr ) F/Fc, where Fc is the critical density of ethane) between 0.27 and 1.76. The rate constants in super- and subcritical ethane range from 2.42 × 108 to 1.36 × 109 M-1 s-1, which is several orders of magnitude below the diffusion-controlled limit (which is on the order of 1011 M-1 s-1 at these conditions). As in several previous reports, the apparent rate constants, based on bulk concentrations of the reactants, increase dramatically with decreasing pressure in the supercritical region. More importantly, at reduced densities below about 0.44, the apparent rate constants based on bulk concentrations decrease with decreasing pressure. Because the rate constants are solvent insensitive in a variety of liquid solvents, we attribute the behavior of the apparent rate constants in ethane to local composition enhancement of C2H5Br around naphthalene. In addition, we present compelling theoretical (based on integral equation calculation) results that confirm a maximum in the local composition of C2H5Br around naphthalene near a reduced density of 0.44. This is the first experimental study of a simple, bimolecular reaction over such a wide range of densities. Moreover, it is the first to show a maximum in the reaction rate, which corresponds to the expected maximum in the local composition enhancement. Introduction There has been significant exploration of the local composition of attractive cosolvents in the vicinity of dilute solutes in supercritical fluid (SCF) mixtures. For example, Kim and Johnston1 used spectral shifts to calculate local compositions of several cosolvents around phenol blue in supercritical carbon dioxide (SC CO2). They demonstrated that the local composition of a cosolvent can be at least 7.5 times that of the bulk. Of particular interest is the finding that the local composition of an attractive cosolvent around a dilute solute in a SCF solution is a function of pressure, with the highest values being at the lowest pressures, which happened to be near the critical point. These results have been corroborated by several researchers using a variety of spectroscopic probes, and many of these studies are discussed in two recent review papers.2,3 Most of these experimental studies were limited to conditions above the critical point because the probe molecules were not sufficiently soluble in the fluids at lower pressures. However, in a single-phase system the local composition of an attractive cosolvent around a solute must surely decrease at lower pressures, diminishing completely in the limit of an ideal gas. This has not been explored previously and is the focus of this current study. * To whom correspondence should be addressed. Telephone: (219) 631-5847. Fax: (219) 631-8366. E-mail: [email protected]. † University of Notre Dame. ‡ Western Michigan University.

The effect of the local composition on kinetic-controlled reactions in SCFs has been studied by numerous researchers.2-14 A primary conclusion that has come from these studies is that the reaction rates of kineticcontrolled reactions can be strongly influenced by the local composition of one of the reactants around the other. For reactions run at conditions close to the critical point and above, this means the reaction rates at the lower pressures, near the critical point, are much higher than the rates at higher pressures. The higher rates at the lower pressures have been attributed to the higher concentration of the reactants in the vicinity of the reaction center. However, the rates of a reaction between a solute and a nonattractive cosolvent are relatively insensitive to pressure.6 As mentioned previously, the primary limitation of these systems has been the solubility of the reactants. The low solubility, especially at conditions below the critical point, has limited the studies to conditions at or above the critical point. The goal of our research is to probe the influence of local composition enhancements on reactions at conditions in the gas-phase region, just below the critical pressure. To achieve that goal, we have examined the quenching of naphthalene fluorescence by C2H5Br in ethane at 40 °C, which is about 8 °C above the critical temperature. Dilute solutions at this temperature can be traversed smoothly from the high-pressure supercritical region to the low-pressure gas-phase region without any change of phase. Using laser excitation at 266 nm, the naphthalene is promoted to its excited state, from which it can emit a photon, producing easily

10.1021/ie000057u CCC: $19.00 © 2000 American Chemical Society Published on Web 06/27/2000

