Temperature Effect on Radiative Lifetimes: The Case of Singlet

Article pubs.acs.org/JPCB

Temperature Effect on Radiative Lifetimes: The Case of Singlet Oxygen in Liquid Solvents Rasmus Lybech Jensen,‡ Lotte Holmegaard,‡ and Peter R. Ogilby* Center for Oxygen Microscopy and Imaging, Chemistry Department, Aarhus University, DK-8000, Aarhus, Denmark S Supporting Information *

ABSTRACT: A change in solvent can have an appreciable effect on the rate constant for the O2(a1Δg) → O2(X3Σg−) radiative transition at ∼1275 nm. The data thus obtained have played an important role in understanding mechanisms by which environment-dependent perturbations can influence forbidden electronic transitions. We now report that the rate constant for O2(a1Δg) radiative deactivation, kr, also responds to changes in temperature. This result can have practical ramifications in experiments that use O2(a1Δg) phosphorescence to quantify yields of photosensitized O2(a1Δg) production. From a fundamental perspective, this result is significant, partly because there is little precedence for temperature-dependent changes in radiative rate constants. The data also require a re-evaluation of the current model by which oxygen is perturbed by solvent. Specifically, the evidence indicates that it is not appropriate to evaluate the interaction as a 1:1 complex between a given solvent molecule M and oxygen. Rather, one must consider an ensemble of solvent molecules surrounding oxygen.

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INTRODUCTION The lowest energy excited electronic state of molecular oxygen, singlet oxygen, O2(a1Δg), is an important reactive intermediate in a wide range of systems. In particular, O2(a1Δg) can oxygenate organic molecules in characteristic reactions that differ from those of oxygen’s triplet ground state, O2(X3Σg−). These reactions define the important role that O2(a1Δg) plays, for example, in biological systems as well as in many polymerbased materials.1−4 In a given system, the chemical reactions of O2(a1Δg) kinetically compete with processes wherein O2(a1Δg) is deactivated to O2(X3Σg−).5 This deactivation could be the result of interactions with (1) another solute, a so-called “quencher” and/or (2) solvent molecules. The overall rate constant for O2(a1Δg) removal, kΔ, can thus be expressed as a sum of bimolecular terms as shown in eq 1, kΔ = k nr[S] + k r[S] + kq[Q ] + k rxn[R ]

own way (i.e., knr does not respond to changes in the solvent in the same way as kr).5,6 Moreover, the inequality knr ≫ kr is applicable for most solvents of practical consequence. As such, it is the nonradiative deactivation channel that defines the solvent contribution to τΔ. On the other hand, solventdependent changes in kr are directly manifested in measurements that rely on the intensity of O2(a1Δg) → O2(X3Σg−) phosphorescence (e.g., O2(a1Δg) quantum yield measurements). As such, despite the inequality knr ≫ kr, solventdependent changes in kr can have appreciable practical significance. From a fundamental perspective, studying the response of knr and kr to changes in the solvent has been pivotal in elucidating ways that environment can perturb a forbidden transition. Thus, this seemingly narrow topic involving O2(a1Δg) is actually relevant to a broad cross section of experimental and computational scientists. On the basis of a phenomenal amount of data, including the results of experiments that quantify solvent H/D isotope effects on τΔ, a model of collision-dependent electronic-to-vibrational energy transfer evolved over the years to account for the effect of solvent on knr.5 However, on the basis of results from temperature-dependent experiments, we recently demonstrated that aspects of this model need to be re-evaluated.7 An appreciable effort has likewise been expended to interpret solvent-dependent kr data, and the currently accepted explanation involves a model in which perturbation by the solvent facilitates mixing between the O2(b1Σg+), O2(a1Δg), and O2(X3Σg−) states such that the O2(a1Δg) → O2(X3Σg−)

