Article pubs.acs.org/JPCA
Effect of Solvent on the O2(a1Δg) → O2(b1Σg+) Absorption Coefficient Mikkel Bregnhøj and Peter R. Ogilby* Center for Oxygen Microscopy and Imaging, Department of Chemistry, Aarhus University, Langelandsgade 140, Aarhus 8000, Denmark S Supporting Information *
ABSTRACT: Radiative transitions between the three lowestlying electronic states of molecular oxygen have long provided a model to study how collision-dependent perturbations influence forbidden processes. In an isolated oxygen molecule, transitions between the O2(X3Σg−), O2(a1Δg), and O2(b1Σg+) states are forbidden as electric-dipole processes. For oxygen dissolved in organic solvents, the probabilities of radiative transitions between these states increase appreciably. Attempts to interpret solventdependent changes in the radiative rate constants have principally relied on O2(b1Σg+) and O2(a1Δg) emission experiments. However, the dominant nonradiative deactivation channels of O2(b1Σg+) make it difficult to quantify solvent effects on the O2(b1Σg+) → O2(a1Δg) radiative process. Thus, an appreciable amount of important information has heretofore not been available. In the present study, we examined the effect of 17 common organic solvents on the O2(a1Δg) → O2(b1Σg+) absorption transition at ∼5200 cm−1 (i.e., ∼1925 nm). The solvent-dependent absorption coefficients at the band maximum, εmax, range from 5 to 50 M−1 cm−1 and correlate reasonably well with the solvent refractive index; εmax is largest in solvents with the largest refractive index. This observation is consistent with a model in which oxygen is perturbed to a greater extent by solvents with a large electronic polarizability. Through the Strickler−Berg equation, we also used these absorption data to obtain the radiative rate constant for the O2(b1Σg+) → O2(a1Δg) transition, and the results are consistent with a model in which the O2(a1Δg) → O2(X3Σg−) transition is said to steal intensity from the O2(b1Σg+) → O2(a1Δg) transition.
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electronic-to-vibrational energy transfer.9 In the present study, we limit ourselves to the effect of the solvent on radiative transitions in oxygen. In an isolated oxygen molecule (e.g., in a low-pressure gasphase system), transitions between the O2(X3Σg−), O2(a1Δg), and O2(b1Σg+) states are forbidden as electric-dipole processes. However, for oxygen dissolved in organic solvents, the probabilities of radiative transitions between these states increase appreciably. The pertinent experimental data in this regard have principally been acquired from O2(b1Σg+) → O2(a1Δ g), O2(b1Σg+) → O2(X3Σg−), and O2(a1Δ g) → O2(X3Σg−) emission studies, with the greatest attention being focused on the O2(a1Δg) → O2(X3Σg−) phosphorescent transition.9,12 The currently accepted model that accounts for the effect of solvent on the O2(a1Δg) → O2(X3Σg−) radiative rate constant, kaX, is that of Minaev.13−15 In brief, Minaev’s thesis is that the O2(a1Δg) → O2(X3Σg−) transition steals intensity from the more probable O2(b1Σg+) → O2(a1Δg) transition. The O2(b1Σg+) → O2(a1Δg) transition is proposed to gain intensity through a solvent-dependent disruption of oxygen’s cylindrical symmetry that lifts the degeneracy of the πx and πy antibonding orbitals, which in turn introduces an
INTRODUCTION Studies that focus on the two lowest-lying excited electronic states of molecular oxygen continue to draw appreciable attention from the scientific community. In this regard, the O2(a1Δg) state is arguably the most important in that it has a characteristic and unique chemistry that results in the oxygenation of many organic molecules,1 including molecules significant in many biological processes.2−5 Although the O2(b1Σg+) state is not known to be chemically reactive, certainly in solution-phase systems,6,7 it is often a precursor to the O2(a1Δg) state and, as such, likewise draws appreciable attention from those interested in oxygenation reactions.8,9 From a different perspective, both the radiative and nonradiative transitions between the O2(b1Σg+) and O2(a1Δg) states and the triplet ground state of oxygen, O2(X3Σg−), provide a wonderful model to study the fundamental effects that perturbing collisions have on highly improbable processes.10,11 However, despite having been studied for many years, there is still much that is not understood about these processes in this presumably most simple system of a homonuclear diatomic molecule. Of particular concern is how the transition probabilities depend on the nature of the collision partner. Much of the work in this field has focused on elucidating the mechanism(s) of solvent-mediated O2(b1Σg+) and O2(a1Δg) nonradiative deactivation, addressing fundamental tenets of © XXXX American Chemical Society
Received: May 29, 2015 Revised: July 1, 2015
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Figure 1. Time- and spectrally resolved absorption data recorded upon 355 nm pulsed laser irradiation of C60 in air-saturated toluene. The data shown here are an average of 10 independent time- and spectrally resolved traces. Each trace was obtained using 710 mirror positions in the stepscan FTIR spectrometer, and for each mirror position, 20 independent kinetic traces were added together. For the conditions under which these data were recorded, the change in sample absorbance, ΔAbs, at time = 0 was ∼4 × 10−4 absorbance units.
solution22 that provide further insight into the mechanism of this solvent-mediated perturbation.
electric-dipolar component into the transition. The introduction of this dipolar character causes the transition probability to increase appreciably. With these points in mind, an interesting and important corollary of Minaev’s thesis is that the ratio of the respective radiative rate constants, kaX/kba, is predicted to be solvent-independent with a value of ∼3 × 10−4.15 Over the years, an increasing amount of experimental data has been acquired to support Minaev’s model.9 An important limitation in this regard, however, is the difficulty of acquiring values for the O2(b1Σg+) → O2(a1Δg) radiative rate constant, kba, in many common liquid solvents. Specifically, to complement most of the kaX values acquired, it is necessary to quantify k ba in solvents that contain C−H and O−H bonds. Unfortunately, the kinetically competing process of O2(b1Σg+) → O2(a1Δg) nonradiative deactivation is so efficient in these solvents that it becomes difficult to perform the required experiments. Thus, much of the evidence to support Minaev’s model comes from gas-phase data and from some rather esoteric liquid solvents that are not easily handled (e.g., lowboiling Freons).9 Approximately 20 years ago, we constructed a step-scan FTIR spectrometer that could record the time-resolved O2(a1Δg) → O2(b1Σg+) absorption spectrum, which occurs at ∼5200 cm−1 (i.e., ∼1925 nm) in liquid solvents.16,17 We subsequently used this instrument to quantify solvent-dependent spectral changes in both the O2(a1Δg) → O2(b1Σg+) and O2(b1Σg+) → O2(a1Δg) transitions.18,19 In proof-of-principle experiments, we also demonstrated that this instrument can be used to quantify kba in a way that is useful to the study of Minaev’s model for the perturbation of oxygen by liquid solvents.20 In the present study, we modified our FTIR spectrometer to obtain a better signal-to-noise ratio and then set out to quantify O2(a1Δg) → O2(b1Σg+) absorption coefficients in a wide range of common organic solvents. The intent was to subsequently use an expression provided by Strickler and Berg21 to obtain the corresponding values of kba. We now report that an extensive set of experimental data obtained from common liquid organic solvents indeed supports Minaev’s general model by which radiative processes in molecular oxygen are perturbed. We also discuss our results in light of recent data on the temperature dependence of oxygen radiative lifetimes in
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RESULTS AND DISCUSSION O2(a1Δg) → O2(b1Σg+) Absorption Spectra. Timeresolved absorption measurements were performed over the spectral range 4800−5600 cm−1 upon pulsed laser irradiation of an O2(a1Δg) photosensitizer in a variety of different airsaturated organic solvents. A representative example of the data thus obtained is shown in Figure 1. The data recorded in the first ∼2 μs after the laser pulse include an appreciable contribution from the absorption of the sensitizer triplet state. This signal is rapidly quenched in the presence of oxygen to yield a single discrete absorption band centered at ∼5200 cm−1 (Figure 1). The three-dimensional data set shown in Figure 1 can be modified in two ways:12,23 (1) It can be compressed along the spectral axis to yield a plot of the change in sample absorbance as a function of time. For the present experiments, the decay function thus observed was always single-exponential, and the corresponding lifetimes, τ, are listed in Table 1. It is important to note that, as also measured in complementary O2(a1Δg) → O2(X3Σg−) phosphorescence experiments, these lifetimes are dominated by the nonradiative O2(a1Δg) deactivation channels (i.e., the rate constant for nonradiative O2(a1Δg) deactivation in these solvents is much greater than the radiative rate constant kaX). (2) It can be compressed along the time axis to yield the spectrum of the transient being observed. The latter was readily quantified using a Gaussian fitting function, and the resultant band maxima and band widths are likewise listed in Table 1. Data such as those shown in Figure 1 are readily assigned to the O2(a1Δg) → O2(b1Σg+) transition on the basis of the following points: (1) The spectra obtained are consistent with what is expected for this transition.18−20 (2) Although this absorption experiment is not the ideal approach for measuring the lifetime of O2(a1Δg) [see the further comments in the Supporting Information (SI)], the τ data obtained are nevertheless consistent with what is expected (Table 1). (3) The transient signal was not observed from deoxygenated solutions. (4) The rate of signal decay increased when a known O2(a1Δg) quencher (e.g., NaN3 or an amine) was added to the solution.16 B
