Fluorescence Emission and Absorption Spectra of Naphthalene in Cyclohexane Solution: Evidence of a Naphthalene–Oxygen Charge–Transfer Complex

Abstract

Molecular fluorescence is typically reduced or “quenched” by dissolved oxygen present in solutions. Quenching mechanisms are broadly categorized as dynamic quenching, and static quenching. Dynamic quenching involves collisions between oxygen and the fluorophore. Static quenching occurs when the fluorophore forms a nonfluorescent complex with oxygen. In a previous study, oxygen quenching of naphthalene showed evidence of static quenching, although the mechanism was not known. The earlier work was limited to low oxygen concentrations (∼2 mM) in cyclohexane, leading to relatively large uncertainties in the value of the static quenching constant. In the present study, oxygen concentrations up to ∼50 mM were used, resulting in a more accurate determination of the static quenching constant. Absorption spectra obtained at higher oxygen concentrations revealed the spectrum of a new species, which we interpret as that of a naphthalene-oxygen charge-transfer complex. The binding energy of the naphthalene-oxygen complex was estimated and compared with that of the benzene-oxygen complex. In the method described herein, the equilibrium (or association) constant for the naphthalene-oxygen complex was assumed to be the static quenching constant, as determined from graphs of relative fluorescence intensities vs oxygen concentration using the Stern–Volmer formalism. The values of the complex molecular absorption coefficients were determined from graphs of absorbance vs oxygen concentration using the value of the static quenching constant from fluorescence data. This method differs from a commonly used method in which graphs of absorbance vs oxygen concentration are used to determine the product of the equilibrium constant and the complex absorption coefficient. The latter method can lead to substantial errors in both these quantities if the spectrum of the free molecule and complex overlap significantly.

Introduction

It is well-known that oxygen quenches molecular fluorescence. Fluorescence lifetimes and quantum yields are reduced, and molecules having longer fluorescence lifetimes are more strongly quenched. There are two types of quenching, dynamic and static.¹ Dynamic quenching results from collisions of the excited state fluorophore with oxygen molecules and is diffusion controlled. The fluorophore, usually in its lowest singlet excited state, interacts with oxygen and is converted via intersystem crossing to a lower energy triplet state. In the case of static quenching, the fluorophore might form a nonfluorescent complex with oxygen. This could be a van der Waals complex or a charge-transfer complex for which the fluorophore and oxygen are electron donor and acceptor, respectively.

Many organic molecules including cyclohexane form weakly bound transient complexes with oxygen giving rise to new absorption bands in the ultraviolet and visible region. These absorption bands were attributed to charge-transfer interactions between the organic molecule and oxygen by Tsubomura and Mulliken.² The theory of charge-transfer complexes is discussed by Mulliken and Person³ and by Birks.⁴ A charge-transfer (CT) complex can be described as an electron donor–acceptor pair, wherein an electron from the donor molecule (e.g., benzene) is transferred to an acceptor molecule (e.g., oxygen). Two electronic states are formed, a ground state and an excited state. In the ground state the donor electron resides primarily in the lowest energy molecular orbital of the donor, whereas in the excited state the transferred electron resides primarily in an unfilled molecular orbital of the acceptor.

In a simplified theory of the electronic interaction, the charge-transfer excited state energy can be represented as a function of the ionization potential of the donor, the electron affinity of the acceptor, and the energy of the dipole moment created by electron transfer. After absorbing a photon, the excited state can subsequently lose energy to form lower energy excited states of the individual molecules. For CT complexes in which oxygen is the acceptor, the lowest singlet state of oxygen (a¹Δ_g), commonly known as “singlet oxygen”, may be formed. The photophysical properties of singlet oxygen, including its production, reaction mechanisms, and applications to biological systems are given in recent reviews.^5,6

The benzene-oxygen CT complex has a well-defined absorption band in the ultraviolet region and has been studied in both the vapor phase⁷ and in solution.⁸ A band located in approximately the same spectral region is expected for a naphthalene-oxygen complex, but to our knowledge has not been reported. However, evidence of this complex has been observed at much longer wavelengths. Dijkgraaf et al.⁹ studied naphthalene in chloroform pressurized to 24 atm oxygen. They observed a weak (ε_max ∼ 1 M^–1 cm^–1) absorption band at ∼345 nm that was not due to an impurity or to singlet–triplet absorption. The absorbance of this band was proportional to the naphthalene concentration and was linear with oxygen pressure, suggesting a charge-transfer band.

Kuriyama et al.¹⁰ studied the absorption spectra of 1-methylnaphthalene at high concentration (0.3 M) in solvents having different refractive indices. Solutions were measured under conditions of saturation with nitrogen and oxygen at atmospheric pressure. A broad band in oxygenated solutions attributed to charge-transfer occurs in 335–370 nm region near the onset of the longest wavelength absorption band of 1-methylnapthalene. This band maximum was found to shift to longer wavelengths as a function parameter (n² – 1)/(2n² + 1) where n is the solvent refractive index, suggesting that a CT excited state is stabilized by dispersive interactions with solvent molecules.

Evidence of molecular complexes with oxygen in solution has been found using fluorescence methods. Lakowicz and Weber¹¹ applied the Stern–Volmer formalism to relative fluorescence intensities as a function of oxygen concentration. A high-pressure optical cell capable of maintaining 1500 psig (∼100 atm) oxygen pressure was used for the measurements. They determined dynamic and static quenching constants in both aqueous and nonaqueous solvents and concluded that in aqueous solvents quenching was purely dynamic, with no evidence of static quenching. Static quenching would have been observed as an upward-curving Stern–Volmer graph with increasing oxygen concentration, whereas the graphs were linear. In contrast, static quenching was observed for several fluorophores (7-methylanthracene, 9-vinylanthracene, and perylene) in dodecane, and for indole in pure ethanol. Static quenching constants ranged from 2.6 M^–1 (perylene) to 6.9 M^–1 (indole); these values are 2–5% of the corresponding dynamic quenching constants. Due to the lack of observed changes in the absorption spectra at high oxygen concentrations, the authors concluded that complex formation was unlikely and attributed the static constant to sphere-of-action quenching.¹

Pagano et al.¹² developed a novel technique that allowed simultaneous determination of fluorescence intensity, fluorescence lifetime, absorbance, and oxygen concentration as oxygen diffused into solution. They applied this method to 1-aminoanthracene in cyclohexane solution and determined the dynamic and static oxygen quenching constants. An interesting result of this study was a relatively large static quenching constant found for 1-aminoanthracene, compared with naphthalene studied here. The authors attributed static quenching to sphere-of-action quenching, although formation of a charge-transfer complex was also considered possible.

Graf et al.¹³ studied van der Waals (vdW) complexes with 9-cyanoanthracene (9-CNA) in a supersonic jet with He, Ne, Ar, and Xe. They observed vdW complex formation with Ar and Xe, but not with O₂. However, they found evidence of O₂ fluorescence quenching when 9-CNA and O₂ were both within a ∼ 20-atom Ar cluster. Lehmann and co-workers found evidence of vdW complexes with O₂ with perylene,¹⁴ and benzo[g,h,i] perylene, and coronene¹⁵ in helium microdroplets using bolometric detection. The experiments using molecular beams and helium nanodroplets suggest that quenching by oxygen via complex formation may be enhanced if fluorophore and oxygen molecules are held more closely together within an inert molecular cluster that functions as a solvent.

Recently, Thorning et al.¹⁶ performed theoretical calculations of the electronic states of the toluene-oxygen charge-transfer complex. The calculations predict a relatively strong absorption band with maximum at ∼215 nm, in approximate agreement with the experimental value for the benzene-oxygen charge-transfer band.^7,8 Weaker absorption bands were predicted in the 300–350 nm region and attributed to singlet–triplet transitions of toluene. Theoretical calculations of oxygen-organic molecule charge-transfer bands are of particular importance in cases wherein charge-transfer bands, typically broad, overlap the electronic transitions of the free molecule, making them difficult to distinguish.