(1)

where R and Q represent the chemical reactant and quencher, respectively, and S represents the solvent. The solventdependent deactivation terms are further subdivided into a nonradiative process, knr, and a radiative process, kr. The latter corresponds to the O2(a1Δg) → O2(X3Σg−) phosphorescence at ∼1275 nm. The reciprocal of the first-order rate constant kΔ defines the lifetime of O2(a1Δg), τΔ. The development of methods to monitor O2(a1Δg) by its 1275 nm phosphorescence in time-resolved solution-phase experiments initiated a ∼20 year period of intense activity in which values of kΔ were obtained from a plethora of systems.5 Of particular interest were studies to elucidate how values of knr and kr varied with the solvent. It is now well-established that both knr and kr depend significantly on the solvent, each in its © 2013 American Chemical Society

Received: October 14, 2013 Revised: November 21, 2013 Published: November 21, 2013 16227

dx.doi.org/10.1021/jp410185n | J. Phys. Chem. B 2013, 117, 16227−16235

The Journal of Physical Chemistry B

Article

transition can steal intensity from the O2(b1Σg+)−O2(a1Δg) transition.5,6,8−14 Moreover, on the basis of empirical correlations between kr and functions of the solvent refractive index (i.e., the optical polarizability of the solvent), it has been argued that polarizable solvents are better suited to perturb oxygen and thus facilitate O2(b1Σg+), O2(a1Δg), and O2(X3Σg−) state mixing.6,11,12,15−18 This point has been carried further, and by showing that kr also correlates with the solvent molar refractivity (i.e., the bulk polarizability normalized by the solvent density), it has been tacitly assumed that the perturbing interaction is best viewed as a molecular event in a 1:1 complex between oxygen and a given solvent molecule M.11−13,19 Given the observation that temperature influences the effect of solvent on k nr and that O 2 (a 1 Δ g ) → O 2 (X 3 Σ g − ) phosphorescence experiments are increasingly performed at a variety of different temperatures,5,7,20−23 we felt that it was incumbent upon us likewise to examine the effect of temperature on kr in a number of common solvents. We now report that the solvent-dependent channel for O2(a1Δg) → O2(X3Σg−) radiative deactivation can indeed depend significantly on temperature; depending on the solvent, kr can either increase or decrease with an increase in temperature. This observation is significant in that temperature-dependent changes in the luminescence intensity of a given solute do not generally reflect a temperature-dependent change in the radiative rate constant but, rather, reflect a change in the competing nonradiative rate constant.24−27 To our knowledge, there is only one case where a slight temperaturedependent change in a radiative rate constant has been observed: the rate constant for 9,10-dichloroanthracene fluorescence in hexane was reported to decrease slightly with an increase in temperature.27 Our results can have practical ramifications in systems where O2(a1Δg) phosphorescence intensities are used to quantify relative yields of O2(a1Δg). We also consider what these results might mean in the context of the currently accepted model for solvent-mediated O2(b1Σg+), O2(a1Δg), and O2(X3Σg−) state mixing.

sensitizer absorbance at the irradiation wavelength of 400 nm was in the range 0.1−0.2. Solvents were used as received: benzene-h6, toluene-h8, CH3CN (all from Sigma, spectroscopic grade) and D2O (Euriso-Top, 99.9% D). 1-Phenalenone, PN, (Aldrich, 97%) was recrystallized from a 2:1 mixture of CH2Cl2 and CH3OH, and a water-soluble sulfonated phenalenone, PNS, was synthesized according to the method of Nonell et al.29 Benzo[cd]pyren-5-one, BP, was prepared and purified as previously described.30 1,3-Diphenylisobenzofuran, DPBF, (Aldrich) was recrystallized from benzene/ethanol under ambient light not absorbed by DPBF to yield yellow needles (mp 130−131 °C).