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Table 1. O2(a1Δg) → O2(b1Σg+) Absorption Coefficients, εab, Recorded at the Absorption Band Maximum (νmax) in 17 Solvents −1 εmax cm−1) ab (M
solvent D2O methanol acetonitrile Freon 113 acetone acetic acid n-hexane 2-propanol 1-octanol CCl4 toluene mesitylene benzene o-xylene benzonitrile bromobenzene CS2
published 6 − − − − − 40 − − − 56 − 56 − − − 52
± 2a
± 4c
±6
c
± 6a
± 5c
νmax (cm−1)
new − 7 16 26 14 10 23 12 21 26 30 35 32 35 36 43 49
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
published 3 5 4 3 4 4 5 6 6 4 5 3 5 5 5 5
5228 5217 5224 5209 − − 5199 − − 5195 5191 − 5197 − 5194 − 5168
± ± ± ±
1a 2b 2b 1b
± 1b
± 1b ± 1b ± 1b ± 1b ± 1b
bandwidth (fwhm) (cm−1) new
− 5215 5219 5206 5218 5223 5202 5208 5191 5192 5193 5194 5195 5191 5193 5184 5171
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
published 5 5 3 3 3 3 3 3 3 3 3 3 3 3 3 3
75 86 82 63 − − 69 − − 72 74 − 76 − 81 − 90
± ± ± ±
2a 5b 5b 2b
± 2b
± 2b ± 2b ± 2b ± 2b ± 2b
new − 77 76 57 82 79 73 62 60 65 70 72 74 73 70 68 81
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
10 10 5 5 5 5 5 5 5 5 5 5 5 5 5 5
τ (μs) publishedd 68 ± 1 10 ± 1 80 ± 2 72000 ± 5000f 51 ± 3 − 31 ± 1 21 ± 2 19 ± 2 73000 ± 10000h 29 ± 1 15 ± 1 31 ± 1 21 ± 2 41 ± 4 45 ± 4 79000 ± 4000i
newe − 10 82 −g 37 15 29 17 15 −g 26 12 27 16 30 40 −g
±2 ±3 ± ± ± ± ±
3 2 2 2 2
± ± ± ± ± ±
2 1 2 1 2 2
a From Andersen and Ogilby.20 bFrom Dam et al.19 cFrom Weldon and Ogilby.16 dIndependently obtained from O2(a1Δg) → O2(X3Σg−) phosphorescence measurements. Data are averages of values obtained from the compilation of Wilkinson et al.,24 unless specified otherwise. e Obtained from our current O2(a1Δg) → O2(b1Σg+) data. fFrom Afshari and Schmidt.25 gThe high-pass filter used in our experiments precluded measurements of τ values longer than ∼1 ms. hAverage of data from air-saturated solutions.25,26 iFrom Schmidt and Afshari.27
Quantifying the O2(a1Δg) → O2(b1Σg+) Absorption Coefficient. To obtain the O2(a1Δg) → O2(b1Σg+) absorption coefficient, εab, it was necessary to extrapolate our observed kinetic signal backward in time to obtain a value for the O2(a1Δg) → O2(b1Σg+) absorbance change, ΔAbs, at time = 0. Typically, these values of ΔAbs were in the range 1−10 × 10−4 absorbance units, depending on our experimental conditions (vide infra). ΔAbs could then be correlated to εab through the Lambert−Beer Law when the concentration of O2(a1Δg) produced in our photosensitized reaction at time = 0 was known. The latter was readily available through known and controlled parameters. The pertinent compilation of terms is shown in eq 1 (further details are provided in the SI): εab =
hcfNAVirr λϕΔηP0(1 − 10−A)leff
that the concentration of O2(a1Δg) in our sample was approximately the same in any plane perpendicular to the propagating beam of the excitation laser. The principal sensitizer chosen for this work, phenalenone (PN), has a solvent-independent quantum yield of O2(a1Δg) that is essentially unity (ϕΔ = 0.98 ± 0.05).29,30 We also ensured that, under all conditions, all of the PN excited states produced by the exciting pulse were quenched by O2(X3Σg−). Finally, selected experiments performed using a different sensitizer (e.g., C60) gave the same results as those obtained using PN. The values of εab thus obtained are shown in Table 1. With the few solvents for which we have previously reported values of εab from O2(a1Δg) → O2(b1Σg+) experiments, we find that our present εab values are systematically smaller (see Table 1). Although measuring these small absorption coefficients is a difficult proposition in itself, we nevertheless attribute this difference to the increased accuracy with which our present optimized FTIR instrument records data. In the measurement of any single εab value, we typically obtain an error of approximately ±20−30% derived from propagation of the errors in the variables in eq 1 (see the SI). Repeating a given experiment ∼3−5 times then allows us to reduce this error, through averaging, to ∼10−20%. Correlating O2(a1Δg) → O2(b1Σg+) Spectra to Solvent Parameters. The data in Table 1 show that εab and νmax change appreciably as a function of the solvent in which oxygen is dissolved. In view of the general history of studies of solvent effects on electronic transitions31,32 and the specific history of studies of solvent effects on electronic transitions in oxygen,9,12 it is incumbent upon us to at least consider how these values correlate with parameters that quantify the dielectric properties of the solvents. Much of the literature on general solvent effects on a given solute focuses on solute spectral shifts.31,32 To this end, the solvent is often characterized as a dielectric continuum, and representative parameters are obtained from functions that include both the static dielectric constant, εst, and the optical
ΔAbs (1)
where h is Planck’s constant, c is the speed of light, NA is Avogadro’s number, f is the repetition rate of the irradiating laser, Virr is the volume of sample irradiated by the laser, leff is the effective path length traversed by the IR probe beam, ϕΔ is the quantum yield of sensitized O2(a1Δg) production, P0 is the incident pump laser power, η is a factor correcting for light reflection off the front face of the sample cuvette (η = 0.95), and A is the absorbance of the sensitizer at the irradiation wavelength λ. Although the use of the moniker “extinction coefficient” is no longer advisible according to the IUPAC rules,28 distinguishing between extinction and absorption is still important in many cases, including the present study, where the molar absorption coefficient is small and light reflected/ scattered by the sample can have an appreciable effect on the measured quantity. We have tried to properly account for some light reflection through our parameter η. Nevertheless, our values of εab likely still differ from the true molar absorption coefficient. For our approach to be most accurate, we ensured that the cross-sectional intensity of our exciting laser resembled a rectangular function (see the SI). In this way, we established C
DOI: 10.1021/acs.jpca.5b05131 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A (i.e., high-frequency) dielectric constant, εop.31,32 The latter is invariably expressed in terms of the solvent refractive index, n, measured in the visible region of the spectrum (i.e., εop = n2). Furthermore, εop and functions of εop [e.g., (εop − 1)/(εop + 1) = (n2 −1)/(n2 + 1)] are generally used to describe the electronic polarizability of a given solvent.31,33 Although our present experiments were not designed to study the effect of the solvent on the spectral shifts of oxygen (i.e., our current data were recorded at a lower spectral resolution than data recorded in our earlier studies19), our present results are nevertheless consistent with our earlier observations. Specifically, we find that the band maximum of the O2(a1Δg) → O2(b1Σg+) transition shifts to smaller wavenumbers as n increases (Table 1). In contrast, there is not as much material in the literature on the effect of the solvent on the probabilities of electronic transitions in a given solute.31,32,34 In this regard, studies of the response of oxygen to changes in the solvent play an important and unique role. For the present case, we find that εab ranges from ∼5 M−1 cm−1 in D2O and methanol to ∼50 M−1 cm−1 in CS2. Moreover, our values of εab show a reasonably good correlation with n as well as n2 (Figure 2). In contrast, there was no correlation between εab and the static dielectric constant of the solvent (see the SI). These observations are consistent with independent reports on the O2(a1Δg) → O2(X3Σg−) radiative transition.9,12,35−37 Upon examining the data in Figure 2, we note that the εab value obtained for Freon 113 deviates the most from the linear correlations with n and n2. Although it is tempting to ascribe this observation to the difficulty of performing experiments with this solvent, for the moment we would rather say that these plots give only a general qualitative assessment of the role played by the solvent. As we have inferred from corresponding plots of kaX against n and functions of n,12,35,36 we conclude that the data in Figure 2 reflect the fact that electronic transitions in oxygen are perturbed to a greater extent by solvents with a larger electronic polarizability. We will return to this point below. From O2(a1Δg) Absorption to O2(b1Σg+) Emission. Our O2(a1Δg) → O2(b1Σg+) data can be used to estimate the rate constant for O2(b1Σg+) → O2(a1Δg) radiative deactivation, kba. As noted in the Introduction, the latter is a useful parameter in the context of Minaev’s model of solvent-perturbed transitions in oxygen. To this end, we used an expression provided by Strickler and Berg21 that equates the integrated absorption coefficient for a transition from a “lower” state to an “upper” state to the radiative rate constant from the same “upper” state to the same “lower” state (eq 2): k ba = n2
8πc ln(10) glower 2 ν NA g upper
Figure 2. Plots of the O2(a1Δg) → O2(b1Σg+) molar extinction coefficient, εab, obtained at the maximum of the O2(a1Δg) → O2(b1Σg+) absorption band against (a) the refractive index, n, and (b) n2 for the solvents in which oxygen was dissolved. The lines shown are linear fits to the data. Similar correlations were observed when εab was plotted against functions of n [e.g., (n2 − 1)/(n2 + 1)]; see the SI. The data recorded from Freon 113 are marked with a circle.