In a previous study, lifetimes and fluorescence intensities of several four polycyclic aromatic hydrocarbons (PAH) were measured in cyclohexane solution.¹⁷ Dynamic and static quenching constants were derived from Stern–Volmer graphs of intensities and fluorescence lifetimes versus oxygen concentration. For two of the PAH studied, naphthalene and pyrene, graphs of relative fluorescence intensity versus oxygen concentration showed an upward curvature at higher oxygen concentrations, evidence of static quenching. In the present study, naphthalene absorption and fluorescence spectra were measured at much higher oxygen concentrations, up to 50 mM versus 2.4 mM in the earlier study. Molecular absorption coefficients for the complex were determined from graphs of absorbance versus oxygen concentration at different oxygen pressures. Determination of the complex absorption coefficients also requires knowledge of the static quenching constant, obtained from fluorescence measurements.

Experimental Methods

All measurements were obtained at ambient laboratory temperature of 20 ± 1 °C. Naphthalene (Aldrich, 99+%) was used without additional purification. Cyclohexane (Acros, HPLC grade, 99%) was used without further purification. Oxygen and nitrogen (both Airgas, Ultra High Purity) were used for all purging or pressurization measurements. Solutions were stored in 30 mL glass vials having screw caps and Teflon liners.

Spectrophotometer Cells

Three types of spectrophotometer cells were used, with cell walls constructed of fused silica. For solutions in which the oxygen content was relatively low, e.g., air-saturated solutions or solutions purged with nitrogen or oxygen, a 1 cm path fluorescence cell with plastic screw cap was used (Starna Cells, type 3-Q-GL14-S). This type of cell can accommodate either a solid cap or a septum cap. For purging experiments, a Restek Thermolite septum was used. Details of the purging procedure are described in ref (17).

For measurements at oxygen concentrations above 1 atm, a nominal 1 cm path cell (actual path length 0.9 cm) designed for high-vacuum studies was used initially (Starna Cells ultra high vacuum (UHV) Stopcock cell, type 700-HLT-3-Q-10H UHV). This cell has a Teflon stopcock and could be pressurized to approximately 5 atm according to the manufacturer.

Although the UHV cell functioned well, the relatively long path length resulted in high absorbance below ∼250 nm due to the presence of a cyclohexane-oxygen charge-transfer complex. Naphthalene has a strong absorption band at ∼220 nm, and features in the naphthalene spectrum in cyclohexane below ∼230 nm could not be accurately determined due to high solvent absorption. For this reason, later studies were performed using a dual-path cell (path lengths 0.1 and 1 cm), with a screw cap (Starna Cells, type 52-Q-GL14-S). The shorter path length allowed use of higher naphthalene concentrations while reducing the solvent background absorption. The manufacturer was not able to provide a shorter path cell with stopcock, so a dual-path cell with screw cap was modified to operate at higher pressures. For this research, a standard Starna plastic screw cap was modified to accept a 1:8 in. (outside diameter) copper tube through the center of the cap. Two o-rings, one a gas seal for the cap to the copper tube and the other a seal for the top of the cell to the inside of the cap, were used. One arm of a brass toggle valve (Swagelok) was attached to the tube in the cell and the other arm attached to a gas manifold with pressure gauge as described below. Pressure testing showed that the cell could be pressurized up to ∼50 psig (4.4 atm) oxygen; higher pressures were not attempted. The cell was oriented in the absorption and fluorescence spectrophotometers such that incident light passed through the 0.1 cm path.

Spectroscopic Instrumentation

Absorption spectra were obtained using a Cary/Varian 300 dual-beam spectrophotometer. A Cary/Varian Eclipse fluorescence spectrophotometer was used for fluorescence measurements. The Cary/Varian instrument has a Peltier-cooled sample holder, and the sample was maintained at 20 C ± 1 °C during measurements. Fluorescence emission measurements were made for multiple excitation wavelengths. Fluorescence intensities at excitation wavelengths below ∼220 nm were low due to strong solvent absorption. In this case, signal averaging for noise reduction was performed by reducing the scan speed from 120 to 30 nm/min and averaging 6–8 scans for a given excitation wavelength.

Experimental parameters are given in Table 1. In this table, λ_ex and λ_em refer to the fluorescence excitation and emission wavelengths, respectively. For the Cary Eclipse fluorometer, the slits are horizontal, and the beam heights and widths at the sample are 1.3 × 7.4 mm² respectively for spectral bandwidths 5 nm (specifications provided by Agilent Technologies). Fluorescence intensities were corrected for the primary inner filter effect,¹⁸ using the slit image dimensions given above.

Table 1. Experimental Parameters Used for Spectroscopic Measurements.

naphthalene conc. (mM)	0.01	0.25 and 0.11	0.02 and 0.01
O2 pressure	1 atm	0–4.4 atm (0–50 psig)	0–4.4 atm (0–50 psig)
cell and path length	septum cell, 1 cm	dual-path cell, 0.1 cm	UHV cell, 0.9 cm
λabs (nm)	190–350	190–350	190–350
SBW absorption (nm)a	2	2	2
λex (nm)		200–300	200–300
λem (nm)		250–450	250–450
SBW excitation (nm)		5	5
SBW emission (nm)		5	5
Scan rate (nm/min)
absorption	200	200	200
fluorescence		120 and 30	120 and 30

^aSBW—spectral bandwidth.

Determination of Dissolved Oxygen Concentrations

The procedure used to determine oxygen concentrations were the same as described ref (17). The oxygen solubility in cyclohexane was assumed to be 0.0114 M at 20 °C at 1 atm based on values given in a critical review.¹⁹ A more recent review of oxygen solubilities²⁰ gives two additional values that are within 2% of this value, although these values are for 25 °C.

Effective molecular absorption coefficients for the cyclohexane-oxygen CT band were derived for the spectral region 210–240 nm using the data of Munck and Scott.²¹ These authors show absorption spectra of oxygen in cyclohexane at three oxygen pressures: 0, 0.18, and 0.84 atm. Their absorbance values were digitized at intervals of 10 nm and fitted to a quartic polynomial in wavelength. This procedure gave values of the effective absorption coefficients at different wavelengths which were used to remove cyclohexane background absorption from the spectra of naphthalene in cyclohexane. These coefficients assumed that all oxygen molecules form a CT complex, although this might not be correct.

Oxygen concentrations in cyclohexane at higher oxygen pressures were assumed to obey Henry’s law. Two studies have considered the validity of Henry’s law for oxygen in cyclohexane. Wild et al.²² studied the solubility of nitrogen and oxygen in cyclohexane at pressures up to 16 atm and at temperatures 20–170 °C. Air was used instead of oxygen due to the reactivity of oxygen at high temperatures. For oxygen, at 39 C, the authors give values of Henry’s constant 1.217 × 10^–3 (mole fraction/atm) at 12.9 atm and 1.205 × 10^–3 at 11.6 atm respectively; the oxygen solubility at 36 °C at 1 atm was 1.21 × 10^–3 using a gas chromatographic method. These values are in good agreement with the value 1.231 × 10^–3 at 1 atm at 20 °C, and 1.239 × 10^–3 at 40 °C given in ref (19).

Brass et al.^20,23 measured the solubilities of nitrogen and oxygen in cyclohexane and methanol at 25 °C at elevated pressures. For oxygen in cyclohexane, they measured oxygen solubilities at 6 pressures from 1.0 to 9.6 atm. Gas solubilities versus pressure were analyzed using least-squares fitting to linear and quadratic functions. They found that a quadratic function gave a better fit, implying that there was a departure from linearity for both oxygen in cyclohexane and in methanol; in contrast, the fits were nearly linear for nitrogen in both solvents. We analyzed their data for oxygen in cyclohexane using a least-squares fit to a quadratic function and obtained values of the linear and quadratic coefficients (mole fraction/atm) 1.312 ± 0.1345 and 0.00846 ± 0.0123, respectively. The standard deviation of the quadratic coefficient is larger than the coefficient itself, and at the 95% confidence level (−0.031–0.048) includes the value zero. We conclude that the oxygen solubility in cyclohexane is likely to be linear with pressure over this range, due to the uncertainty in the data. In summary, both studies support the conclusion that oxygen solubility in cyclohexane obeys Henry’s law in the range of ∼0–10 atm. The maximum pressure used in the present study was 4.4 atm.

Oxygenation of Solutions

For studies at atmospheric pressures, solutions were purged with nitrogen or oxygen in a 1 cm path fused silica cell with screw cap and rubber septum as described above. A Teflon liner (0.25 mm thick) was inserted between the septum and cap in order reduce the risk of septum contamination. The purging system and procedures were the same as described previously.¹⁷ The gas flow rate was 2.5 cm³/min and the purging time 20 min. A nitrogen purging time of 20 min was found to reduce oxygen content to ∼1% of the air-saturated value. At the nitrogen flow rate used, typically ∼1% of the cyclohexane was lost. Naphthalene solutions were weighed before and after purging and absorbance values corrected for solvent loss.