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measured fluorescence. However, in the presence of a quencher like C2H5Br, the excited-state naphthalene will lose its energy through the nonemissive competing pathway of energy transfer. This will result in a decreased fluorescence intensity and a shortened fluorescence lifetime after the laser excitation pulse. The fluorescence quenching of naphthalene by C2H5Br is a simple, bimolecular, energy-transfer reaction. As shown below, it is a kinetic-controlled reaction in liquid solvents and, like the quenching of anthracene with C2H5Br that we have studied previously, occurs by heavyatom-induced intersystem crossing.8 In this study the reactants, naphthalene and C2H5Br, are both sufficiently soluble in ethane at 40 °C to allow investigation over a wide range of densities, well into the low-density gas-phase region. Ethane was used as a solvent for this reaction rather than CO2 because CO2 forms complexes with naphthalene,15 resulting in quenching of naphthalene fluorescence by CO2. This was corroborated by our measurements of naphthalene fluorescence lifetimes in SC CO2, which were much shorter than those obtained in liquid solutions. Ethane has moderate critical properties (Tc ) 305.4 K, Pc ) 48.8 bar, and Fc ) 6.875 mol/ L)16 and serves as an excellent solvent in which to examine this reaction. Experimental Section Materials and Apparatus. Naphthalene (Aldrich, 99+%, scintillation grade), bromoethane (Aldrich, 99+%), acetonitrile (Aldrich, 99.9+%, HPLC grade), cyclohexane (Aldrich, 99.9+%, HPLC grade), and hexane (Aldrich, 99+%) were used as received. Nitrogen (Mittler, 99.5%) for deaerating was also used as received. Ethane (Scott Specialty Gases, ultrahigh-purity grade 99.99%) was passed through high-pressure charcoal traps (Alltech) before use. Fluorescence lifetime excitation was accomplished by a Quanta Ray DCR-1 Nd:YAG laser system (266 nm, ∼10 mJ, and pulse width ∼6 ns) at the Radiation Laboratory at the University of Notre Dame, operated in fluorescence mode. Transient fluorescence signals were recorded with a PMT, digitized with a Tektronix 7912 AD digitizer, and controlled by a VAX-11/708. Lifetime analysis was performed with Microcal Origin, Version 6, software from Microcal Software Inc. The high-pressure stainless steel optical cell used in this experiment was fitted with Suprasil quartz windows and equipped for 90° detection. The capacity was approximately 2.5 mL. The cell has been described previously.17 Procedure. Solutions of 2 × 10-5 M naphthalene in various liquid solvents were prepared and placed in 1-cm path length Suprasil cuvettes, and the cuvettes were capped with white rubber septa (Aldrich). Using syringe needles, the solution was deaerated for 20 min with nitrogen gas to remove the oxygen (O2). Various amounts of liquid C2H5Br were injected into the cuvette using a 5-µL syringe (Hamilton) to perform the quenching studies. High-pressure naphthalene/ethane and naphthalene/ ethane/C2H5Br samples were prepared by injecting a small amount of a stock naphthalene/hexane solution into the high-pressure cell. The cell was sealed, evacuated to remove the O2 and hexane, and filled to the desired pressure with pure ethane or an ethane/C2H5Br solution from an Isco model 260D syringe pump up to the highest pressure studied. Samples of a particular

Table 1. Lennard-Jones Parameters Used in the Integral Equation Calculations, along with the Bulk Mole Fractions ethane-ethane C2H5Br-C2H5Br naphthalene-naphthalene

/k (K)

σ (Å)