important to note that the factor of n2 in eq 2 is an inherent part of the derivation of this expression that accounts for the solvent-dependent change in the speed of light through that particular medium.21,34 It should not be confused with an experimental correction factor (generally n2 as well) that must be applied when emission experiments are performed in different solvents to account for the fact that the optical detector used in these experiments is invariably in a medium (air) that has a different refractive index than the solvent studied.35,36,38 Although the Strickler−Berg expression was originally derived for strongly allowed transitions, we assume that it nevertheless provides an adequate approach to model the weak transitions in oxygen.20,23,39 The radiative rate constants kba thus obtained from our O2(a1Δg) → O2(b1Σg+) data are listed in Table 2. Radiative Rate Constants for the O 2 (a 1 Δ g ) → O2(X3Σg−) Transition. As noted in the Introduction, a key aspect of Minaev’s approach to interpret solvent effects on radiative transitions in oxygen is to compare values of kba with values of the O2(a1Δg) → O2(X3Σg−) radiative rate constant
∞
∫−∞ εab(ν) dν
(2)
where ν is the transition energy in cm−1 and the coefficients gupper and glower quantify the degeneracies of the upper and lower states, respectively. Because the O2(a1Δg) state is doubly degenerate,10 the ratio of g coefficients is equal to 2 in this case. Furthermore, because the Stokes shift between the O2(a1Δg) → O2(b1Σg+) and O2(b1Σg+) → O2(a1Δg) transitions is extremely small18 and the equilibrium nuclear geometries are essentially the same in the O2(a1Δg) and O2(b1Σg+) states,10 it is sufficiently accurate to use the band maximum of the O2(a1Δg) → O2(b1Σg+) absorption profile as a measure of the solvent-dependent transition energy ν. Finally, it is D
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Table 2. Solvent Parameters and Rate Constants for the O2(b1Σg+) → O2(a1Δg) and O2(a1Δg) → O2(X3Σg−) Radiative Transitions solvent
na
VvdW (mM−1)b
R (mM−1)c
doc (Å)d
μ (g/mol)e
D2O methanol acetonitrile Freon 113 acetone acetic acid n-hexane 2-propanol 1-octanol CCl4 toluene mesitylene benzene o-xylene benzonitrile bromobenzene CS2
1.338 1.329 1.344 1.358 1.359 1.371 1.375 1.377 1.430 1.460 1.497 1.499 1.501 1.505 1.528 1.560 1.627
11.5 21.7 28.4 58.7 39.0 31.4 68.3 42.2 93.3 49.8 59.5 81.8 48.4 70.7 60.5 61.0 31.2
3.77 8.23 11.06 26.38 16.16 12.98 30.13 17.59 40.83 26.55 30.99 40.85 26.25 35.85 31.44 33.96 21.40
3.38 3.77 3.97 4.58 4.22 4.04 4.73 4.28 5.06 4.43 4.59 4.91 4.40 4.76 4.61 4.62 4.04
12.32 16.01 17.98 27.33 20.63 20.88 23.33 20.88 25.69 26.49 23.75 25.27 22.70 24.59 24.24 26.58 22.53
kba (s−1)f 199 235 528 659 507 373 777 356 626 854 1146 1378 1289 1396 1413 1671 2528
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
67 93 153 138 120 91 146 101 146 192 161 206 187 204 236 225 324
kaX (s−1)g 0.18 0.32 0.45 1.35 0.59 0.44 0.60 0.47 0.97 1.10 1.44 1.72 1.50 1.70 1.80 1.97 3.11
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
0.02 0.03 0.05 0.14h 0.06 0.13i 0.06 0.05 0.29i 0.11 0.14 0.17j 0.15 0.17k 0.18 0.20 0.31
104·kaX/kba 9.0 13.4 8.5 20.5 11.6 11.9 7.7 13.2 15.4 12.9 12.6 12.5 11.6 12.2 12.7 11.8 12.3
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
3.2 5.5 2.5 4.8 4.5 4.6 1.6 4.0 5.9 3.2 2.2 2.2 2.0 2.2 2.5 2.0 2.0
a Solvent refractive index at 20 °C at 589 nm (Na D line). bSolvent van der Waals volume. cSolvent molar refraction. dOxygen−solvent collision distance calculated using van der Waals radii. eReduced mass of the 1:1 oxygen−solvent pair. fObtained through eq 2 from our O2(a1Δg) → O2(b1Σg+) data. gObtained from Poulsen et al.,40 unless otherwise specified. The errors shown reflect only relative uncertainties and do not consider the absolute error of ±30% derived from the uncertainty in Schmidt’s standard value in benzene.41 hFrom Schmidt and Afshari42 and normalized to kaX = 1.5 s−1 for benzene. iCalculated from the correlation of kaX with n.35,36,40 jFrom Hild and Schmidt.43 kThe value for p-xylene was used.40
kaX.13−15 To this end, it is incumbent upon us likewise to compile values of kaX to complement each of our kba values. Over the past ∼30 years, accurate relative solvent-dependent values of kaX have been acquired from O2(a1Δg) → O2(X3Σg−) phosphorescence experiments.9,35,36,40,43 However, for the present application, it is necessary to normalize these relative values in such a way that they acquire meaning in an absolute sense. To our knowledge, there have been only two attempts to quantify absolute values of O2(a1Δ g) phosphorescence quantum yields in the pertinent solvents to yield data that can then be used to obtain an absolute value of kaX.41,44 Although different approaches were used in these two studies, the results obtained are equivalent within the margin of error for such a difficult experiment. For our present work, we opted to use kaX = 1.5 ± 0.5 s−1 obtained by Schmidt for experiments performed in benzene.37,41 Using this standard, we normalized the relative values of kaX pertinent to our present study, and the resultant first-order rate constants are listed in Table 2. Correlating the O2(b1Σg+) → O2(a1Δg) and O2(a1Δg) → O2(X3Σg−) Transitions. Our data yield a kaX/kba ratio that is indeed relatively constant and independent of the solvent, as predicted by Minaev (Table 2 and Figure 3). Thus, we confirm that, irrespective of the solvent involved, the O2(b1Σg+) → O2(a1Δg) transition is perturbed to the same extent as the O2(a1Δg) → O2(X3Σg−) transition. This is embodied in Minaev’s fundamental tenet that, as a consequence of solvent perturbation, the O2(a1Δg) → O2(X3Σg−) transition steals intensity from the O2(b1Σg+) → O2(a1Δg) transition. It is again interesting to note that in Figure 3 the point for Freon 113 deviates the most from the linear correlation. If we ascribe more meaning to this plot than to the plots shown in Figure 2, and on the basis of our discussion regarding Figure 4 below, it is likely that the deviation seen here principally reflects the fact that the reported value of 1.35 ± 0.14 s−1 for kaX in Freon 113 is too large (Table 2). Indeed, if we give credence to the correlation between kaX and the solvent refractive index n
Figure 3. Plot of the first-order rate constant for the O2(a1Δg) → O2(X3Σg−) radiative transition, kaX, against the first-order rate constant for the O2(b1Σg+) → O2(a1Δg) radiative transition, kba. Values of the latter were obtained from our O2(a1Δg) → O2(b1Σg+) absorption experiments through eq 2. The solid line is a linear fit to the data with a slope of (12.2 ± 0.8) × 10−4. The data point obtained with Freon 113 is marked with a circle.
that has been established using many solvents,35,36 one would expect a kaX value of ∼0.4 s−1 for Freon 113. Our newer, extensive, and more accurate data set of kba values also yields an average kaX/kba ratio of (12.2 ± 0.8) × 10−4, which is ∼1.6 times greater than that obtained from our preliminary data published in 2002 (7.4 × 10−4).20 However, it is still quite remarkable that our experimental kaX/kba numbers come close to the kaX/kba ratio of ∼3 × 10−4 predicted by Minaev. This factor of 4 difference between experiment and theory is easily understood, arguably expected, given the errors and assumptions associated with each approach. E
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linearly correlated with values of log(R), and the slope of this line is indeed ∼2. Continuing our discussion about the possibilities of anomalous data from selected solvents, we note now that the kba data for Freon 113 do not deviate from the linear correlation shown in Figure 4. Rather, the point that now stands out most in this regard comes from CS2. Historically, experiments to record kaX data with CS2 have been difficult to perform, and values over a wide range have been reported.35 Thus, it is reasonable to assume that our O2(a1Δg) → O2(b1Σg+) experiments could be subject to the same problem. Schmidt has also extensively discussed the possibility that the behavior of CS2 in particular is not adequately represented by the treatment of eq 3.37,43 In considering the treatment of Schmidt as applied to our data (Figure 4), it is important to recognize that we are still dealing with molar properties. Although the variables in the expression for the parameter P were derived from the perspective of a gas-phase system, with a slight modification this formulation could also be used to describe collisions between oxygen and an ensemble of surrounding solvent molecules.43 The reason for mentioning this point here is that we have recently shown that kaX data recorded as a function of temperature are best explained using a model in which the perturbation of O2(a1Δg) occurs through a collection of solvent molecules, not through a 1:1 complex between oxygen and a single solvent molecule.22 We therefore infer that our kba data would likewise best be interpreted in the context of an ensemble-based model of solvent molecules.
Figure 4. Plot of log(kba/P′) against log(R) using O2(a1Δg) → O2(b1Σg+) absorption data obtained from 17 solvents. The solid line is a linear fit to the data and has a slope of 2.1 ± 0.1. The data points obtained with CS2 and 1-octanol are marked with a square and a triangle, respectively.
In conclusion, the data shown in Table 2 and Figure 3 are certainly consistent with Minaev’s perspective of solventperturbed transitions in oxygen. The Perturbation from a Molecular Perspective. In extensive interpretations of both O2(a1Δg) → O2(X3Σg−) and O2(b1Σg+) → O2(a1Δg) emission data, Schmidt and coworkers37,43 have also taken the concentration of the perturbing molecule into account to obtain second-order radiative rate constants kaX and kba (i.e., in units of M−1 s−1). Schmidt further defined a parameter P (eq 3) that accounts for (1) the oxygen− solvent collision frequency and (2) the expected inherent dependence of the radiative rate constant on n2 (vide supra):37,43 P = n2VvdW −2/3doc 2NA
8πkT μ
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CONCLUSION We have provided an extensive set of O2(a1Δg) → O2(b1Σg+) absorption data that provides unique insight into the mechanism by which liquid organic solvents perturb the probability of electronic transitions in molecular oxygen. Our data are consistent with a general picture in which oxygen is perturbed to a greater extent by solvents with large electronic polarizabilities.