Solutions purged with oxygen at atmospheric pressure were prepared in the same manner. To determine the cyclohexane oxygen concentration, the spectrum of cyclohexane purged for 20 min with nitrogen (to remove oxygen) was subtracted from the cyclohexane spectrum and the oxygen concentration calculated as described above. For naphthalene in cyclohexane solutions, the spectrum of naphthalene in cyclohexane at the same naphthalene concentration, after purging with nitrogen for 20 min, was subtracted from the sample naphthalene solution, so that only absorption due to the cyclohexane-oxygen charge-transfer band was present.

For solutions with oxygen pressures above 1 atm a UHV stopcock cell (0.9 cm path) or dual-path screw-cap cell (0.1 and 1 cm path length) with modified cap was used. Although the manufacturer stated that the cells could withstand 5 atm pressure, they would not guarantee this. For this reason, the highest oxygen pressure used was ∼50 psig (4.4 atm). The cell was housed in a Plexiglas safety enclosure while being pressurized.

The cell was connected to a manifold consisting of an oxygen tank, pressure gauge readable to ∼ ±0.3 psig, particulate filter, and tubing. Wire-reinforced polyvinyl tubing was connected to a side arm of the cell, and the cell and the line flushed with oxygen prior to pressurization of the solution. To remove trapped air, the lines were pressurized at the intended pressure several times and the pressure released prior to opening the valve at the cell. For a series of measurements at different pressures, the initial sample pressure was 5 or 10 psig. After acquiring data at a particular pressure, the cell with the same solution was returned to the manifold and pressurized to a higher pressure, e.g., 15 psig, and the measurements repeated. The same solution was thereby pressurized and measured at intervals of 5 psig up to a final pressure of ∼50 psig. A series of measurements using pure cyclohexane were made at the same nominal pressures. At least 48 h elapsed before making absorption and fluorescence measurements to establish an equilibrium dissolved oxygen concentration.

Determination of Naphthalene–Oxygen Complex Absorption Coefficients

If a molecule in solution forms a complex with oxygen, the total absorbance A of the solution, neglecting other absorption bands, e.g., solvent impurities or a solvent-oxygen complex, is given by

1

where ε_m and ε_c are the molar absorption coefficients of the free solute molecule and complex with oxygen respectively at a given wavelength, and c_m and c_c are the concentrations of free molecule and complex. If the initial concentration of the free molecule is c_m0, then

2

Substituting eq 2 into eq 1 gives

3

If molecule M forms a 1:1 complex with oxygen, with an equilibrium constant K

4

5

If [O₂] is much larger than [M] as is the case here (typically 100×), then

6

From eq 6, the concentrations of the free molecule and the complex are

7

8

Substituting eq 8 into eq 3 gives

9

If K[O₂] ≪ 1, eq 9 becomes

10

From eq 10, a graph of A/c_m0 versus oxygen concentration should give a straight line with slope equal to (ε_c – ε_m) K, from which ε_c can be determined if the naphthalene molar absorptivity ε_m, K, and [O₂] are known.

Results

Absorption Measurements

Naphthalene 0.01 mM Absorption Spectra in 1 cm Path Cell Purged with O₂

Naphthalene in cyclohexane solutions studied previously¹⁷ were purged with nitrogen and absorption spectra obtained for purge times of up to 15 min. The spectrum for the longest purge time was subtracted from spectra taken at shorter purge times to estimate oxygen concentrations. Small absorbance changes (∼0.01 or less) appeared in the resulting spectra at ∼220 nm and were correlated with oxygen concentration. This phenomenon was not explored further until after the results had been published. Subsequently, naphthalene solutions were purged with oxygen for periods of up to 20 min and compared with solutions prior to purging. This procedure revealed larger spectral changes at wavelengths below ∼230 nm due to oxygen.

An example of the effect of higher oxygen concentration is shown in Figure 1, which shows absorption spectra of naphthalene in cyclohexane obtained before and after purging with oxygen. Spectra of cyclohexane obtained before and after purging using the same purging time were subtracted from the naphthalene spectra, and background-subtracted spectra are shown in Figure 2. Note that the naphthalene absorbance after purging is slightly less than the spectrum before purging below ∼230 nm. The “after purging” spectrum absorbance was corrected for a small loss of solvent, resulting in a slight increase in concentration during purging. The difference spectrum suggests the presence of a naphthalene-oxygen complex having absorption coefficients less than those of naphthalene in the 230–220 nm region. Absorbance differences below 215 nm are less accurate because absorbance values of naphthalene solutions purged with oxygen are greater than 3, the approximate limit of absorbance linearity (within 1–2%). Absorbance values below 215 nm are reduced by the presence of instrument stray light and were not corrected for this effect.

Figure 1.

Absorption spectra of naphthalene 0.01 mM in cyclohexane and cyclohexane, 1 cm path septum cell, before and after purging the solution with oxygen.

Figure 2.

Absorption spectra of naphthalene 0.01 mM in cyclohexane, 1 cm path septum cell, before and after purging solution with oxygen, cyclohexane backgrounds subtracted. Oxygen concentrations ∼2.4 mM and 11 mM respectively before and after purging.

Spectra obtained before and after purging with oxygen shown in Figure 2 are averages of three determinations comparable to the one shown in Figure 1. Absorbance differences between the spectra taken before and after oxygen purging are near the noise level (0.001) except below ∼230 nm. The largest negative absorbance for the difference spectrum in Figure 2 is ∼−0.05 ± 0.01 at 222 nm and can be used to derive a value of (ε_c – ε_m) using eq 10. The value derived is significantly larger (∼5×) than expected from data using a 0.1 cm path cell at higher oxygen concentrations described below. This is probably because the absorption spectra of oxygen-purged solutions were measured within a few minutes of purging and were not at equilibrium; locally high oxygen concentrations could result in locally high concentrations of a naphthalene-oxygen complex. As noted above, much longer equilibration times were allowed for measurements at higher oxygen concentrations.

As shown in Figure 1, absorption due to the cyclohexane-oxygen complex below 250 nm is significant with a 1 cm path cell. For this reason, measurements at higher oxygen concentrations were made using a dual-path cell, 0.1 cm path.

Methodology for the Determination of Parameters ε_c, K, a, and K_d

In this section, we give a brief description of the experimental procedures and how these were used to obtain important parameters. Absorption spectra of naphthalene in cyclohexane were obtained over a range of oxygen pressures at fixed naphthalene concentration. Spectra of cyclohexane were obtained at the same nominal pressures used for naphthalene solutions. Spectra of naphthalene were obtained by subtracting solvent backgrounds, after correcting for differences in oxygen concentrations.

Naphthalene absorbances were plotted versus oxygen pressure, and the graphs analyzed by the linear least-squares method to give values of slopes and intercepts. From the slopes, the values of the molecular absorption coefficient differences (ε_c– ε_m) were estimated as described above. The value of ε_c at a given wavelength was determined from the value for ε_m along with the value of the constants K or a obtained from analysis of fluorescence data, described below.

During the same experiments as for recording absorption spectra, fluorescence spectra were measured at the same nominal oxygen pressures. Data was analyzed by plotting ratios of fluorescence intensity relative to the oxygen-free intensity as a function of oxygen concentration (Stern–Volmer graphs). The resulting graphs are not linear, and generally exhibit a slight upward displacement at higher oxygen concentration due to the presence of a static complex. The constants K and a represent formation constants for a complex and a charge-transfer complex, respectively. The dynamic quenching constant K_d was also determined as part of the same nonlinear curve fitting procedure. The values of ε_c, K_d, K, and a are given in the tables below.

Naphthalene 0.25 mM Absorption Spectra in Dual-Path Cell Pressurized with O₂

Naphthalene solutions in cyclohexane and cyclohexane were pressurized with oxygen up to ∼50 psig, Measurements were made at intervals of 5 psig O₂ as determined by a pressure gauge. Oxygen pressures at which data were taken are given in Table 2 for naphthalene and cyclohexane. Since the oxygen concentrations for naphthalene vs cyclohexane differ for the same nominal pressures, the cyclohexane spectra were corrected so that the cyclohexane-oxygen charge-transfer absorbance values in the 230–240 nm spectral region matched those for the corresponding naphthalene spectrum. The cyclohexane sample having the oxygen concentration nearest to that for naphthalene was used for correction. The correction procedure is described in more detail in Supporting Information.