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RESULTS AND DISCUSSION 1. The Data. 1.1. O2(a1Δg) Phosphorescence Measurements. In experiments performed over the temperature range 10−70 °C, O2(a1Δ g) was produced upon pulsed-laser irradiation of a photosensitizer dissolved in a given solvent. The O2(a1Δg) thus produced was monitored by its O2(a1Δg) → O2(X3Σg−) phosphorescence at ∼1275 nm in time-resolved experiments. Data were recorded using four different solvents: D2O, acetonitrile, toluene, and benzene. The use of D2O instead of H2O allows us to capitalize on the fact that τΔ is greater in D2O than H2O, and this facilitates data analysis and reduces the error in our measurements. PNS was the sensitizer used in D2O, and this produces O2(a1Δg) with a quantum efficiency, ϕΔ, of 0.97 ± 0.06.31 In the other three solvents, PN was used as the sensitizer, and this compound produces O2(a1Δg) with an identical quantum efficiency of 0.98 ± 0.05.30,32 Selected control experiments were also performed in toluene using BP as a sensitizer, and this compound produces O2(a1Δg) with a quantum efficiency of 0.96 ± 0.05.30 Examples of the temperature-dependent O2(a1Δg) phosphorescence signals thus recorded are shown in Figure 1. Under these photosensitized conditions, relative values of the bimolecular rate constant for O2(a1Δg) radiative deactivation at a given temperature, kr(T), can be expressed as shown in eq 2 where IΔ(T) is the intensity of the 1275 nm O2(a1Δg) phosphorescence signal at the temperature T, κ is an instrumental parameter, EL is the incident laser fluence, and

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EXPERIMENTAL SECTION Time-resolved O2(a1Δg) phosphorescence measurements were performed upon pulsed-laser excitation of a photosensitizer using an approach and instrumentation that has previously been described.28 Data were recorded from air-saturated samples in a sealed, 1cm path length cuvette. The sealed cuvette ensures that solvent evaporation will not have an adverse influence over the time course of our experiments at higher temperatures. The cuvette was placed in a home-built holder through which temperaturecontrolled water was circulated. A Neslab RTE-101 warming/ cooling unit was used to control the water temperature. The temperature in the sample cuvette was continuously monitored by a platinum resistance thermometer immersed in the solvent being studied, and the samples were gently stirred during measurements using a magnetic stir bar. Recording the timeresolved O2(a1Δg) phosphorescence signal from a thermally equilibrated sample typically took 20−180 s. For a given measurement in a given solvent on a given day, five such measurements were independently recorded and then averaged. Depending on the solvent, analogous measurements were independently made 4−8 times on different days, and the results thus obtained were used to determine our standard deviation (see Supporting Information). In all cases, the

Figure 1. Examples of uncorrected PN-sensitized time-resolved O2(a1Δg) phosphorescence traces used to quantify the effect of temperature on kr. The data shown here were obtained in toluene at 20 °C (solid line) and at 60 °C (dashed line). 16228



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A is the absorbance of the sensitizer.15 IΔ can refer to either the intensity of the time-resolved phosphorescence signal at time = 0 or to the integral of the time-resolved trace normalized by τΔ.33 With respect to the latter, the O2(a1Δg) phosphorescent signal decay always followed first-order kinetics; thus, values of τΔ were readily obtained. k r(T ) =