bulk xi

215.7 554.4 388.2

4.443 6.45 5.018

0.99 0.01 0.000001

mole fraction of C2H5Br in ethane were prepared in an Isco model 260D high-pressure syringe pump by placing an appropriate amount of liquid C2H5Br in a Rheodyne HPLC injection loop. This was then flushed into the Isco pump with pure ethane at 138 bar and 40 °C from another Isco pump. Sufficient time was allowed for the samples in the pump to mix fully. The experiments were run from high to low pressure by releasing a naphthalene/ethane or naphthalene/C2H5Br/ethane solution from the cell. The solution density was required at each condition studied in order to estimate quencher concentrations. Because both naphthalene and C2H5Br concentrations were quite low, the solution density was determined from an accurate equation of state for pure ethane.18 Mole fractions of C2H5Br ranged between 0.0030 and 0.012, yielding concentrations of C2H5Br ranging from 0.0056 to 0.14 M. For all high-pressure experiments, the temperature within the high-pressure optical cell was monitored and controlled with a platinum resistance thermometer that made direct contact with the supercritical fluid mixtures and an Omega (model CS-6071A) temperature controller equipped with a Watlow Firerod cartridge heater. Pressure was monitored at the optical cell with a Heise (model 901A) digital pressure gauge. The optical cell temperature and pressure were typically maintained at (0.1 °C and (0.1 bar, respectively. Integral Equation Studies In the analysis of the experimental results, we present the results of integral equation analysis to examine the local composition of C2H5Br around naphthalene in super- and subcritical ethane at 40 °C. Integral equation calculations are a theoretical method to determine the radial distribution function (and, therefore, fluid structure and thermodynamic properties) given the interaction potential between the molecules. We used the integral equation method of Zhang et al.19 and Roberts et al.,6 which is based on the Ornstein-Zernike relation between the total correlation function and the direct correlation function, along with the Percus-Yevick closure. The equations were solved with the LabikGillan numerical technique, which combines NewtonRaphson and direct iteration methods. For a detailed explanation of the methodology, please refer to the work by Zhang et al.19 As a first approximation, we have used LennardJones (spherical) potentials for the species involved. The parameters used are summarized in Table 1, along with the bulk compositions of the species used in the calculations. The parameters for ethane and naphthalene were taken directly from Reid et al.20 The C2H5Br parameters were estimated from critical parameters given in Reid et al.20 The value of the parameters chosen can have a significant effect on the outcome of the results. The two primary factors that effect local composition are energetics and molecular packing (i.e., the Lennard-Jones energy and size parameters). A higher attractive energy between particles tends to pull them closer together. As

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Ind. Eng. Chem. Res., Vol. 39, No. 8, 2000 Table 2. Rate Constants for the Quenching of Naphthalene Fluorescence by C2H5Br in Various Solvents, along with Their Physical Properties solvent

dielectric constant

viscosity (cP)

temp (°C)

kbi (M-1 s-1)

ethane (45.7 bar) ethane (111.6 bar) hexane cyclohexane acetonitrile

1.09a 1.46a 1.88c,d 2.02c,e 37.5c,e

0.0128b 0.0421b 0.313c,e 1.0c,e 0.38c,f

40 40 23 26 26

1.17 × 109 2.42 × 108 1.50 × 108 1.85 × 108 2.13 × 108

a Reference 18. b References 20 and 28. c Reference 29. d Liquid data at 25 °C. e Liquid data at 20 °C. f Liquid data at 15 °C.

Figure 1. Stern-Volmer plots for quenching of naphthalene fluorescence by C2H5Br in liquid solvents at room temperature.

was shown in Roberts et al.,6 the solute typically has a larger energy parameter than the main solvent (i.e., ethane). In this case, if the cosolvent has a larger energy parameter than the solvent, it will preferentially occupy the region close to the solute, leading to increased local compositions of the cosolvent. As presented below, this is what we observe for the naphthalene/ethane/C2H5Br system. On the other hand, if the solvent and cosolvent have similar energy parameters, there will be very little or no preferential solvation. Experimental Results The fluorescence quenching reaction of naphthalene with C2H5Br was studied at 40 °C, which corresponds to a reduced temperature of 1.03. This temperature was selected, instead of one closer to the critical temperature of 32.2 °C, to avoid critical opalescence. The experiments were conducted from high to low pressure, by release of a homogeneous solution. The low-pressure limit was determined by the point where it was no longer possible to obtain a good signal. To obtain bimolecular rate constants, fluorescence lifetimes (τ) of the fluorophore (naphthalene) were measured at 321.5 nm at different pressures and different quencher (C2H5Br) concentrations. Stern-Volmer plots were constructed (τ/τ0 versus quencher concentration), and the Stern-Volmer constants, KSV, were determined from the slopes of the graphs. In the relationship shown below, τ0 is the lifetime of the fluorophore in the absence of the quencher.