Table 2. Oxygen Pressures for Naphthalene 0.25 mM in Cyclohexane and Cyclohexane, Dual-Path Cell.

pressure (psig)	naphthalene [O2] mM	cyclohexane [O2] mM	solvent spectrum for correction (psig)
air-saturated	2.36	2.49
10	10.0	11.4	10
15	17.9	16.9	15
20	19.7	21.7	20
25	27.7	26.0	25
30	35.3	30.2	35
35	40.4	35.0	40
40	45.5	39.6	45
45	50.1	44.5	50
50	54.7	49.8	55
55		53.4

Graphs of cyclohexane absorbance vs oxygen concentration were linear over the oxygen concentration range 0–50 mM, as expected from Henry’s law. Graphs of naphthalene absorbance vs oxygen concentration were linear up to absorbance ∼3. These graphs, using data from Tables 2 and 4 are included in Supporting Information.

Table 4. Oxygen Pressures and Concentrations Used for 0.11 mM Naphthalene in Cyclohexane and Cyclohexane, Dual-Path Cell.

pressure (psig)	naphthalene [O2] mM	cyclohexane [O2] mM	solvent spectrum for correction (psig)
air-saturated	2.37	2.43
10	12.0	9.53	10
15	16.0	15.2	15
20	16.3	16.5	20
30	33.6	33.9	35
35	38.5	39.7	40
40	44.0	44.1	45
45	47.3	49.2	50
50	51.8	49.2	50
50	52.7	49.2	50

Absorbance values were graphed as a function of oxygen concentration and linear least-squares coefficients calculated assuming a linear dependence of absorbance with concentration. Examples for wavelengths 275, 250, 230, 225, 222, and 215 nm are shown in Figure 3. Absorbance values at 15 wavelengths from 290–200 nm at different oxygen concentrations and graphs for other wavelengths are given in Supporting Information.

Figure 3.

Absorbance vs oxygen concentration, naphthalene 0.25 mM in cyclohexane in dual-path cell, 275, 250, 230, 225, 222, and 215 nm, 0.1 cm path length.

The value of (ε_c – ε_m) at a given wavelength was determined from the value of the slope of absorbance vs oxygen concentration using eq 10. The value of ε_c can be determined using the value of ε_m at this wavelength and the value of K from fluorescence measurements, discussed in a later section. Values of ε_m for naphthalene were obtained from an average of 11 measurements of air-saturated solutions with naphthalene concentration 0.01 mM using a 1 cm fused silica cell. The errors in the values of (ε_c – ε_m) were derived from the corresponding errors in the values of the slopes. A negative value of the slope implies ε_c < ε_m and conversely.

Calculated values of (ε_c – ε_m) are given in Table 3. For these calculations, the value of K in eq 10 was 0.003 mM^–1, as discussed in a later section. Standard errors of estimates and the 95% probability range of (ε_c – ε_m) are included in the table. In Table 3 and all following tables, the units of ε_c and ε_m are mM^–1cm^–1.

Table 3. Naphthalene 0.25 mM in Cyclohexane in Dual-Path Cell, Values for (ε_c – ε_m), ε_c, and ε_m (mM cm^–1) and Error Estimates (Δ) Assuming K = 0.003 mM^–1.

λ (nm)	εc – εm	Δ(εc – εm)	Δ(εc – εm) lowa	Δ(εc – εm) higha	εm	Δεm	εc	Δεc
290	0.47	0.16	0.11	0.82	2.01	0.20	2.48	0.26
275	1.02	0.22	0.52	1.52	5.58	0.17	6.60	0.28
250	0.254	0.08	0.08	0.43	2.24	0.11	2.49	0.14
240	0.012	0.13	–0.27	0.3	1.23	0.15	1.24	0.20
230	–0.841	0.07	–1.01	–0.68	2.54	0.41	1.70	0.41
227	–2.23	0.86	–4.18	–0.28	10.5	1.05	8.27	1.36
225	–6.25	3.02	–13.1	0.59	34.3	3.77	28.05	4.83
222	–37	6.83	–52.5	–21.6	105	3.15	67.96	7.52
221	–7.6	1.78	–11.65	–3.56	100	4.00	92.40	4.38
220	–10.9	5.05	–22.3	0.56	88.2	4.41	77.34	6.70
215	6.91	2.53	1.20	12.6	62.2	3.73	69.11	4.51
210	1.99	1.16	–0.63	4.61	33.2	3.65	35.19	3.83
205	–2.64	1.05	–5.02	–0.27	20.3	4.26	17.66	4.39
200	–5.94	1.7	–9.79	–2.1	12.5	5.13	6.56	5.40

^aRange of values expected for (ε_c – ε_m), 95% probability.

The 95% probability levels for Δ(ε_c – ε_m) show that for some wavelengths, such as 275, 230, 227, 222, and 221 nm the associated signs are either both positive or both negative, implying that ε_c is significantly greater or smaller than ε_m at these wavelengths.

Naphthalene 0.11 mM Absorption Spectra in a Dual-Path Cell Pressurized with O₂

Absorbance data using a naphthalene solution concentration 0.11 mM were obtained prior to the above measurements using similar oxygen concentrations. Oxygen pressures for naphthalene and cyclohexane are given in Table 4. Graphs of absorbance vs oxygen pressure are shown in Figure 4 for wavelengths 275, 250, 230, 225, 222, and 215 nm. Absorbance values and graphs for other wavelengths are given in Supporting Information.

Figure 4.

Absorbance vs oxygen concentration, naphthalene 0.11 mM in cyclohexane in dual-path cell at 275, 250, 230, 225, 222, and 215 nm.

Values of (ε_c – ε_m) and error estimates were obtained from the slopes of absorbance vs oxygen concentration using eq 10, as described above, and are given in Table 5. The value of K used was the same as for the data in Table 3.

Table 5. Naphthalene 0.11 mM in Cyclohexane in Dual-Path Cell, Values for (ε_c – ε_m), ε_c, and ε_m (mM cm^–1) and Error Estimates Assuming K = 0.003 mM^–1.

λ (nm)	εc – εm	Δ(εc – εm)	Δ(εc – εm) lowa	Δ(εc – εm) higha	εm	Δεm	εc	Δεc
290	–0.26	0.25	–0.81	0.29	2.01	0.20	1.75	0.32
275	0	0.23	–0.51	0.52	5.58	0.17	5.58	0.28
250	–0.2	0.22	–0.68	0.29	2.24	0.11	2.04	0.25
240	0.07	0.15	–0.27	0.4	1.23	0.15	1.30	0.21
230	0.49	0.35	–0.3	1.28	2.54	0.41	3.03	0.54
227	–0.19	0.5	–1.31	0.92	10.5	1.05	10.3	1.16
225	–9.37	1.68	–13.1	–5.62	34.3	3.77	24.9	4.13
222	–8.34	1.71	–12.2	–4.52	105	3.15	96.7	3.58
221	6.53	1.78	2.95	11.8	100	4.00	107	4.38
220	8.44	1.7	4.65	12.28	88.2	4.41	96.6	4.73
215	13.12	2.48	7.6	18.6	62.2	3.73	75.3	4.48
210	11.13	3.67	2.96	19.3	33.2	3.65	44.3	5.18
205	13.54	4.9	2.63	24.5	20.3	4.26	33.8	6.49
200	11.87	6.39	–2.36	26.1	12.5	5.13	24.4	8.19

^aRange of values expected for (ε_c – ε_m), 95% probability.

Values of ε_c in Table 5 differ from those in Table 3 due to two sources of error: a lower naphthalene concentration, and the error associated with subtracting the cyclohexane-oxygen background absorption, discussed in Supporting Information.

Absorption spectra of naphthalene and the complex using data from Tables 3 and 5 are shown in Figure 5. In this figure, ε_c (a) refers to the data obtained using 0.11 mM naphthalene and ε_c (b) refers to 0.25 mM naphthalene solution.

Figure 5.

Absorption spectra of the naphthalene-oxygen complex ε_c and naphthalene ε_m derived from two data sets having naphthalene concentrations 0.11 mM (a) and 0.25 mM (b).