n2589(temperature 1)/n2589(temperature 2) will be the same as the relative effect quantified by the ratio n21275(temperature 1)/ n21275(temperature 2). 1.4. Correction for a Temperature-Dependent Inner Filter Effect at 1275 nm. We next consider whether solvent absorption of the emitted light can influence a given measurement (i.e., the inner filter effect). The issue here is whether the solvent absorption at 1275 nm changes as a function of temperature. More explicitly, we need to ascertain whether, over the spectral bandwidth of the O2(a1Δg) → O2(X3Σg−) transition, the integrated solvent absorption appreciably changes with temperature. If it does change, we need to make the appropriate correction for the sample path length through which the emitted light is transmitted. Of the four solvents examined in the present study, we found that this issue of a temperature-dependent inner filter effect is pertinent only for D2O; the spectral profile of D2O around 1275 nm reflects the extent of “H”-bonding which, in turn, depends on temperature.37−39 As the temperature was increased over the range 20−60 °C, the pertinent transmittance of D2O over the spectral bandwidth of O2(a1Δg) emission decreased by 1.6% (see spectra in the Supporting Information). This change was factored into the values of κ in eq 2. 1.5. Possible Temperature-Dependent Change in the O2(a1Δg) Emission Spectrum. Although there is a solventdependent shift of the O2(a1Δg) phosphorescence spectrum, the magnitude of the shift is comparatively small over a wide range of different solvents.5,6,40,41 Thus, for experiments in which an interference filter is used to spectrally isolate O 2 (a 1 Δ g ) phosphorescence, a full-width-half-maximum (fwhm) band-pass of 50 nm for the filter is sufficient to ensure that light emitted over the entire bandwidth of the O2(a1Δg) phosphorescence spectrum is always transmitted through the filter, irrespective of the solvent-dependent shift.15,16 For our present experiments, we assumed that, over the limited temperature range studied, any analogous temperature-dependent shift in the O2(a1Δg) spectrum is likewise small and that we always collect light emitted over the entire bandwidth of O2(a1Δg) phosphorescence using a filter with a fwhm of ∼80 nm. This assumption was validated by the fact that, in an independent temperature-dependent control experiment, we recorded identical results using a long-pass filter to isolate O2(a1Δg) phosphorescence (cut-on at 1200 nm). 1.6. Correction for Temperature-Dependent Changes in the Sensitizer Absorbance. Another parameter in eq 2 that could possibly change as a function of the sample temperature is the absorbance, A, of the O2(a1Δg) sensitizer. In this regard, it is pertinent to note that for these time-resolved O2(a1Δg) phosphorescence measurements, a spectrally broad femtosecond laser was used as the excitation source.28 Likewise, for the DPBF bleaching study (vide inf ra), a corresponding spectrally broad (fwhm ≈ 10 nm) filtered output of a cw metal−halide lamp was used to irradiate the sensitizer. Given these irradiation conditions, a slight temperature-dependent change in the absorption spectrum of our sensitizer, along with corresponding changes in the concentration of the sensitizer (i.e., reflecting changes in the solvent density), could result in a net change of absorbed photons and be reflected in IΔ. Control experiments in which the absorption spectra of BP were recorded indicated the lack of a significant temperaturedependent change in the sensitizer absorbance integrated over the pertinent spectral range. However, corresponding experiments performed using PN indicated a ∼10% decrease in the

IΔ(T )n2 κϕΔ[S]E L(1 − 10−A)

(2)

Although not explicitly indicated in eq 2, it should be recognized that the solvent refractive index, n, and the concentration of the solvent, [S], also depend on the temperature, and appropriate values must be used for a given experiment. Likewise, temperature-dependent changes in parameters that contribute to the relative magnitude of κ (e.g., the solvent-mediated inner-filter effect) need to be considered. Details of the corrections pertinent to our study are provided in the sections below. 1.2. Correction for the Thermal Expansion of the Solvent. Including [S] in eq 2, as shown, allows us to express kr as a bimolecular rate constant with the units of s−1 M−1. Temperature-dependent changes in the solvent density, ρ, and hence in the solvent concentration, [S], were incorporated using published data as reproduced in our earlier study on the nonradiative deactivation of O2(a1Δg).7 Because dρ/dT is not necessarily constant (e.g., for D2O, the plot of ρ against T is not a linear function), corrections for [S] in eq 2 were made for each temperature examined using the actual data from the plot of ρ against T. 1.3. Correction for the Temperature-Dependent Change in the Solvent Refractive Index. The term n2 in eq 2 accounts for the fact that the O2(a1Δg) that is emitting is in a solvent of refractive index n, whereas the optical detector sits outside the sample cuvette and is surrounded by air.34 Implicit in the accurate implementation of eq 2 is that we use n measured at 1275 nm, the wavelength of the O2(a1Δg) → O2(X3Σg−) transition. However, to our knowledge, all previous studies of the effect of solvent on kr for the O2(a1Δg) → O2(X3Σg−) transition have employed the more readily accessible value of n measured at the sodium D line (i.e. ∼589 nm). The assumption in these cases has been that the relative effect as quantified by the ratio n2589(solvent 1)/n2589(solvent 2) will be the same as the relative effect quantified by the ratio n21275(solvent 1)/ n21275(solvent 2). For the present study, we first set out to ascertain whether the assumption mentioned above is indeed valid for data recorded at room temperature. For our current detector/ sample geometry, we looked at the effect of solvent on IΔ using a sensitizer where ϕΔ is always ∼1.0 (i.e., PN and PNS, vide supra) and then normalized the data in two independent ways; first using n2589(solvent 1)/n2589(solvent 2) and then using n21275(solvent 1)/n21275(solvent 2). We found that, irrespective of whether n589 or n1275 was used, we always obtained identical relative values of kr that reproduced the currently accepted solvent effects on kr at room temperature.5,6,11,13,15,16,18 For a temperature-dependent study, we are further constrained by the fact that we need accurate values of n recorded over the pertinent range of temperatures used in our experiments, and such values are only readily available for n recorded at 589 nm. Using established values of n589 obtained at each pertinent temperature,35,36 we assume that the corresponding relative effect as quantified by the ratio 16229