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EXPERIMENTAL SECTION Instrumentation. The general description of our step-scan FTIR spectrometer and the use of this instrument to record and quantify O2(a1Δg) → O2(b1Σg+) absorption at ∼5200 cm−1 in liquid solvents has been published elsewhere.16,17,19,20,23 A description of the modifications to this instrument and the details of the approach used for the present study are given in the SI. Chemicals. Solvents were HPLC-grade and were used as received. C60 (Sigma-Aldrich, 99.5%) was used as received, whereas PN (Sigma-Aldrich, 97%) was recrystallized from ethanol before use. To avoid potential complications associated with photoinitiated degradation of these sensitizers over the course of our experiments, a flow cell was used to ensure sample consistency.
(3)
where VvdW refers to the van der Waals volume of a given solvent molecule, doc is the collision distance between oxygen and a given solvent molecule, and μ is the reduced mass of the colliding pair. Schmidt then divided the values of kaX and kba by P, and the base-10 logarithms of the resultant numbers were plotted against the base-10 logarithms of the solvent molar refractions R (where R is equal to (n2 − 1)/(n2 + 2) divided by the solvent concentration).37,43 This plot yielded a slope of ∼2, allowing one to infer that the corrected radiative rate constant is proportional to the square of R. Because a radiative rate constant is likewise proportional to the square of the transition moment,45 this correlation appears to indicate that the solventinduced transition dipole in oxygen indeed is directly correlated with R and hence the solvent’s electronic polarizability. We subjected our new and more extensive kba data set to the treatment of Schmidt described above, except that we did not include n2 in the parameter P because this was already considered when we used the Strickler−Berg expression to obtain kba from εab (eq 2). Pertinent parameters for this exercise are shown in Table 2, and the results are shown in Figure 4, where P′ = P/ n2. The values of log(kba/P′) indeed appear to be
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ASSOCIATED CONTENT
S Supporting Information *
Details of the modified step-scan FTIR spectrometer and the approach used to record O2(a1Δg) → O2(b1Σg+) spectra; plot of the O2(a1Δg) → O2(b1Σg+) absorption coefficient against the solvent static dielectric constant; plots of the O2(a1Δg) → O2(b1Σg+) absorption coefficient against functions of the F
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(18) Keszthelyi, T.; Poulsen, T. D.; Ogilby, P. R.; Mikkelsen, K. V. O2(a1Δg) Absorption and O2(b1Σg+) Emission in Solution: Quantifying the a-b Stokes Shift. J. Phys. Chem. A 2000, 104, 10550−10555. (19) Dam, N.; Keszthelyi, T.; Andersen, L. K.; Mikkelsen, K. V.; Ogilby, P. R. Effect of Solvent on the O2(a1Δg) - O2(b1Σg+) Absorption Spectrum: Demonstrating the Importance of Equilibrium vs Nonequilibrium Solvation. J. Phys. Chem. A 2002, 106, 5263−5270. (20) Andersen, L. K.; Ogilby, P. R. Absorption Spectrum of Singlet Oxygen in D2O: Enabling the Test of a Model for the Effect of Solvent on Oxygen’s Radiative Transitions. J. Phys. Chem. A 2002, 106, 11064−11069. (21) Strickler, S. J.; Berg, R. A. Relationship between Absorption Intensity and Fluorescence Lifetime of Molecules. J. Chem. Phys. 1962, 37, 814−822. (22) Jensen, R. L.; Holmegaard, L.; Ogilby, P. R. Temperature Effect on Radiative Lifetimes: The Case of Singlet Oxygen in Liquid Solvents. J. Phys. Chem. B 2013, 117, 16227−16235. (23) Keszthelyi, T.; Weldon, D.; Andersen, T. N.; Poulsen, T. D.; Mikkelsen, K. V.; Ogilby, P. R. Radiative Transitions of Singlet Oxygen: New Tools, New Techniques, and New Interpretations. Photochem. Photobiol. 1999, 70, 531−539. (24) Wilkinson, F.; Helman, W. P.; Ross, A. B. Rate Constants for the Decay and Reactions of the Lowest Electronically Excited Singlet State of Molecular Oxygen in Solution. An Expanded and Revised Compilation. J. Phys. Chem. Ref. Data 1995, 24, 663−1021. (25) Afshari, E.; Schmidt, R. Isotope-Dependent Quenching of Singlet Molecular Oxygen by Ground-State Oxygen in Several Perhalogenated Solvents. Chem. Phys. Lett. 1991, 184, 128−132. (26) Schmidt, R. Influence of Heavy Atoms on the Deactivation of Singlet Oxygen (1Δg) in Solution. J. Am. Chem. Soc. 1989, 111, 6983− 6987. (27) Schmidt, R.; Afshari, E. Collisional Deactivation of O2(1Δg) by Solvent Molecules. Comparative Experiments with 16O2 and 18O2. Ber. Bunsenges. Phys. Chem. 1992, 96, 788−794. (28) Braslavsky, S. E. Glossary of Terms Used in Photochemistry (IUPAC Recommendations). Pure Appl. Chem. 2007, 79, 293−465. (29) Arnbjerg, J.; Paterson, M. J.; Nielsen, C. B.; Jørgensen, M.; Christiansen, O.; Ogilby, P. R. One- and Two-Photon Photosensitized Singlet Oxygen Production: Characterization of Aromatic Ketones as Sensitizer Standards. J. Phys. Chem. A 2007, 111, 5756−5767. (30) Schmidt, R.; Tanielian, C.; Dunsbach, R.; Wolff, C. Phenalenone, a Universal Reference Compound for the Determination of Quantum Yields of Singlet Oxygen Sensitization. J. Photochem. Photobiol., A 1994, 79, 11−17. (31) Suppan, P.; Ghoneim, N. Solvatochromism; Royal Society of Chemistry: Cambridge, U.K., 1997. (32) Reichardt, C. Solvents and Solvent Effects in Organic Chemistry; VCH: Weinheim, Germany, 1988. (33) Atkins, P.; de Paula, J. Physical Chemistry; Oxford University Press: Oxford, U.K., 2006. (34) Hirayama, S.; Phillips, D. Correction for Refractive Index in the Comparison of Radiative Lifetimes in Vapour and Solution Phases. J. Photochem. 1980, 12, 139−145. (35) Scurlock, R. D.; Nonell, S.; Braslavsky, S. E.; Ogilby, P. R. Effect of Solvent on the Radiative Decay of Singlet Molecular Oxygen (a1Δg). J. Phys. Chem. 1995, 99, 3521−3526. (36) Scurlock, R. D.; Ogilby, P. R. The Effect of Solvent on the Rate Constant for the Radiative Deactivation of Singlet Molecular Oxygen (a1Δg). J. Phys. Chem. 1987, 91, 4599−4602. (37) Schmidt, R.; Shafii, F.; Hild, M. The Mechanism of the Solvent Perturbation of the a-X Radiative Transition of O2. J. Phys. Chem. A 1999, 103, 2599−2605. (38) Demas, J. N.; Crosby, G. A. The Measurement of Photoluminescence Quantum Yields. A Review. J. Phys. Chem. 1971, 75, 991−1024. (39) Weldon, D.; Poulsen, T. D.; Mikkelsen, K. V.; Ogilby, P. R. Singlet Sigma: The ″Other″ Singlet Oxygen in Solution. Photochem. Photobiol. 1999, 70, 369−379.
solvent optical dielectric constant; and information relevant to eq 1 and the associated errors. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b05131.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Danish National Research Foundation. The authors thank Tommy Kessler (Aarhus University) for his assistance in modifying the FTIR spectrometer.