Values of (ε_c – ε_m), and therefore ε_c, are expected to be more accurate for 0.25 mM naphthalene solution than 0.11 mM solution because of the greater naphthalene concentration. Results for ε_c using the UHV stopcock cell over a more limited wavelength range are given in the next section.

Naphthalene 0.02 mM Absorption Spectra in UHV Stopcock Cell Pressurized with O₂

Absorbance measurements were made over a relatively limited wavelength range, 290–227 due to high solvent absorbance at shorter wavelengths. Experimental parameters are given in Table 1 and oxygen pressures in Table 6. Absorbance values are given in Supporting Information.

Table 6. Oxygen Pressures and Concentrations used for Naphthalene 0.02 mM in Cyclohexane and Cyclohexane, UHV Cell.

pressure (psig) or as noted	naphthalene [O2] mM	cyclohexane [O2] mM
N2-purged	0	0
air-saturated	1.77	2.09
air-saturated	1.95	2.14
O2-purged	10.5	10.8
5	14.4	14.9
10	17.9	18.5
15	21.8	22.5
20	25.4	26.0
25	29.2	29.7
30	33.2	33.3
35	36.8	37.3
40	41.0	41.0
45	44.6	45.0
50	50.2	48.8

Cyclohexane spectra were subtracted from the naphthalene spectra after correcting for the difference in oxygen concentration between the two solutions at the same nominal pressure as discussed previously. Absorbance values at seven wavelengths from 290–225 nm at different oxygen concentrations, 0–50 mM, were fitted to a linear equation from which the values of (ε_c – ε_m) were determined from least-squares coefficients. The data is summarized in Table 7.

Table 7. Naphthalene 0.02 mM, UHV Cell, (ε_c – ε_m) Values and Error Estimates Δ(ε_c – ε_m), K = 0.003 mM^–1.

λ (nm)	(εc – εm)	Δ(εc – εm)	Δ(εc – εm) lowa	Δ(εc – εm) higha	εm	εc
290	0.60	0.48	–0.43	1.64	2.01	2.61
275	–0.06	0.90	–2.01	1.90	5.58	5.52
250	0.31	0.42	–0.61	1.24	2.24	2.55
240	0.07	0.22	–0.40	0.54	1.23	1.30
230	–1.20	0.82	–2.98	0.58	2.54	1.34
227	–2.55	12.0	–35.9	30.8	10.5	7.95
225	–47.7	38.2	–153.8	58.3	34.3	–13.41

^aRange of values expected for (ε_c – ε_m) 95% probability.

For wavelengths 227 and 225 nm, only data for the first six oxygen concentrations (0–17.9 mM in Table 6) were used. At wavelengths below 230 nm, errors due to subtraction of the cyclohexane absorption result in large errors, as indicated by the negative value of ε_c at 225 nm. At 227 and 225 nm, graphs of absorbance vs oxygen concentration become increasing nonlinear (trending to smaller values) at higher oxygen concentration. The reason for the nonlinearity is not understood but might be a result of subtracting the absorption spectrum of pure naphthalene to obtain the solvent background correction factor. The correction method did not account for additional absorption by the naphthalene-oxygen complex.

Values of ε_c in Table 7 are in fair agreement with values obtained using the dual-path cell for wavelengths 230 nm and greater. For all wavelengths, the 95% confidence values for Δ(ε_c – ε_m) include zero, implying ε_c and ε_m are not significantly different.

Fluorescence Measurements

Fluorescence Intensity Ratios and Stern–Volmer Analyses

As noted above, fluorescence quenching can occur via two mechanisms, dynamic and static. The dynamic quenching constant K_d = k_d τ₀, where k_d is the dynamic quenching rate and τ₀ is the fluorescence lifetime time in the absence of oxygen.¹ The static constant K is the equilibrium constant involving naphthalene and oxygen in cyclohexane. These constants can be determined from the quantity F₀/F where F₀ and F are the fluorescence intensities in the absence and presence of oxygen respectively.

Derivation of the Stern–Volmer quenching formula for F₀/F given by Lakowicz¹ assumes that the complex does not fluoresce. In this case, the fluorescence intensity ratio F₀/F, for a given excitation wavelength is given by the equation

11

If both the free molecule and the complex fluoresce when excited at the same excitation wavelength, the above equation becomes

12

The quantity α = (ε_c/ε_m) (ϕ_c/ϕ_m0), where ε_c, ε_m, ϕ_m0, ϕ_c are the molar absorption coefficients and fluorescence quantum efficiencies of the free molecule in the absence of oxygen and the complex respectively.

If a charge-transfer complex is formed between the solute molecule and oxygen, then according to Orgel and Mulliken²⁴ the concentration of the complex c_c is given by the following relationship, where a is the formation constant

13

In this case, eq 12 becomes

14

If a [O₂] ≪ 1, eq 14 becomes

15

eq 15 is similar in form to eq 11, with a replacing K.

Values of the constants K_d, K, a, and α, and their standard deviations, were determined using a nonlinear least-squares fitting method (MicroMath Scientist).

Naphthalene 0.25 mM in Cyclohexane Solution, Dual-Path Cell, F₀/F Values

Fluorescence intensities were measured at different oxygen pressures after the absorbance measurements described above. Cyclohexane was measured at the same nominal pressures as the naphthalene solution. At pressures of 30 psig and above, and wavelengths below 220, multiple scans (up to eight) were measured and averaged to obtain higher signal-to-noise ratios. Cyclohexane backgrounds were subtracted, and the integrated fluorescence intensities measured between 310–400 nm using GRAMS/AI software (Thermo Electron Corp.).

Values of F₀/F at 13 different oxygen concentrations, 0–55 mM for 12 excitation wavelengths are given in Supporting Information. Graphs for six of these wavelengths in the range 275–200 nm are shown in Figure 6. In the graphs, use of a quadratic least-squares equation is intended to show trends in the data only; least-squares coefficients obtained were not used to determine values of K_d and K. Note that the curvature is slightly upward at higher oxygen concentrations for longer excitation wavelengths but becomes downward sloping at shorter excitation wavelengths. Possible reasons for this behavior are discussed in a later section. For excitation at 275–210 nm the graphs show a slight upward curvature at higher oxygen concentration, consistent with the presence of a nonfluorescent complex.

Figure 6.

Stern–Volmer graphs for naphthalene 0.25 mM in cyclohexane, dual-path cell, excitation at 275, 250, 230, 220, 210, and 200 nm. Vertical axes values are units F₀/F, the ratio of fluorescence intensity in the absence of oxygen to that in the presence of oxygen.

Values obtained for K_d, K, and α and their standard deviations assuming complex formation (eq 12) are given in Table 8. Parameter values assuming charge-transfer complex formation (eq 14) are given in Table 9. Parameter values and standard deviations were determined using MicroMath Scientist.

Table 8. Naphthalene 0.25 mM, Values for K_d, K and α Obtained from Stern–Volmer Analyses and Equation 12 (Δ = Standard Deviation).

λ (nm)	Kd (mM–1)	ΔKd (mM–1)	K (mM–1)	ΔK (mM–1)	α	Δα
275	2.316	0.036	0.0026	0.0004	0
250	2.280	0.056	0.0028	0.0006	0
245	2.277	0.045	0.0027	0.0005	0
240	2.303	0.042	0.0027	0.0004	0
235	2.311	0.112	0.0039	0.0012	0
230	2.320	0.115	0.0032	0.0012	0
225	2.171	0.112	0.0029	0.0012	0
220	2.186	0.054	0.0040	0.0006	0
215	2.189	0.061	0.0037	0.0007	0
210	2.132	0.157	0.0030	0.0018	0
205	2.025	0.824	0.0060	0.027	0.0098	0.013
200	1.836	0.424	0.0046	0.017	0.023	0.047

Table 9. Naphthalene 0.25 mM, Values for K_d, a and α Determined from Stern–Volmer Analyses Using Equation 14 (Δ = Standard Deviation).

λ (nm)	Kd (mM–1)	ΔKd (mM–1)	a (mM–1)	Δa (mM–1)	α	Δα
275	2.331	0.031	0.0022	0.0002	0
250	2.300	0.048	0.0023	0.0004	0
245	2.290	0.037	0.0023	0.0003	0
240	2.320	0.035	0.0023	0.0003	0
235	2.346	0.093	0.0030	0.0007	0
230	2.345	0.098	0.0025	0.0008	0
225	2.191	0.096	0.0024	0.0008	0
220	2.215	0.041	0.0031	0.0003	0
215	2.215	0.031	0.0030	0.0004	0
210	2.150	0.048	0.0025	0.0011	0
205	2.115	0.279	0.0055	0.0074	0.018	0.014
200	1.740	0.250	0.0064	0.0071	0.016	0.009

In the tables below, statistical parameters for nonzero values for α could not be calculated, implying a very small value of α, probably <0.01. Calculations for 275–210 assumed the initial value α = 0.