τ0/τ ) 1 + KSV[quencher]

(1)

The bimolecular quenching rate constant, kbi, is related to the Stern-Volmer constant, KSV, by the following relationship:

kbi ) KSV/τ0

(2)

First, we measured the bimolecular rate constants for the fluorescence quenching of naphthalene by C2H5Br in a variety of liquid solvents. This work confirmed that the reaction is kinetically controlled and that it is not strongly influenced by solvent polarity or viscosity. Stern-Volmer plots for the fluorescence quenching of naphthalene by C2H5Br in various liquid solvents are shown in Figure 1. They are clearly linear over the concentration range studied and yield Stern-Volmer constants (i.e., slopes) of 16.42 M-1 for hexane, 20.38

Figure 2. Fluorescence lifetimes of naphthalene at 40 °C as a function of pressure in pure ethane, as well as in several ethane/ C2H5Br mixtures (concentrations given in mole fractions in the figure).

M-1 for cyclohexane, and 20.01 M-1 for acetonitrile. The fluorescence lifetimes of naphthalene in these solvents in the absence of quencher were found to be 109.4 ns for hexane, 110.4 ns for cyclohexane, and 93.8 ns for acetonitrile, all of which are in good agreement with literature values.21 Using these lifetimes and SternVolmer constants, we calculated bimolecular rate constants of 1.50 × 108 M-1 s-1 in hexane, 1.85 × 108 M-1 s-1 in cyclohexane, and 2.13 × 108 M-1 s-1 in acetonitrile. In each of these solvents, the rate constant is about 2 orders of magnitude below the diffusion control limit. Moreover, they are independent of the viscosity and dielectric constant of the solvent (see Table 2). Therefore, the quenching of naphthalene fluorescence by C2H5Br is a kinetic-controlled reaction whose rate is independent of the solvent. Thus, this reaction is an excellent probe of solvent effects on kinetic-controlled reactions in SCFs. We then measured the bimolecular rate constants for the quenching of naphthalene by C2H5Br in ethane at 40 °C and pressures from 34.8 to 111.6 bar. All experiments were carried out from high to low pressure at constant mole fractions of both the fluorophore and the quencher, as described above. The lifetimes of naphthalene are shown in Figure 2 as a function of pressure in pure ethane, as well as in ethane/C2H5Br mixtures at the four mole fractions of C2H5Br noted on the figure. In pure ethane the lifetime of naphthalene changes about 25% over the pressure range studied. This is expected because fluorescence lifetimes can be affected by changes in the refractive index of the solvent, which varies substantially over the pressure range investigated, as well as changes in the fluorescence quantum

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Figure 3. Stern-Volmer plots for quenching of naphthalene fluorescence by C2H5Br in ethane at 40 °C for the lowest, highest, and four intermediate pressures studied.

Figure 4. Bimolecular rate constants based on bulk concentrations as a function of pressure for naphthalene fluorescence quenched by C2H5Br in ethane at 40 °C.

yield, the extinction coefficient, and small absorption spectral shifts.8,22 With C2H5Br present, the lifetimes dip at intermediate pressures. This is due to the high reaction rates at those pressures, as discussed below. From these measured fluorescence lifetimes and the C2H5Br molar concentrations (determined from the mole fractions and the solution densities at 40 °C), we constructed Stern-Volmer plots of τ/τ0 versus the bulk concentration of C2H5Br at each pressure. These are shown at several example pressures in Figure 3. As expected, these Stern-Volmer plots are linear over the entire concentration range studied. From the SternVolmer plots and the lifetimes of naphthalene in pure ethane (τ0), we calculated the bimolecular rate constants at each pressure based on the bulk C2H5Br concentrations. These bimolecular rate constants are shown as a function of pressure in Figure 4 and as a function of density in Figure 5. The rate constants increase from a value of 2.42 × 108 M-1 s-1 at a pressure of 111.6 bar to a value of 1.36 × 109 M-1 s-1 at a pressure of 45.7 bar, a 5.6-fold increase over that pressure range. Below 45.7 bar, the rate constants decrease. As can be seen in the density plot (Figure 5), the bimolecular rate constants based on bulk concentrations are relatively symmetric around a density of about 3 mol/L (45.7 bar at 40 °C).

Figure 5. Bimolecular rate constants based on bulk concentrations as a function of density for naphthalene fluorescence quenched by C2H5Br in ethane at 40 °C.