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REFERENCES
(1) Clennan, E. L.; Pace, A. Advances in Singlet Oxygen Chemistry. Tetrahedron 2005, 61, 6665−6691. (2) Davies, M. J. Singlet Oxygen-Mediated Damage to Proteins and its Consequences. Biochem. Biophys. Res. Commun. 2003, 305, 761− 770. (3) Redmond, R. W.; Kochevar, I. E. Spatially-Resolved Cellular Responses to Singlet Oxygen. Photochem. Photobiol. 2006, 82, 1178− 1186. (4) Klotz, L.-O.; Kröncke, K.-D.; Sies, H. Singlet Oxygen-Induced Signaling Effects in Mammalian Cells. Photochem. Photobiol. Sci. 2003, 2, 88−94. (5) Ogilby, P. R. Singlet Oxygen: There is Indeed Something New Under the Sun. Chem. Soc. Rev. 2010, 39, 3181−3209. (6) Scurlock, R. D.; Wang, B.; Ogilby, P. R. Chemical Reactivity of Singlet Sigma Oxygen (b1Σg+) in Solution. J. Am. Chem. Soc. 1996, 118, 388−392. (7) Bodesheim, M.; Schmidt, R. Chemical Reactivity of Sigma Singlet Oxygen O2(b1Σg+). J. Phys. Chem. A 1997, 101, 5672−5677. (8) Bregnhøj, M.; Blázquez-Castro, A.; Westberg, M.; Breitenbach, T.; Ogilby, P. R. Direct 765 nm Optical Exciation of Molecular Oxygen in Solution and in Single Mammalian Cells. J. Phys. Chem. B 2015, 119, 5422−5429. (9) Schweitzer, C.; Schmidt, R. Physical Mechanisms of Generation and Deactivation of Singlet Oxygen. Chem. Rev. 2003, 103, 1685− 1757. (10) Paterson, M. J.; Christiansen, O.; Jensen, F.; Ogilby, P. R. Overview of Theoretical and Computational Methods Applied to the Oxygen-Organic Molecule Photosystem. Photochem. Photobiol. 2006, 82, 1136−1160. (11) Minaev, B. F. Electronic Mechanisms of Molecular Oxygen Activation. Russ. Chem. Rev. 2007, 76, 989−1011. (12) Ogilby, P. R. Solvent Effects on the Radiative Transitions of Singlet Oxygen. Acc. Chem. Res. 1999, 32, 512−519. (13) Minaev, B. F. Solvent-Induced Emission of Molecular a1Δg Oxygen. J. Mol. Struct.: THEOCHEM 1989, 183, 207−214. (14) Minaev, B. F.; Lunell, S.; Kobzev, G. I. The Influence of Intermolecular Interaction on the Forbidden near-IR Transitions in Molecular Oxygen. J. Mol. Struct.: THEOCHEM 1993, 284, 1−9. (15) Minaev, B. F.; Ågren, H. Collision-Induced b1Σg+-a1Δg, b1Σg+X3Σg−, and a1Δg-X3Σg− Transition Probabilities in Molecular Oxygen. J. Chem. Soc., Faraday Trans. 1997, 93, 2231−2239. (16) Weldon, D.; Ogilby, P. R. Time-Resolved Absorption Spectrum of Singlet Oxygen in Solution. J. Am. Chem. Soc. 1998, 120, 12978− 12979. (17) Andersen, L. K.; Ogilby, P. R. A Nanosecond Near-IR Step-Scan FT Absorption Spectrometer: Monitoring Singlet Oxygen, Organic Molecule Triplet States, and Associated Thermal Effects Upon Pulsed Laser Irradiation of a Photosensitizer. Rev. Sci. Instrum. 2002, 73, 4313−4325. G
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Effect of Solvent on the O2(a1Δg) → O2(b1Σg+) Absorption Coefficient Mikkel Bregnhøj and Peter R. Ogilby* Center for Oxygen Microscopy and Imaging, Department of Chemistry, Aarhus University, Langelandsgade 140, Aarhus 8000, Denmark S Supporting Information *
ABSTRACT: Radiative transitions between the three lowestlying electronic states of molecular oxygen have long provided a model to study how collision-dependent perturbations influence forbidden processes. In an isolated oxygen molecule, transitions between the O2(X3Σg−), O2(a1Δg), and O2(b1Σg+) states are forbidden as electric-dipole processes. For oxygen dissolved in organic solvents, the probabilities of radiative transitions between these states increase appreciably. Attempts to interpret solventdependent changes in the radiative rate constants have principally relied on O2(b1Σg+) and O2(a1Δg) emission experiments. However, the dominant nonradiative deactivation channels of O2(b1Σg+) make it difficult to quantify solvent effects on the O2(b1Σg+) → O2(a1Δg) radiative process. Thus, an appreciable amount of important information has heretofore not been available. In the present study, we examined the effect of 17 common organic solvents on the O2(a1Δg) → O2(b1Σg+) absorption transition at ∼5200 cm−1 (i.e., ∼1925 nm). The solvent-dependent absorption coefficients at the band maximum, εmax, range from 5 to 50 M−1 cm−1 and correlate reasonably well with the solvent refractive index; εmax is largest in solvents with the largest refractive index. This observation is consistent with a model in which oxygen is perturbed to a greater extent by solvents with a large electronic polarizability. Through the Strickler−Berg equation, we also used these absorption data to obtain the radiative rate constant for the O2(b1Σg+) → O2(a1Δg) transition, and the results are consistent with a model in which the O2(a1Δg) → O2(X3Σg−) transition is said to steal intensity from the O2(b1Σg+) → O2(a1Δg) transition.
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electronic-to-vibrational energy transfer.9 In the present study, we limit ourselves to the effect of the solvent on radiative transitions in oxygen. In an isolated oxygen molecule (e.g., in a low-pressure gasphase system), transitions between the O2(X3Σg−), O2(a1Δg), and O2(b1Σg+) states are forbidden as electric-dipole processes. However, for oxygen dissolved in organic solvents, the probabilities of radiative transitions between these states increase appreciably. The pertinent experimental data in this regard have principally been acquired from O2(b1Σg+) → O2(a1Δ g), O2(b1Σg+) → O2(X3Σg−), and O2(a1Δ g) → O2(X3Σg−) emission studies, with the greatest attention being focused on the O2(a1Δg) → O2(X3Σg−) phosphorescent transition.9,12 The currently accepted model that accounts for the effect of solvent on the O2(a1Δg) → O2(X3Σg−) radiative rate constant, kaX, is that of Minaev.13−15 In brief, Minaev’s thesis is that the O2(a1Δg) → O2(X3Σg−) transition steals intensity from the more probable O2(b1Σg+) → O2(a1Δg) transition. The O2(b1Σg+) → O2(a1Δg) transition is proposed to gain intensity through a solvent-dependent disruption of oxygen’s cylindrical symmetry that lifts the degeneracy of the πx and πy antibonding orbitals, which in turn introduces an
INTRODUCTION Studies that focus on the two lowest-lying excited electronic states of molecular oxygen continue to draw appreciable attention from the scientific community. In this regard, the O2(a1Δg) state is arguably the most important in that it has a characteristic and unique chemistry that results in the oxygenation of many organic molecules,1 including molecules significant in many biological processes.2−5 Although the O2(b1Σg+) state is not known to be chemically reactive, certainly in solution-phase systems,6,7 it is often a precursor to the O2(a1Δg) state and, as such, likewise draws appreciable attention from those interested in oxygenation reactions.8,9 From a different perspective, both the radiative and nonradiative transitions between the O2(b1Σg+) and O2(a1Δg) states and the triplet ground state of oxygen, O2(X3Σg−), provide a wonderful model to study the fundamental effects that perturbing collisions have on highly improbable processes.10,11 However, despite having been studied for many years, there is still much that is not understood about these processes in this presumably most simple system of a homonuclear diatomic molecule. Of particular concern is how the transition probabilities depend on the nature of the collision partner. Much of the work in this field has focused on elucidating the mechanism(s) of solvent-mediated O2(b1Σg+) and O2(a1Δg) nonradiative deactivation, addressing fundamental tenets of © XXXX American Chemical Society
Received: May 29, 2015 Revised: July 1, 2015
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Figure 1. Time- and spectrally resolved absorption data recorded upon 355 nm pulsed laser irradiation of C60 in air-saturated toluene. The data shown here are an average of 10 independent time- and spectrally resolved traces. Each trace was obtained using 710 mirror positions in the stepscan FTIR spectrometer, and for each mirror position, 20 independent kinetic traces were added together. For the conditions under which these data were recorded, the change in sample absorbance, ΔAbs, at time = 0 was ∼4 × 10−4 absorbance units.
solution22 that provide further insight into the mechanism of this solvent-mediated perturbation.