The average values of K_d and K in Table 8 for 275–210 nm are 2.25 and 0.0032 mM^–1 respectively. The average values of K_d and a in Table 9 for the same wavelengths are 2.27 and 0.0025 mM^–1 respectively.

For comparison, values of K_d and K obtained previously¹⁷ for naphthalene in cyclohexane at oxygen pressures from zero to the air-saturated (0.21 atm) value were 2.10 mM^–1 (std. dev. 0.13) and 0.066 mM^–1 (std. dev. 0.028) respectively. The values of K_d and K in ref (17) were derived from a least-squares fit to a quadratic polynomial (eq 11) and the fluorescence excitation wavelength was 265 nm.

Naphthalene 0.11 mM Solution, Dual-Path Cell, F₀/F Values

Prior to the measurements above, a similar set of data was obtained using 0.11 mM naphthalene in cyclohexane. Values of F₀/F were determined for 7 wavelengths, 275–215 nm, at 13 different oxygen pressures 0–52.7 mM. Low signal-to-noise ratios for intensities excited below 210 nm prevented these data from being analyzed using the method described above. For greater accuracy at wavelengths below 220 nm, cyclohexane backgrounds were subtracted from naphthalene spectra. The resulting band intensities for 220–200 nm excitation were estimated by summing intensities from 320–350 nm, the region of greatest naphthalene intensity. Values of F₀/F at different wavelengths and oxygen concentrations are given in Supporting Information.

Values of K_d, K, and α using eq 12 are given in Table 10. As noted previously, in some cases a nonzero initial value of did not allow the calculation of statistical parameters, and α was assumed equal to zero.

Table 10. Naphthalene 0.11 mM, Dual-Path Cell, K_d, K and a Calculated from F₀/F Values.

λ (nm)	Kd (mM–1)	ΔKd (mM–1)	K (mM–1)	ΔK (mM–1)	α	Δα
275	2.251	0.133	0.0060	0.0035	0.0019	0.0016
250	2.271	0.123	0.0061	0.0032	0.0016	0.0015
240	2.247	0.100	0.0069	0.0013	0
230	2.347	0.218	0.0051	0.0053	0	0.0041
225	2.291	0.084	0.0047	0.0010	0
220	2.194	0.181	0.0089	0.0051	0.0021	0.0013
220a	2.226	0.144	0.0073	0.0040	0.0031	0.0010
215	2.167	0.291	0.0100	0.0086	0.0024	0.0016
215a	2.308	0.060	0.0029	0.0006	0
210a	2.193	0.224	0.0070	0.0072	0.0082	0.0020
205a	2.063	0.558	0.0096	0.0245	0.0159	0.0160
200a	1.809	1.598	0.0032	0.0931	0.0621	1.3626

^aSolvent backgrounds subtracted, and emission bands integrated 320–350 nm.

Naphthalene 0.01 mM, UHV Cell, F₀/F Values

Due to the longer UHV cell path length (0.9 cm) and therefore larger cyclohexane background absorption, absorbance values for wavelengths below 225 nm were >3 and subject to error. For this reason, data for oxygen pressures >35 psig (37 mM [O₂]) were not used to calculate parameter values for 225 nm excitation. Values of K_d, K, and α are given in Table 11.

Table 11. Naphthalene 0.01 mM, UHV Cell, K_d, K, and α Values from F₀/F Analyses.

λ (nm)	Kd (mM–1)	ΔKd (mM–1)	K (mM–1)	ΔK (mM–1)	α	Δα
275	2.185	0.054	0.0051	0.0054	0
265	2.082	0.092	0.0092	0.0028	0.0025	0.0007
250	2.132	0.124	0.0070	0.0035	0.0006	0.0018
240	2.103	0.447	0.0122	0.0140	0.0021	0.0024
240a	1.963	0.268	0.0180	0.0100	0.0030	0.0007
230	2.739	0.376	0.0079	0.0084	0.0008	0.0084
230a	2.537	0.452	0.0148	0.0126	0.0025	0.0100
225b	2.432	0.155	0.0066	0.0189	0

^aFluorescence spectrum smoothed using a fifth order, 13-point Savitzky-Golay polynomial for O₂ pressures 30–50 psig.

^bMaximum O₂ pressure 35 psig.

Summary of K_d and K Values Derived from F₀/F Stern–Volmer Analyses

F₀/F values were obtained for three different naphthalene concentrations using two different spectrophotometer cells. Data was analyzed to determine values of the dynamic quenching constant K_d, the static quenching constants K and a, and the quantity α = (ε_c/ε_m)(ϕ_c/ϕ_m0). The values of K_d and for the three data sets A,B, and C are summarized in Tables 12 and 13.

Table 12. Values of K_d (mM^–1) Obtained from Different Data Sets, A–C^a.

λ (nm)	A (Kd)	A (ΔKd)	B (Kd)	B (ΔKd)	C (Kd)	C (ΔKd)
275	2.316	0.036	2.251	0.113	2.185	0.054
250	2.280	0.056	2.271	0.123	2.132	0.124
240	2.303	0.042	2.247	0.100	2.103	0.447
230	2.320	0.115	2.347	0.218	2.739	0.376
225	2.171	0.112	2.291	0.084	2.432	0.155
220	2.186	0.054	2.226	0.144
215	2.129	0.061	2.308	0.060
210	2.132	0.157	2.193	0.224
average	2.230	0.079	2.254	0.133	2.318	0.231

^aA—Naphthalene 0.25 mM, dual-path cell; B— 0.11 M dual-path cell; C—0.01 mM, UHV cell.

Table 13. Values of K (mM^–1) Obtained from Different Data Sets A–C^a.

λ (nm)	A (K)	A (ΔK)	B (K)	B (ΔK)	C (K)	C (ΔK)
275	0.0026	0.0004	0.0060	0.0035	0.0051	0.0054
250	0.0028	0.0006	0.0061	0.0032	0.0070	0.0035
240	0.0027	0.0004	0.0069	0.0013	0.0122	0.0140
230	0.0032	0.0012	0.0051	0.0053	0.0079	0.0084
225	0.0029	0.0012	0.0047	0.0010	0.0066	0.0189
220	0.0040	0.0006	0.0073	0.0040
215	0.0030	0.0004	0.0029	0.00065
210	0.0030	0.0018	0.0070	0.0072
average	0.00303	0.0008	0.0053	0.00327	0.0078	0.010

^aA—Naphthalene 0.25 mM, dual-path cell; B—0.11 mM, dual-path cell; C—0.01 mM, UHV cell.

The average values of K_d for the three data sets in Table 12 for the wavelength range 275–210 nm are in good agreement, with data set A having the smallest standard deviations. The values of K_d obtained earlier¹⁷ for naphthalene were 2.07 and 2.13 mM^–1 from lifetime and intensity (F₀/F) measurements respectively at low O₂ concentrations (<2.4 mM). Values of K in Table 13 range from 0.003 to 0.008 mM^–1, with the values of data set A having the smallest deviations. These K values are much lower than the value given in ref (17) for excitation at 265 nm, 0.066 ± 0.028 mM^–1, where 0.028 is the standard deviation. At the 95% confidence level, the range of K values is 0.006–0.126. In the present study, the value of K is 0.0026 mM^–1, standard deviation 0.0004 for 275 nm excitation. The range of K at the 95% confidence level is 0.0017–0.0035 mM^–1, a much narrower range than in the previous study, for which the maximum oxygen concentrations were ∼2.4 mM. The higher oxygen concentrations (∼50 mM) used in this study result in higher concentrations of the complex, and therefore a more accurate estimate of K.

Comparison of the Static Quenching Constants K and a

In this study, two static quenching models were considered: a model in which naphthalene forms a ground state complex with oxygen, for which the equilibrium constant is K, and a model in which a contact charge-transfer complex is formed with formation constant a. For the case of complex with equilibrium constant K, the complex concentration is given by eq 7 above. For a contact charge-transfer complex, according to Orgel and Mulliken,²⁴ the complex concentration is assumed to be proportional to the concentrations of the donor (naphthalene) and acceptor (oxygen) as given by eq 13.