Discussion The experimental results in Table 2 show that, for the quenching of naphthalene fluorescence by C2H5Br, the rate constants based on bulk concentrations in a variety of liquid solvents and in SC ethane at 111.6 bar (Pr ) 2.29) are nearly identical. This is consistent with the conclusion that this reaction is relatively solvent insensitive. However, the rate constant based on bulk concentrations of reactants in ethane at 45.7 bar (Pr ) 0.94) is about 5.6 times higher than that at 111.6 bar. In fact, Figure 4 shows that the reaction rate increases as the pressure is decreased. There are several factors that could contribute to this trend. These include changes in bulk solvent properties such as dielectric constant, the thermodynamic pressure effect on the rate constant due to general molecular interactions, and a change in the mechanism resulting in the formation of a highly polar transition state. Also, increases in the local density augmentation or local composition enhancement of one reactant around the other could cause this type of apparent rate constant behavior. Each of these possibilities is explored below. To explore the effect of bulk solvent properties on the reaction, the reaction was run in a variety of liquid solvents, as summarized in Table 2. Although the viscosities and dielectric constants of the three liquid solvents and high-pressure ethane vary widely, the reaction rates are all approximately 2 × 108 M-1 s-1. This indicates that this reaction is not affected significantly by these properties. The thermodynamic pressure effect due to molecular interactions can be estimated from transition state theory using the Peng-Robinson equation of state, as has been described in more detail elsewhere.5-7 For this reaction, we found that the Peng-Robinson equation (with binary interaction parameters set to zero) predicted that the bimolecular rate constants should increase slightly with increasing pressure over the entire pressure range. This is opposite to the trend observed experimentally for the bimolecular rate constants based on bulk concentrations for all pressures above 45.7 bar. Thus, we conclude that the observed behavior cannot be explained by the thermodynamic pressure effect on the actual rate constant itself. Another possibility is that there is a change in the fluorescence quenching mechanism to the formation of a charge-transfer complex. However, if this were the case, low dielectric constant solvents would reverse the

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quenching process, as demonstrated by Ware and Novros.23 Because this is not the case in our system, we conclude that the reaction does proceed by heavyatom-induced intersystem crossing and does not involve a charge-transfer complex. The other possible explanations for the interesting maximum in the apparent bimolecular rate constants are increased local density of the solvent and increased local composition. The local density augmentation around the naphthalene could account for a slight enhancement of the reaction rate, because a higher local density would lead to a higher concentration of quencher molecules near the fluorophore. However, experimental and theoretical studies of local density enhancement have shown that local densities are generally no greater than twice the bulk density,8,24-26 meaning that local density augmentation alone would not account for the large increase in the apparent rate constant. Studies of the local composition, however, have shown local enhancement of the cosolvent composition to be up to 10 times higher than the bulk composition.1,3,5,7,8,19 This could account for a higher reaction rate at intermediate pressures, which would appear as a higher rate constant when bulk concentrations of reactants were used in the analysis. Zhang et al.8 examined an energy-transfer reaction very similar to the one presented here. In particular, they studied the quenching of anthracene fluorescence by C2H5Br in SC CO2. This reaction occurs by the same mechanism as the fluorescence quenching of naphthalene by C2H5Br, and its rate is also insensitive to the solvent. They observed a dramatic increase in the apparent rate constant (based on bulk reactant concentrations) at the lowest pressures accessible, which were near the critical point. They came to the conclusion that the increase in the apparent reaction rate constant was actually due to enhancement of the local composition of C2H5Br around anthracene. They verified this by using spectral shifts in the same fashion as Kim and Johnston1 to measure the local composition of C2H5Br around anthracene as a function of pressure. After calculating the bimolecular rate constant using the local compositions rather than the bulk compositions, they found the reaction to be solvent insensitive over the entire range of pressures, which was more in line with expectations. The reactions of C2H5Br with both naphthalene and anthracene occur by heavy-atom-induced intersystem crossing, and both reactions are relatively solvent insensitive. The similarity between the two reactions leads us to believe that the dramatic increase in the apparent rate constant we observe for the naphthalene/C2H5Br reaction may be a result of the increased local C2H5Br composition around the naphthalene, as was concluded for the anthracene/C2H5Br reaction. The main difference between the current study of the fluorescence quenching of naphthalene by C2H5Br and the previous study of the quenching of anthracene is that in the present study we were able to obtain rate constants at much lower pressures. The experimental apparent bimolecular rate constant results at these lower pressures are very revealing. In particular, at pressures of less than 45.7 bar, the apparent rate constants decrease with decreasing pressure; i.e., the apparent rate constant at 45.7 bar is the maximum, with lower values at pressures on either side. This is shown clearly in Figure 4 as a function of pressure, as