electric-dipolar component into the transition. The introduction of this dipolar character causes the transition probability to increase appreciably. With these points in mind, an interesting and important corollary of Minaev’s thesis is that the ratio of the respective radiative rate constants, kaX/kba, is predicted to be solvent-independent with a value of ∼3 × 10−4.15 Over the years, an increasing amount of experimental data has been acquired to support Minaev’s model.9 An important limitation in this regard, however, is the difficulty of acquiring values for the O2(b1Σg+) → O2(a1Δg) radiative rate constant, kba, in many common liquid solvents. Specifically, to complement most of the kaX values acquired, it is necessary to quantify k ba in solvents that contain C−H and O−H bonds. Unfortunately, the kinetically competing process of O2(b1Σg+) → O2(a1Δg) nonradiative deactivation is so efficient in these solvents that it becomes difficult to perform the required experiments. Thus, much of the evidence to support Minaev’s model comes from gas-phase data and from some rather esoteric liquid solvents that are not easily handled (e.g., lowboiling Freons).9 Approximately 20 years ago, we constructed a step-scan FTIR spectrometer that could record the time-resolved O2(a1Δg) → O2(b1Σg+) absorption spectrum, which occurs at ∼5200 cm−1 (i.e., ∼1925 nm) in liquid solvents.16,17 We subsequently used this instrument to quantify solvent-dependent spectral changes in both the O2(a1Δg) → O2(b1Σg+) and O2(b1Σg+) → O2(a1Δg) transitions.18,19 In proof-of-principle experiments, we also demonstrated that this instrument can be used to quantify kba in a way that is useful to the study of Minaev’s model for the perturbation of oxygen by liquid solvents.20 In the present study, we modified our FTIR spectrometer to obtain a better signal-to-noise ratio and then set out to quantify O2(a1Δg) → O2(b1Σg+) absorption coefficients in a wide range of common organic solvents. The intent was to subsequently use an expression provided by Strickler and Berg21 to obtain the corresponding values of kba. We now report that an extensive set of experimental data obtained from common liquid organic solvents indeed supports Minaev’s general model by which radiative processes in molecular oxygen are perturbed. We also discuss our results in light of recent data on the temperature dependence of oxygen radiative lifetimes in
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RESULTS AND DISCUSSION O2(a1Δg) → O2(b1Σg+) Absorption Spectra. Timeresolved absorption measurements were performed over the spectral range 4800−5600 cm−1 upon pulsed laser irradiation of an O2(a1Δg) photosensitizer in a variety of different airsaturated organic solvents. A representative example of the data thus obtained is shown in Figure 1. The data recorded in the first ∼2 μs after the laser pulse include an appreciable contribution from the absorption of the sensitizer triplet state. This signal is rapidly quenched in the presence of oxygen to yield a single discrete absorption band centered at ∼5200 cm−1 (Figure 1). The three-dimensional data set shown in Figure 1 can be modified in two ways:12,23 (1) It can be compressed along the spectral axis to yield a plot of the change in sample absorbance as a function of time. For the present experiments, the decay function thus observed was always single-exponential, and the corresponding lifetimes, τ, are listed in Table 1. It is important to note that, as also measured in complementary O2(a1Δg) → O2(X3Σg−) phosphorescence experiments, these lifetimes are dominated by the nonradiative O2(a1Δg) deactivation channels (i.e., the rate constant for nonradiative O2(a1Δg) deactivation in these solvents is much greater than the radiative rate constant kaX). (2) It can be compressed along the time axis to yield the spectrum of the transient being observed. The latter was readily quantified using a Gaussian fitting function, and the resultant band maxima and band widths are likewise listed in Table 1. Data such as those shown in Figure 1 are readily assigned to the O2(a1Δg) → O2(b1Σg+) transition on the basis of the following points: (1) The spectra obtained are consistent with what is expected for this transition.18−20 (2) Although this absorption experiment is not the ideal approach for measuring the lifetime of O2(a1Δg) [see the further comments in the Supporting Information (SI)], the τ data obtained are nevertheless consistent with what is expected (Table 1). (3) The transient signal was not observed from deoxygenated solutions. (4) The rate of signal decay increased when a known O2(a1Δg) quencher (e.g., NaN3 or an amine) was added to the solution.16 B
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Table 1. O2(a1Δg) → O2(b1Σg+) Absorption Coefficients, εab, Recorded at the Absorption Band Maximum (νmax) in 17 Solvents −1 εmax cm−1) ab (M
solvent D2O methanol acetonitrile Freon 113 acetone acetic acid n-hexane 2-propanol 1-octanol CCl4 toluene mesitylene benzene o-xylene benzonitrile bromobenzene CS2
published 6 − − − − − 40 − − − 56 − 56 − − − 52
± 2a
± 4c
±6
c
± 6a
± 5c
νmax (cm−1)
new − 7 16 26 14 10 23 12 21 26 30 35 32 35 36 43 49
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
published 3 5 4 3 4 4 5 6 6 4 5 3 5 5 5 5
5228 5217 5224 5209 − − 5199 − − 5195 5191 − 5197 − 5194 − 5168
± ± ± ±
1a 2b 2b 1b
± 1b
± 1b ± 1b ± 1b ± 1b ± 1b
bandwidth (fwhm) (cm−1) new
− 5215 5219 5206 5218 5223 5202 5208 5191 5192 5193 5194 5195 5191 5193 5184 5171
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
published 5 5 3 3 3 3 3 3 3 3 3 3 3 3 3 3
75 86 82 63 − − 69 − − 72 74 − 76 − 81 − 90
± ± ± ±
2a 5b 5b 2b
± 2b
± 2b ± 2b ± 2b ± 2b ± 2b
new − 77 76 57 82 79 73 62 60 65 70 72 74 73 70 68 81
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
10 10 5 5 5 5 5 5 5 5 5 5 5 5 5 5
τ (μs) publishedd 68 ± 1 10 ± 1 80 ± 2 72000 ± 5000f 51 ± 3 − 31 ± 1 21 ± 2 19 ± 2 73000 ± 10000h 29 ± 1 15 ± 1 31 ± 1 21 ± 2 41 ± 4 45 ± 4 79000 ± 4000i
newe − 10 82 −g 37 15 29 17 15 −g 26 12 27 16 30 40 −g
±2 ±3 ± ± ± ± ±
3 2 2 2 2
± ± ± ± ± ±
2 1 2 1 2 2
a From Andersen and Ogilby.20 bFrom Dam et al.19 cFrom Weldon and Ogilby.16 dIndependently obtained from O2(a1Δg) → O2(X3Σg−) phosphorescence measurements. Data are averages of values obtained from the compilation of Wilkinson et al.,24 unless specified otherwise. e Obtained from our current O2(a1Δg) → O2(b1Σg+) data. fFrom Afshari and Schmidt.25 gThe high-pass filter used in our experiments precluded measurements of τ values longer than ∼1 ms. hAverage of data from air-saturated solutions.25,26 iFrom Schmidt and Afshari.27
Quantifying the O2(a1Δg) → O2(b1Σg+) Absorption Coefficient. To obtain the O2(a1Δg) → O2(b1Σg+) absorption coefficient, εab, it was necessary to extrapolate our observed kinetic signal backward in time to obtain a value for the O2(a1Δg) → O2(b1Σg+) absorbance change, ΔAbs, at time = 0. Typically, these values of ΔAbs were in the range 1−10 × 10−4 absorbance units, depending on our experimental conditions (vide infra). ΔAbs could then be correlated to εab through the Lambert−Beer Law when the concentration of O2(a1Δg) produced in our photosensitized reaction at time = 0 was known. The latter was readily available through known and controlled parameters. The pertinent compilation of terms is shown in eq 1 (further details are provided in the SI): εab =
hcfNAVirr λϕΔηP0(1 − 10−A)leff
that the concentration of O2(a1Δg) in our sample was approximately the same in any plane perpendicular to the propagating beam of the excitation laser. The principal sensitizer chosen for this work, phenalenone (PN), has a solvent-independent quantum yield of O2(a1Δg) that is essentially unity (ϕΔ = 0.98 ± 0.05).29,30 We also ensured that, under all conditions, all of the PN excited states produced by the exciting pulse were quenched by O2(X3Σg−). Finally, selected experiments performed using a different sensitizer (e.g., C60) gave the same results as those obtained using PN. The values of εab thus obtained are shown in Table 1. With the few solvents for which we have previously reported values of εab from O2(a1Δg) → O2(b1Σg+) experiments, we find that our present εab values are systematically smaller (see Table 1). Although measuring these small absorption coefficients is a difficult proposition in itself, we nevertheless attribute this difference to the increased accuracy with which our present optimized FTIR instrument records data. In the measurement of any single εab value, we typically obtain an error of approximately ±20−30% derived from propagation of the errors in the variables in eq 1 (see the SI). Repeating a given experiment ∼3−5 times then allows us to reduce this error, through averaging, to ∼10−20%. Correlating O2(a1Δg) → O2(b1Σg+) Spectra to Solvent Parameters. The data in Table 1 show that εab and νmax change appreciably as a function of the solvent in which oxygen is dissolved. In view of the general history of studies of solvent effects on electronic transitions31,32 and the specific history of studies of solvent effects on electronic transitions in oxygen,9,12 it is incumbent upon us to at least consider how these values correlate with parameters that quantify the dielectric properties of the solvents. Much of the literature on general solvent effects on a given solute focuses on solute spectral shifts.31,32 To this end, the solvent is often characterized as a dielectric continuum, and representative parameters are obtained from functions that include both the static dielectric constant, εst, and the optical
ΔAbs (1)
where h is Planck’s constant, c is the speed of light, NA is Avogadro’s number, f is the repetition rate of the irradiating laser, Virr is the volume of sample irradiated by the laser, leff is the effective path length traversed by the IR probe beam, ϕΔ is the quantum yield of sensitized O2(a1Δg) production, P0 is the incident pump laser power, η is a factor correcting for light reflection off the front face of the sample cuvette (η = 0.95), and A is the absorbance of the sensitizer at the irradiation wavelength λ. Although the use of the moniker “extinction coefficient” is no longer advisible according to the IUPAC rules,28 distinguishing between extinction and absorption is still important in many cases, including the present study, where the molar absorption coefficient is small and light reflected/ scattered by the sample can have an appreciable effect on the measured quantity. We have tried to properly account for some light reflection through our parameter η. Nevertheless, our values of εab likely still differ from the true molar absorption coefficient. For our approach to be most accurate, we ensured that the cross-sectional intensity of our exciting laser resembled a rectangular function (see the SI). In this way, we established C
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The Journal of Physical Chemistry A (i.e., high-frequency) dielectric constant, εop.31,32 The latter is invariably expressed in terms of the solvent refractive index, n, measured in the visible region of the spectrum (i.e., εop = n2). Furthermore, εop and functions of εop [e.g., (εop − 1)/(εop + 1) = (n2 −1)/(n2 + 1)] are generally used to describe the electronic polarizability of a given solvent.31,33 Although our present experiments were not designed to study the effect of the solvent on the spectral shifts of oxygen (i.e., our current data were recorded at a lower spectral resolution than data recorded in our earlier studies19), our present results are nevertheless consistent with our earlier observations. Specifically, we find that the band maximum of the O2(a1Δg) → O2(b1Σg+) transition shifts to smaller wavenumbers as n increases (Table 1). In contrast, there is not as much material in the literature on the effect of the solvent on the probabilities of electronic transitions in a given solute.31,32,34 In this regard, studies of the response of oxygen to changes in the solvent play an important and unique role. For the present case, we find that εab ranges from ∼5 M−1 cm−1 in D2O and methanol to ∼50 M−1 cm−1 in CS2. Moreover, our values of εab show a reasonably good correlation with n as well as n2 (Figure 2). In contrast, there was no correlation between εab and the static dielectric constant of the solvent (see the SI). These observations are consistent with independent reports on the O2(a1Δg) → O2(X3Σg−) radiative transition.9,12,35−37 Upon examining the data in Figure 2, we note that the εab value obtained for Freon 113 deviates the most from the linear correlations with n and n2. Although it is tempting to ascribe this observation to the difficulty of performing experiments with this solvent, for the moment we would rather say that these plots give only a general qualitative assessment of the role played by the solvent. As we have inferred from corresponding plots of kaX against n and functions of n,12,35,36 we conclude that the data in Figure 2 reflect the fact that electronic transitions in oxygen are perturbed to a greater extent by solvents with a larger electronic polarizability. We will return to this point below. From O2(a1Δg) Absorption to O2(b1Σg+) Emission. Our O2(a1Δg) → O2(b1Σg+) data can be used to estimate the rate constant for O2(b1Σg+) → O2(a1Δg) radiative deactivation, kba. As noted in the Introduction, the latter is a useful parameter in the context of Minaev’s model of solvent-perturbed transitions in oxygen. To this end, we used an expression provided by Strickler and Berg21 that equates the integrated absorption coefficient for a transition from a “lower” state to an “upper” state to the radiative rate constant from the same “upper” state to the same “lower” state (eq 2): k ba = n2
8πc ln(10) glower 2 ν NA g upper
Figure 2. Plots of the O2(a1Δg) → O2(b1Σg+) molar extinction coefficient, εab, obtained at the maximum of the O2(a1Δg) → O2(b1Σg+) absorption band against (a) the refractive index, n, and (b) n2 for the solvents in which oxygen was dissolved. The lines shown are linear fits to the data. Similar correlations were observed when εab was plotted against functions of n [e.g., (n2 − 1)/(n2 + 1)]; see the SI. The data recorded from Freon 113 are marked with a circle.