For naphthalene concentration 0.25 mM, two models were used assuming that the complex concentration c_c is given by eq 7 or by eq 13, giving values for K or a. For ten excitation wavelengths, for which the constants appeared to be relatively independent of wavelength, 275–210 nm, the average values of K and a were 3.2 ± 0.9 and 2.5 ± 0.5 M^–1 respectively. Statistical analyses²⁵ were used to compare the mean values of K and a, to determine whether they were significantly different at the 95% level. They were found to be significantly different, but by a small margin (3%). Standard deviations were not significantly different at the 95% level. For these reasons, the values were averaged, and their standard deviations pooled to give K or a = 2.8 ± 0.73 M^–1. These results suggest that the method used here does not distinguish between a weak molecular complex and a contact charge-transfer complex.

Summary of α Values Derived from F₀/F Stern–Volmer Analyses

The quantity α = (ε_c/ε_m) (ϕ_c/ϕ_m0), where ε_c, ε_m, ϕ_m0, ϕ_c are the molar absorption coefficients and fluorescence quantum efficiencies of the free molecule in the absence of oxygen and the complex, respectively. Values of α are small, on the order of 0.01 or less. Since the free molecule absorption coefficient ε_m and complex coefficient ε_c at a given wavelength have similar magnitudes, this implies that the fluorescence quantum efficiency of the complex is much less than that of naphthalene, for which Berlman²⁶ gives a value of 0.23 in deoxygenated cyclohexane for 265 nm excitation. Fluorescence spectra obtained in this study at higher oxygen concentrations showed no significant difference from the spectrum of pure naphthalene.

For excitation wavelengths greater than ∼210 nm, the approximation α ∼ 0 is valid. At shorter excitation wavelength, Stern–Volmer graphs for F₀/F vs [O₂] a larger α value is predicted, as discussed in a later section.

Discussion

Benzene–Oxygen Complex

Of the aromatic hydrocarbons, the oxygen complex with benzene has been the most thoroughly studied. Lim and Kowalski⁸ measured the absorption spectrum of pure benzene and benzene in carbon tetrachloride at high oxygen pressure (68 atm). A new band with a maximum at approximately 225 nm was found for which the absorbance was proportional to oxygen pressure. The molar absorption coefficient at the band maximum was ∼900 M^–1 cm^–1. The authors assigned the band to a contact charge-transfer transition. The intensity of the band was believed to be due to mixing of the charge-transfer state with the benzene ¹B_1u and ¹E_1u states. Birks et al.⁷ observed a similar band in the vapor phase spectrum of benzene with oxygen, with an absorbance maximum at 219 nm.

Gooding et al.²⁷ analyzed absorption spectra of benzene at different oxygen pressures using the Benesi–Hildebrand/Drago–Rose method.²⁸⁻³⁰ Assuming a 1:1 complex, they obtained a value of K = 7.5 ± 2.5 M^–1 for the equilibrium constant and ε (218 nm) = 14 ± 4 M^–1 cm^–1 for the absorption coefficient. The authors estimated the enthalpy of formation ΔH₂₉₈ = −7.9 kJ/mol. Grover et al.³¹ studied benzene and hexafluorobenzene in the vapor phase using photoionization and mass spectrometry and obtained a value of ΔH₂₉₈ = −4.0 ±1.5 kJ/mol for benzene. Casero and Joens³² measured the benzene-oxygen charge-transfer vapor absorption spectrum at different temperatures and obtained ΔH₂₉₈ = −4.3 ± 1.0 kJ/mol. The general conclusion from these studies was that the benzene-oxygen complex is weak, with dissociation energy ∼2RT (5 kJ/mol) at room temperature and is a contact charge-transfer complex.

A theoretical calculation of the benzene-oxygen complex by Granucci and Persico³³ obtained a dissociation energy D₀ = 5.36 kJ/mol, as compared with an experimental value³¹ of 6.7 ± 1.3 kJ/mol. The calculated benzene-oxygen distance having minimum energy was 3.30 A, with the oxygen molecule parallel to the benzene plane and centered above the ring. The authors concluded that the binding energy is due almost entirely to dispersion forces rather than charge transfer. Wesolowski et al.³⁴ performed calculations for benzene with oxygen with several models including a model similar to that of Granucci and Persico. Their values for the complex dissociation energy and intermolecular distance were 2.34 kJ/mol and 3.55 A respectively.

Birks et al.⁷ calculated the energy of the charge transfer state for the benzene-oxygen complex as follows, using their notation.

16

Where E_CT is the energy of the charge-transfer (CT) state, I_D is the ionization potential of benzene, A_A is the electron affinity of oxygen, ΔE_E is the energy of formation of the excited state charge-transfer complex ³(Bz-O₂)* and ΔE_N is the energy of formation of the ground state complex ³(Bz-O₂).

From experimental data cited above ΔE_N is ∼4 kJ/mol or 0.04 eV. The values used by Birks et al. for I_D and A_A were 9.23 and 0.67 eV respectively, although more recent values are 9.24 and 0.45 eV.³⁵ The E_CT absorbance maximum is 219 nm or 5.66 eV. Using these values ΔE_E is calculated to be 3.13 eV.

If charge transfer involves the transfer of one electron with charge separation R, and dipole energy ΔE_E = 3.13 eV, R (in Angstrom units) can be calculated from eq 17(9)

17

This equation gives R = 4.5 A as the dipole separation; the value given by Birks et al. is 5.0 A.

Naphthalene–Oxygen Complex

We are not aware of calculations for the dissociation energy or intermolecular distance for the analogous naphthalene-oxygen complex, either for the ground state or excited state. We used the procedures described above to determine some of these parameters for the excited state complex.

The maximum of the naphthalene-oxygen CT band is assumed to be at 221 nm or 5.61 eV. The values of I_D, and I_A are 8.14 and 0.45 eV, respectively.³⁵ The value for ΔE_N is assumed to be the same as for benzene, 0.04 eV. Using eq 16, the calculated value of ΔE_E is 2.12 eV, compared with the benzene value 3.13 eV. The R value calculated is 6.8 A, vs 4.5 A for benzene.

An estimate of the free energy ΔG for the ground state complex can be obtained using the value of K derived previously, 2.8 ± 0.7 M^–1. eq 18 is strictly valid only for the vapor phase but provides an estimate for comparison with the benzene-oxygen complex.

18

Gooding et al.²⁷ obtained the value ΔG₂₉₅ = −5.0 ± 1.3 kJ/mol for benzene–oxygen in the vapor phase, but later estimated ΔG₂₉₅ ∼ −3.3 kJ/mol based on other measurements. This value is close to the value obtained for naphthalene in cyclohexane solution.

Charge-Transfer Absorption Spectra in Cryogenic Oxygen Matrices

Absorption spectra of benzene, benzene derivatives, and other molecules including naphthalene have been studied at low temperatures in argon and oxygen matrices. In argon, there is relatively little perturbation of the lowest singlet electronic transitions, and in some cases vibronic structure is evident. In an oxygen matrix, CT absorption bands also appear, usually at shorter wavelengths than the lowest free molecule transition. Rest et al.³⁶ obtained absorption spectra of benzene, toluene, styrene, and indene in argon and oxygen matrices at 10 K. For benzene, vibronic bands associated with the first excited singlet state appear starting at 265 nm, followed by a broad absorption band with peak at ∼235 nm. In an argon matrix, only the vibronic bands of benzene appear, at approximately the same wavelengths as in oxygen. The authors attributed the broad 235 nm band to a CT band, which is red-shifted ∼0.4 eV from the vapor phase. Rest et al. obtained ΔE_E and R values of 3.3 ± 0.2 eV and 4.4 ± 0.3 A respectively for benzene. These values are in good agreement with the values 3.13 eV and 4.5 A for benzene in the vapor phase determined by Birks et al.

Hashimoto and Akimoto³⁷ studied benzene, methyl-substituted benzenes, and naphthalene in argon and oxygen matrices at 11 K. Their results for benzene and the substituted benzenes are similar to those of Rest et al., although the vibronic structure of benzene and toluene is less evident. Spectral differences between these data and that of Rest et al. might be due to the lower aromatic hydrocarbon: oxygen ratios used, 1:250 for benzene and 1:1000 for naphthalene compared with 1:1 used by Rest et al. For benzene, the CT band maximum was at ∼238 nm, with an estimated absorption coefficient of 5400. The CT band overlaps the benzene vibronic bands at longer wavelengths, and the vibronic structure is broadened. The benzene CT band shows a vapor–solid phase red shift of ∼0.4 eV.