well as in Figure 5 as a function of density. Of course, the values shown in the figures are bimolecular rate constants based on bulk concentrations of the reactants. Because the quenching of naphthalene by C2H5Br should be relatively solvent insensitive, this suggests that the increase in the reaction rates shown in the figures may actually be due to an increase in the local composition of C2H5Br around naphthalene. This interpretation suggests that in the supercritical region the local C2H5Br concentration increases with decreasing pressure, as has been shown by spectroscopic measurements.1-3 More interestingly, it shows that at some pressure (i.e., about 45.7 bar) the local composition of C2H5Br around the naphthalene decreases as the pressure is reduced further. Although, to our knowledge, this eventual decrease in the local C2H5Br concentration at lower pressures has not been measured experimentally, it clearly must occur because there is no local composition enhancement in the limit of an ideal gas. Thus, the data shown in Figures 4 and 5 strongly support the theory that the apparent increase in the rate constants at intermediate densities is actually a result of the increased local composition of C2H5Br around naphthalene. Using a fluorescence quenching reaction, we have found the point at which the local structure around a dilute solute molecule begins to break up and heads toward the low-pressure, ideal gas limit. Our understanding of the maximum in the local composition is as follows. At low pressures the average distance between the molecules is so large that the attractive forces are negligible and, subsequently, there is no preferential solvation in the system. However, as the pressure is increased, the average distance between molecules decreases and the differences in the attractive potentials result in the preferential solvation of some species, such as the preferential solvation of naphthalene by bromoethane, as occurs here. As the pressure is increased further, the extent of this preferential solvation increases. At the maximum in the local composition enhancement, there is still plenty of free volume for the molecules to arrange themselves in their energetically preferred positions. Conversely, as the pressure is increased further, the free volume decreases, limiting the ability of the molecules to arrange themselves in the energetically favorable, but entropically unfavorable, condition. At even higher pressures, i.e., in the limit of liquidlike densities, the degree of preferential solvation is determined both by the attractive potentials between the molecules and by packing or size effects, as is the case in liquid solutions. The maximum in the local composition enhancement is simply the density where the molecules are close enough to be attracted to each other but not so close that they are limited by size, packing, and the lack of free volume. An interesting feature of the data, which is most clearly shown in Figure 5, is that the local composition enhancement, and its subsequent effect on the reaction rates, is apparently not a phenomenon related to the critical point. In fact, the maximum in the reaction rates, and the subsequent maximum in the local composition enhancement, occurs at a reduced density of 0.44. At the critical temperature and density, the isothermal compressibilities (and other properties such as the constant-pressure heat capacity) diverge.27 Although we are operating at 40 °C, 8 °C above the critical temperature of ethane, we still expect the maximum in the isothermal compressibility to be at a density not far

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Figure 6. Integral equation calculations of local compositions of C2H5Br around naphthalene in ethane at 40 and 63 °C.