important to note that the factor of n2 in eq 2 is an inherent part of the derivation of this expression that accounts for the solvent-dependent change in the speed of light through that particular medium.21,34 It should not be confused with an experimental correction factor (generally n2 as well) that must be applied when emission experiments are performed in different solvents to account for the fact that the optical detector used in these experiments is invariably in a medium (air) that has a different refractive index than the solvent studied.35,36,38 Although the Strickler−Berg expression was originally derived for strongly allowed transitions, we assume that it nevertheless provides an adequate approach to model the weak transitions in oxygen.20,23,39 The radiative rate constants kba thus obtained from our O2(a1Δg) → O2(b1Σg+) data are listed in Table 2. Radiative Rate Constants for the O 2 (a 1 Δ g ) → O2(X3Σg−) Transition. As noted in the Introduction, a key aspect of Minaev’s approach to interpret solvent effects on radiative transitions in oxygen is to compare values of kba with values of the O2(a1Δg) → O2(X3Σg−) radiative rate constant
∞
∫−∞ εab(ν) dν
(2)
where ν is the transition energy in cm−1 and the coefficients gupper and glower quantify the degeneracies of the upper and lower states, respectively. Because the O2(a1Δg) state is doubly degenerate,10 the ratio of g coefficients is equal to 2 in this case. Furthermore, because the Stokes shift between the O2(a1Δg) → O2(b1Σg+) and O2(b1Σg+) → O2(a1Δg) transitions is extremely small18 and the equilibrium nuclear geometries are essentially the same in the O2(a1Δg) and O2(b1Σg+) states,10 it is sufficiently accurate to use the band maximum of the O2(a1Δg) → O2(b1Σg+) absorption profile as a measure of the solvent-dependent transition energy ν. Finally, it is D
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Table 2. Solvent Parameters and Rate Constants for the O2(b1Σg+) → O2(a1Δg) and O2(a1Δg) → O2(X3Σg−) Radiative Transitions solvent
na
VvdW (mM−1)b
R (mM−1)c
doc (Å)d
μ (g/mol)e
D2O methanol acetonitrile Freon 113 acetone acetic acid n-hexane 2-propanol 1-octanol CCl4 toluene mesitylene benzene o-xylene benzonitrile bromobenzene CS2
1.338 1.329 1.344 1.358 1.359 1.371 1.375 1.377 1.430 1.460 1.497 1.499 1.501 1.505 1.528 1.560 1.627
11.5 21.7 28.4 58.7 39.0 31.4 68.3 42.2 93.3 49.8 59.5 81.8 48.4 70.7 60.5 61.0 31.2
3.77 8.23 11.06 26.38 16.16 12.98 30.13 17.59 40.83 26.55 30.99 40.85 26.25 35.85 31.44 33.96 21.40
3.38 3.77 3.97 4.58 4.22 4.04 4.73 4.28 5.06 4.43 4.59 4.91 4.40 4.76 4.61 4.62 4.04
12.32 16.01 17.98 27.33 20.63 20.88 23.33 20.88 25.69 26.49 23.75 25.27 22.70 24.59 24.24 26.58 22.53
kba (s−1)f 199 235 528 659 507 373 777 356 626 854 1146 1378 1289 1396 1413 1671 2528
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
67 93 153 138 120 91 146 101 146 192 161 206 187 204 236 225 324
kaX (s−1)g 0.18 0.32 0.45 1.35 0.59 0.44 0.60 0.47 0.97 1.10 1.44 1.72 1.50 1.70 1.80 1.97 3.11
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
0.02 0.03 0.05 0.14h 0.06 0.13i 0.06 0.05 0.29i 0.11 0.14 0.17j 0.15 0.17k 0.18 0.20 0.31
104·kaX/kba 9.0 13.4 8.5 20.5 11.6 11.9 7.7 13.2 15.4 12.9 12.6 12.5 11.6 12.2 12.7 11.8 12.3
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
3.2 5.5 2.5 4.8 4.5 4.6 1.6 4.0 5.9 3.2 2.2 2.2 2.0 2.2 2.5 2.0 2.0
a Solvent refractive index at 20 °C at 589 nm (Na D line). bSolvent van der Waals volume. cSolvent molar refraction. dOxygen−solvent collision distance calculated using van der Waals radii. eReduced mass of the 1:1 oxygen−solvent pair. fObtained through eq 2 from our O2(a1Δg) → O2(b1Σg+) data. gObtained from Poulsen et al.,40 unless otherwise specified. The errors shown reflect only relative uncertainties and do not consider the absolute error of ±30% derived from the uncertainty in Schmidt’s standard value in benzene.41 hFrom Schmidt and Afshari42 and normalized to kaX = 1.5 s−1 for benzene. iCalculated from the correlation of kaX with n.35,36,40 jFrom Hild and Schmidt.43 kThe value for p-xylene was used.40
kaX.13−15 To this end, it is incumbent upon us likewise to compile values of kaX to complement each of our kba values. Over the past ∼30 years, accurate relative solvent-dependent values of kaX have been acquired from O2(a1Δg) → O2(X3Σg−) phosphorescence experiments.9,35,36,40,43 However, for the present application, it is necessary to normalize these relative values in such a way that they acquire meaning in an absolute sense. To our knowledge, there have been only two attempts to quantify absolute values of O2(a1Δ g) phosphorescence quantum yields in the pertinent solvents to yield data that can then be used to obtain an absolute value of kaX.41,44 Although different approaches were used in these two studies, the results obtained are equivalent within the margin of error for such a difficult experiment. For our present work, we opted to use kaX = 1.5 ± 0.5 s−1 obtained by Schmidt for experiments performed in benzene.37,41 Using this standard, we normalized the relative values of kaX pertinent to our present study, and the resultant first-order rate constants are listed in Table 2. Correlating the O2(b1Σg+) → O2(a1Δg) and O2(a1Δg) → O2(X3Σg−) Transitions. Our data yield a kaX/kba ratio that is indeed relatively constant and independent of the solvent, as predicted by Minaev (Table 2 and Figure 3). Thus, we confirm that, irrespective of the solvent involved, the O2(b1Σg+) → O2(a1Δg) transition is perturbed to the same extent as the O2(a1Δg) → O2(X3Σg−) transition. This is embodied in Minaev’s fundamental tenet that, as a consequence of solvent perturbation, the O2(a1Δg) → O2(X3Σg−) transition steals intensity from the O2(b1Σg+) → O2(a1Δg) transition. It is again interesting to note that in Figure 3 the point for Freon 113 deviates the most from the linear correlation. If we ascribe more meaning to this plot than to the plots shown in Figure 2, and on the basis of our discussion regarding Figure 4 below, it is likely that the deviation seen here principally reflects the fact that the reported value of 1.35 ± 0.14 s−1 for kaX in Freon 113 is too large (Table 2). Indeed, if we give credence to the correlation between kaX and the solvent refractive index n
Figure 3. Plot of the first-order rate constant for the O2(a1Δg) → O2(X3Σg−) radiative transition, kaX, against the first-order rate constant for the O2(b1Σg+) → O2(a1Δg) radiative transition, kba. Values of the latter were obtained from our O2(a1Δg) → O2(b1Σg+) absorption experiments through eq 2. The solid line is a linear fit to the data with a slope of (12.2 ± 0.8) × 10−4. The data point obtained with Freon 113 is marked with a circle.
that has been established using many solvents,35,36 one would expect a kaX value of ∼0.4 s−1 for Freon 113. Our newer, extensive, and more accurate data set of kba values also yields an average kaX/kba ratio of (12.2 ± 0.8) × 10−4, which is ∼1.6 times greater than that obtained from our preliminary data published in 2002 (7.4 × 10−4).20 However, it is still quite remarkable that our experimental kaX/kba numbers come close to the kaX/kba ratio of ∼3 × 10−4 predicted by Minaev. This factor of 4 difference between experiment and theory is easily understood, arguably expected, given the errors and assumptions associated with each approach. E
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linearly correlated with values of log(R), and the slope of this line is indeed ∼2. Continuing our discussion about the possibilities of anomalous data from selected solvents, we note now that the kba data for Freon 113 do not deviate from the linear correlation shown in Figure 4. Rather, the point that now stands out most in this regard comes from CS2. Historically, experiments to record kaX data with CS2 have been difficult to perform, and values over a wide range have been reported.35 Thus, it is reasonable to assume that our O2(a1Δg) → O2(b1Σg+) experiments could be subject to the same problem. Schmidt has also extensively discussed the possibility that the behavior of CS2 in particular is not adequately represented by the treatment of eq 3.37,43 In considering the treatment of Schmidt as applied to our data (Figure 4), it is important to recognize that we are still dealing with molar properties. Although the variables in the expression for the parameter P were derived from the perspective of a gas-phase system, with a slight modification this formulation could also be used to describe collisions between oxygen and an ensemble of surrounding solvent molecules.43 The reason for mentioning this point here is that we have recently shown that kaX data recorded as a function of temperature are best explained using a model in which the perturbation of O2(a1Δg) occurs through a collection of solvent molecules, not through a 1:1 complex between oxygen and a single solvent molecule.22 We therefore infer that our kba data would likewise best be interpreted in the context of an ensemble-based model of solvent molecules.