In the case of naphthalene, only a single broad band with a maximum of ∼260 nm appears, with an absorption coefficient ∼8000. Assuming that the naphthalene CT band is red-shifted 0.4 eV from the vapor, the CT band maximum in oxygen is expected at ∼240 nm. The naphthalene spectrum in oxygen compared with argon appears to have considerable intensity between 260 and 225 nm, with a possible maximum near 230 nm. This suggests that the apparent absorption maximum at 260 nm in oxygen is a combination of naphthalene and a naphthalene-oxygen CT band, with the latter having a maximum at approximately 230–240 nm. Assuming the CT band maximum is at 240 nm, the calculated value of ΔE_E is 2.57 eV, compared with 2.12 eV in cyclohexane. Assuming that a single naphthalene electron is transferred to oxygen, the calculated dipole length R in an oxygen matrix is 5.6 vs 6.8 A in cyclohexane. Values obtained from the literature for E_CT and related quantities for benzene and naphthalene are summarized in Table 14.

Table 14. Values of E_CT, ΔE_E and R for Benzene and Naphthalene.

	benzene vapor	benzene solutionc	benzene O2 matrixd	naphthalene solutionf	naphthalene O2 matrixe
ECT (nm)	218a	220c	235d	221	∼240
	219b		238e
ΔEE (eV)	2.90b (3.13)		3.3d	2.12	2.57
R (A)	5.0b (4.5)		4.4d	6.8	5.6

^aGooding et al.²⁷

^bBirks et al.⁷, values updated in this work in parentheses.

^cLim and Kowalski⁸.

^dRest et al.³⁶

^eHashimoto and Akimoto³⁷

^fThis work.

Intensity of the Charge-Transfer Band at Different Wavelengths

Tsubomura and Mulliken² give an approximate formula for estimating the intensity of the CT band from the intensities of the corresponding absorption bands in the free molecule

19

where β is the interaction energy between the wave functions of the free molecule and the complex, and ΔW is the energy difference between the CT state and free molecule state in proximity. The quantity f is the oscillator strength of the free molecule transition and Δf is the intensity borrowed by the CT transition. The terms β and ΔW in the above equation are equivalent to the terms a and ΔE used by Birks.⁷

For naphthalene the lowest singlet states above the ground state, in order of increasing energy are ¹B_3u, ¹B_2u, and ¹B_3u. The first transition, starting at ∼312 nm in cyclohexane, is weak and is overlapped by the stronger ¹B_2u transition with a maximum at ∼276 nm. The second ¹B_3u transition is much stronger with a peak at ∼222 nm. The f values for the second and third transitions were measured as 0.11 and 1.26 respectively, in good agreement with experimental values quoted by Hashimoto et al.³⁸

The intensity borrowed by the CT band near the strong naphthalene absorption band at 222 nm has approximately the same intensity as the free molecule transition, so Δf/f ∼ 1. The energy separation of the naphthalene maximum from the CT maximum at 221 nm is ∼200 cm^–1. Using these values gives β = 200 cm^–1. Assuming the same value of β is appropriate for the interaction of the CT band with the naphthalene ¹B_3u transition at 276 nm, Δf/f ∼ 5 × 10^–4. However, the intensity of the CT transition in the 275 nm spectral region is comparable to that of the ¹B_2u naphthalene transition, implying Δf/f ∼ 1. For the ¹B_2u transition either the value of β must be very much larger (∼9000 cm^–1) or the intermolecular separation R (eq 17) for ΔE_E must be smaller. Charge transfer interactions involve different orientations of the donor–acceptor pair and a range of interaction distances, so that it is reasonable to assume that some pairs will be closer together and more favorably oriented for charge transfer when the pair absorbs light. If the relative intensity Δf/f borrowed from the ¹B_2u transition is assumed to be approximately the same as for the ¹B_3u transition, and assuming β ∼ 200 cm^–1, R is calculated to be 2.2 A, compared with 3.4 A for E_CT determined from the second ¹B_3u band maximum at 221 nm.

Unusual Behavior of F₀/F Graphs at Short Wavelengths

Figure 6 shows graphs of F₀/F at several excitation wavelengths between 275 and 200 nm. For excitation at 275–210 the graphs show a slight increase in slope with oxygen concentration. At 205 and 200 nm, the graphs show downward slopes at higher oxygen concentrations. Possible explanations for this behavior are that either the complex becomes more fluorescent, or that the naphthalene fluorescence is reduced by some other mechanism. The naphthalene-oxygen CT complex is likely nonfluorescent. This implies that the quantum efficiency of naphthalene is reduced when excited at 205 nm and shorter wavelengths.

Values of the parameter α in Tables 8 and 9 indicate that the value of α increases at 205 and 200 nm, with values ranging from 0.01–0.02. These values of α were obtained when F₀/F vs [O₂] values were fitted to oxygen concentrations using a nonlinear least-squares method. The data was also fitted to a quadratic polynomial, with the values of K_d and K fixed at 2.3 and 0.003 mM^–1, respectively, the average values for 275–210 nm excitation. Values of α obtained using a quadratic polynomial were 0.018 and 0.043 for 205 and 200 nm excitation, respectively. It seems unlikely that K_d varies with excitation wavelength, since emission is from the lowest naphthalene excited singlet state. The parameters K or a should not vary with excitation wavelength because they are associated with the ground state complex.

Since α = (ε_c/ε_m)(ϕ_c/ϕ_m0) and the molecular absorption coefficients of naphthalene and the complex are similar, α is approximately equal to the ratio of quantum efficiencies. As noted above, α is very small, probably <0.01. Assuming ε_c = ε_c and ϕ_m0 = 0.23,²⁶ the CT complex quantum efficiency ϕ_c < 0.0023. For excitation at 200 or 205, assuming α = 0.02 and ϕ_c = 0.002, the naphthalene quantum efficiency ϕ_m0 = ∼0.1. The unusual behavior of the F₀/F graphs at short wavelengths suggests a lower naphthalene quantum efficiency due to photodecomposition or other processes.

Conclusions

We have shown evidence for the absorption spectrum of a naphthalene-oxygen charge-transfer band in cyclohexane solution. The spectrum of the naphthalene-oxygen complex overlaps the naphthalene spectrum, and for this reason is difficult to distinguish from naphthalene. A fluorescence quenching method was used to determine the value of the complex equilibrium constant K or the charge-transfer coefficient a. Molecular absorption coefficients of the naphthalene-oxygen complex were determined using this value of K or a. The values of K and a obtained are not significantly different, and the average value is 2.8 ± 0.7 M^–1.

The charge-transfer complex appears to be essentially nonfluorescent. This observation is consistent with time-resolved triplet–triplet absorption measurements of Logunov and Rodgers, who studied both naphthalene and 1-methylnaphthalene.^39,40 They concluded that the excited state naphthalene-oxygen complex undergoes rapid internal conversion to the lowest naphthalene triplet state.

Previous studies of molecular complexes have been analyzed using the Benesi–Hildebrand method or a variant thereof to determine values of K and the complex extinction coefficients. Attempts to improve upon these methods have been discussed by Orgel and Mulliken²⁴ and by Murrell and co-workers.⁴¹ Gooding et al.²⁷ commented: “Although it was our original intent to examine oxygen complexation with a variety of gas-phase organic molecules by using the Drago–Rose/Benesi–Hildebrand spectrophotometric method, we found that the M–O₂ CT absorption band often overlapped with absorption bands due to allowed transitions in the organic molecule. It was thus very difficult to obtain absorbance values as accurate as those measured for the benzene-O₂ complex.” In the present work, K was determined using an independent fluorescence method that allowed determination of the molecular absorption coefficients of the complex. This method might prove to be a useful alternative for studies of weak molecular complexes provided that the donor or acceptor molecule is fluorescent.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.4c10448.

• Absorption and fluorescence data used to determine the molecular absorption coefficients for the naphthalene-oxygen complex are given in tables corresponding to the relevant table in the manuscript; an estimate of the error associated with spectral background subtraction and the calculated absorption coefficients is also given (PDF)

The authors declare no competing financial interest.

Author Status

^† J.E.K.: Deceased.