from the critical density. In fact, the equation of state for pure ethane18 indicates that the maximum in the isothermal compressibility at 40 °C is at a reduced density of about 0.88. Thus, the maximum in the local composition enhancement (at Fr ) 0.44) does not coincide with the maximum in compressibility (at Fr ) 0.88) so the local composition maximum should probably not be attributed to critical phenomena. It is interesting to note that the local density augmentation of a pure fluid around a dilute solute, which has been studied by several researchers,2,3 also reaches a maximum at densities well below the critical point. Further confirmation that the changes in the rate of the fluorescence quenching of naphthalene with C2H5Br are due to changes in the local compositions might be obtained with spectroscopic measurements of the local compositions. Unfortunately, neither the absorption nor the fluorescence spectrum of naphthalene shifts with the addition of C2H5Br, so we were unable to measure the local composition of C2H5Br around naphthalene in ethane. In lieu of experimental evidence of local composition enhancement, we have performed an integral equation analysis to examine the trends of local composition enhancement. We used Lennard-Jones (spherical) potentials with the parameters given in Table 1 to estimate local compositions in a theoretical naphthalene/C2H5Br/ethane system. The results are shown in Figure 6, which gives the local composition enhancement of C2H5Br around naphthalene as a function of density in a 0.0001 mol % naphthalene/1 mol % C2H5Br/99 mol % ethane mixture at 40 and 63 °C. The cutoff radii were chosen to represent a single sphere of solvent solution around the central naphthalene molecule. A sphere of radius r ) 1.725 corresponds to a shell of ethane molecules, while a sphere of radius r ) 1.854 corresponds to a shell of the slightly larger C2H5Br molecules. Of course, a real solvent mixture would include both ethane and bromoethane molecules. As seen in the graph for both temperatures, the exact value of this cutoff radius in this range makes very little difference in the local compositions. The first thing that can be seen in Figure 6 is that the local composition passes through a maximum, with lower values at higher and lower pressures. Most importantly, the maximum in the local composition at 40 °C from the integral equation calculations occurs at a density remarkably similar to the density where the maximum in the apparent rate constants occurs. The magnitude of the local composition enhancement from the integral equation calculations is not as high as the experimental data suggest, but this is not surprising because of the simple potential used in the calculations. The potentials used are spherical Lennard-Jones potentials with parameters estimated from critical properties. This is a very crude approximation. The real

molecules are not spherical and could, perhaps, be better represented by ellipsoids with partial charges, by explicit atoms, or by a united atom model. We anticipate that these improvements in the ethane, bromoethane, and naphthalene potentials would provide more quantitative agreement with the experimental results. Moreover, if higher energy parameters or lower size parameters from C2H5Br were used with the simple spherical Lennard-Jones potential, the calculated local compositions would be higher. Yet, these simple calculations clearly show the qualitative behavior of the local composition enhancements. The local compositions for this system at 63 °C are also shown in Figure 6. The magnitude of the local composition enhancement is less at this temperature, as expected, because the system should become more random as the temperature is raised. In addition, the maximum in the local composition is shifted to a slightly lower density. Therefore, at 63 °C one would expect to see an enhancement in the rate of the quenching reaction of naphthalene with bromoethane, but the enhancement should be less pronounced than that at 40 °C and the maximum should be at a slightly lower density. We believe that the experimental data presented here for the naphthalene quenching by C2H5Br in sub- and supercritical ethane, along with the local compositions calculated from integral equation theory, provide compelling evidence that reaction rates in dense gases, as well as in supercritical fluids, can be enhanced by the increased local composition of one of the reactants around the other. Conclusions We have used fluorescence lifetime measurements to determine the reaction rate constants for naphthalene fluorescence quenched by C2H5Br. Results in liquids show that the reaction is kinetic-controlled and solvent insensitive. Results in ethane at 40 °C show a dramatic increase in the apparent rate constants (based on bulk reactant concentrations) at intermediate pressures, reaching a maximum at about a reduced density of 0.44. Rather than being due to a change in the rate constants themselves, this behavior is attributed to the increase in the local composition of C2H5Br around naphthalene. Integral equation studies of the local composition of C2H5Br around naphthalene reinforce the conclusion that the changes in the observed rates as a function of pressure are due to local composition changes. We believe that this study provides the most compelling evidence available that reaction rates in dense gases and supercritical fluids can be enhanced dramatically by the increased local composition of one of the reactants around the other. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. The work described herein was also supported by the Texaco Fellowship through the Notre Dame Center for Catalysis and Reaction Engineering. The researchers are also grateful to the Radiation Laboratory at the University of Notre Dame for the use of the Nd:YAG laser system used to measure naphthalene fluorescence lifetimes and to Professor Lloyd L. Lee, who originally provided assistance in the development of the ternary integral equation code.

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Received for review January 14, 2000 Revised manuscript received May 15, 2000 Accepted May 16, 2000 IE000057U