Figure 4. Plot of log(kba/P′) against log(R) using O2(a1Δg) → O2(b1Σg+) absorption data obtained from 17 solvents. The solid line is a linear fit to the data and has a slope of 2.1 ± 0.1. The data points obtained with CS2 and 1-octanol are marked with a square and a triangle, respectively.
In conclusion, the data shown in Table 2 and Figure 3 are certainly consistent with Minaev’s perspective of solventperturbed transitions in oxygen. The Perturbation from a Molecular Perspective. In extensive interpretations of both O2(a1Δg) → O2(X3Σg−) and O2(b1Σg+) → O2(a1Δg) emission data, Schmidt and coworkers37,43 have also taken the concentration of the perturbing molecule into account to obtain second-order radiative rate constants kaX and kba (i.e., in units of M−1 s−1). Schmidt further defined a parameter P (eq 3) that accounts for (1) the oxygen− solvent collision frequency and (2) the expected inherent dependence of the radiative rate constant on n2 (vide supra):37,43 P = n2VvdW −2/3doc 2NA
8πkT μ
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CONCLUSION We have provided an extensive set of O2(a1Δg) → O2(b1Σg+) absorption data that provides unique insight into the mechanism by which liquid organic solvents perturb the probability of electronic transitions in molecular oxygen. Our data are consistent with a general picture in which oxygen is perturbed to a greater extent by solvents with large electronic polarizabilities.
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EXPERIMENTAL SECTION Instrumentation. The general description of our step-scan FTIR spectrometer and the use of this instrument to record and quantify O2(a1Δg) → O2(b1Σg+) absorption at ∼5200 cm−1 in liquid solvents has been published elsewhere.16,17,19,20,23 A description of the modifications to this instrument and the details of the approach used for the present study are given in the SI. Chemicals. Solvents were HPLC-grade and were used as received. C60 (Sigma-Aldrich, 99.5%) was used as received, whereas PN (Sigma-Aldrich, 97%) was recrystallized from ethanol before use. To avoid potential complications associated with photoinitiated degradation of these sensitizers over the course of our experiments, a flow cell was used to ensure sample consistency.
(3)
where VvdW refers to the van der Waals volume of a given solvent molecule, doc is the collision distance between oxygen and a given solvent molecule, and μ is the reduced mass of the colliding pair. Schmidt then divided the values of kaX and kba by P, and the base-10 logarithms of the resultant numbers were plotted against the base-10 logarithms of the solvent molar refractions R (where R is equal to (n2 − 1)/(n2 + 2) divided by the solvent concentration).37,43 This plot yielded a slope of ∼2, allowing one to infer that the corrected radiative rate constant is proportional to the square of R. Because a radiative rate constant is likewise proportional to the square of the transition moment,45 this correlation appears to indicate that the solventinduced transition dipole in oxygen indeed is directly correlated with R and hence the solvent’s electronic polarizability. We subjected our new and more extensive kba data set to the treatment of Schmidt described above, except that we did not include n2 in the parameter P because this was already considered when we used the Strickler−Berg expression to obtain kba from εab (eq 2). Pertinent parameters for this exercise are shown in Table 2, and the results are shown in Figure 4, where P′ = P/ n2. The values of log(kba/P′) indeed appear to be
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ASSOCIATED CONTENT
S Supporting Information *
Details of the modified step-scan FTIR spectrometer and the approach used to record O2(a1Δg) → O2(b1Σg+) spectra; plot of the O2(a1Δg) → O2(b1Σg+) absorption coefficient against the solvent static dielectric constant; plots of the O2(a1Δg) → O2(b1Σg+) absorption coefficient against functions of the F
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(18) Keszthelyi, T.; Poulsen, T. D.; Ogilby, P. R.; Mikkelsen, K. V. O2(a1Δg) Absorption and O2(b1Σg+) Emission in Solution: Quantifying the a-b Stokes Shift. J. Phys. Chem. A 2000, 104, 10550−10555. (19) Dam, N.; Keszthelyi, T.; Andersen, L. K.; Mikkelsen, K. V.; Ogilby, P. R. Effect of Solvent on the O2(a1Δg) - O2(b1Σg+) Absorption Spectrum: Demonstrating the Importance of Equilibrium vs Nonequilibrium Solvation. J. Phys. Chem. A 2002, 106, 5263−5270. (20) Andersen, L. K.; Ogilby, P. R. Absorption Spectrum of Singlet Oxygen in D2O: Enabling the Test of a Model for the Effect of Solvent on Oxygen’s Radiative Transitions. J. Phys. Chem. A 2002, 106, 11064−11069. (21) Strickler, S. J.; Berg, R. A. Relationship between Absorption Intensity and Fluorescence Lifetime of Molecules. J. Chem. Phys. 1962, 37, 814−822. (22) Jensen, R. L.; Holmegaard, L.; Ogilby, P. R. Temperature Effect on Radiative Lifetimes: The Case of Singlet Oxygen in Liquid Solvents. J. Phys. Chem. B 2013, 117, 16227−16235. (23) Keszthelyi, T.; Weldon, D.; Andersen, T. N.; Poulsen, T. D.; Mikkelsen, K. V.; Ogilby, P. R. Radiative Transitions of Singlet Oxygen: New Tools, New Techniques, and New Interpretations. Photochem. Photobiol. 1999, 70, 531−539. (24) Wilkinson, F.; Helman, W. P.; Ross, A. B. Rate Constants for the Decay and Reactions of the Lowest Electronically Excited Singlet State of Molecular Oxygen in Solution. An Expanded and Revised Compilation. J. Phys. Chem. Ref. Data 1995, 24, 663−1021. (25) Afshari, E.; Schmidt, R. Isotope-Dependent Quenching of Singlet Molecular Oxygen by Ground-State Oxygen in Several Perhalogenated Solvents. Chem. Phys. Lett. 1991, 184, 128−132. (26) Schmidt, R. Influence of Heavy Atoms on the Deactivation of Singlet Oxygen (1Δg) in Solution. J. Am. Chem. Soc. 1989, 111, 6983− 6987. (27) Schmidt, R.; Afshari, E. Collisional Deactivation of O2(1Δg) by Solvent Molecules. Comparative Experiments with 16O2 and 18O2. Ber. Bunsenges. Phys. Chem. 1992, 96, 788−794. (28) Braslavsky, S. E. Glossary of Terms Used in Photochemistry (IUPAC Recommendations). Pure Appl. Chem. 2007, 79, 293−465. (29) Arnbjerg, J.; Paterson, M. J.; Nielsen, C. B.; Jørgensen, M.; Christiansen, O.; Ogilby, P. R. One- and Two-Photon Photosensitized Singlet Oxygen Production: Characterization of Aromatic Ketones as Sensitizer Standards. J. Phys. Chem. A 2007, 111, 5756−5767. (30) Schmidt, R.; Tanielian, C.; Dunsbach, R.; Wolff, C. Phenalenone, a Universal Reference Compound for the Determination of Quantum Yields of Singlet Oxygen Sensitization. J. Photochem. Photobiol., A 1994, 79, 11−17. (31) Suppan, P.; Ghoneim, N. Solvatochromism; Royal Society of Chemistry: Cambridge, U.K., 1997. (32) Reichardt, C. Solvents and Solvent Effects in Organic Chemistry; VCH: Weinheim, Germany, 1988. (33) Atkins, P.; de Paula, J. Physical Chemistry; Oxford University Press: Oxford, U.K., 2006. (34) Hirayama, S.; Phillips, D. Correction for Refractive Index in the Comparison of Radiative Lifetimes in Vapour and Solution Phases. J. Photochem. 1980, 12, 139−145. (35) Scurlock, R. D.; Nonell, S.; Braslavsky, S. E.; Ogilby, P. R. Effect of Solvent on the Radiative Decay of Singlet Molecular Oxygen (a1Δg). J. Phys. Chem. 1995, 99, 3521−3526. (36) Scurlock, R. D.; Ogilby, P. R. The Effect of Solvent on the Rate Constant for the Radiative Deactivation of Singlet Molecular Oxygen (a1Δg). J. Phys. Chem. 1987, 91, 4599−4602. (37) Schmidt, R.; Shafii, F.; Hild, M. The Mechanism of the Solvent Perturbation of the a-X Radiative Transition of O2. J. Phys. Chem. A 1999, 103, 2599−2605. (38) Demas, J. N.; Crosby, G. A. The Measurement of Photoluminescence Quantum Yields. A Review. J. Phys. Chem. 1971, 75, 991−1024. (39) Weldon, D.; Poulsen, T. D.; Mikkelsen, K. V.; Ogilby, P. R. Singlet Sigma: The ″Other″ Singlet Oxygen in Solution. Photochem. Photobiol. 1999, 70, 369−379.
solvent optical dielectric constant; and information relevant to eq 1 and the associated errors. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b05131.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Danish National Research Foundation. The authors thank Tommy Kessler (Aarhus University) for his assistance in modifying the FTIR spectrometer.
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REFERENCES
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DOI: 10.1021/acs.jpca.5b05131 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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DOI: 10.1021/acs.jpca.5b05131 J. Phys. Chem. A XXXX, XXX, XXX−XXX