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spectrum, and as such, changes in the DPBF absorption spectrum can be used to quantify the amount of O2(a1Δg) present in the system.16,45−48 To optimize our accuracy with this approach, experiments were performed using a DPBF concentration of 1.2 × 10−2 M, thereby ensuring that we trap all of the O2(a1Δg) produced by BP (i.e., trapping of O2(a1Δg) by DPBF, krxn[DPBF] ≈ 1 × 107 s−1, clearly wins the kinetic competition against solvent mediated deactivation of O2(a1Δg), (τΔ)−1 ≈ 3.3 × 104 s−1). Because experiments were performed at such a high DPBF concentration, it was necessary to dilute our samples after the irradiation period just so that we could reduce the DPBF absorbance and accurately measure subtle changes in DPBF concentration. Experiments were performed under conditions where temperature- and reaction-dependent changes in the sample oxygen concentration had no effect. Data were corrected for temperature-dependent changes in BP absorption, and we verified that changes in DPBF concentration were only observed upon irradiation in the presence of BP. The data obtained indicate that ϕΔ for BP is independent of temperature over the range 20−60 °C in toluene (Figure 2). Because all subsequent temperature-dependent measurements of kr obtained using PN matched those using BP (vide inf ra), we conclude that ϕΔ for PN is likewise independent of temperature. Thus, the published statement43 that ϕΔ for PN decreases with an increase in temperature must be erroneous, and the data of these authors must, rather, reflect a temperature-dependent change in kr, as outlined below. 1.9. Temperature-Dependent Changes in kr. Experiments to obtain photosensitized values of IΔ were performed over a relatively wide temperature range. The data thus obtained were then corrected for the pertinent temperature-dependent parameters as outlined in our discussion above. For benzene, toluene, and CH3CN, the kr values thus obtained decreased with an increase in temperature (e.g., Figure 3). On the other hand, in D2O, kr increased with an increase in temperature. Although the magnitude of this latter change was comparatively small (Table 1), we were nevertheless able to consistently repeat this observation. To more clearly illustrate the temperature-dependent phenomenon, we present data in Table 1 simply in terms of the observed changes between room temperature (i.e., 20 °C) and a high-temperature domain. Data recorded in this way also facilitate the repetition of experiments that, in turn, allows us to reach a statistically significant threshold. As can be seen in Table 1, depending on the solvent, the temperature-dependent change in kr can indeed be appreciable. 2. Interpreting the Data. 2.1. A Multiple Parameter Model. It is overly simplistic, indeed naı̈ve, to think that the magnitude of kr in a given solvent depends on only one property of that solvent. Admittedly, one property may be more important than others. For example, in the Introduction, we mentioned that empirical correlations between isothermal values of kr obtained in a wide range of solvents correlate with the refractive index, n, of these solvents. These data thus point to the apparent importance of the solvent polarizability in perturbing the O2(a1Δg) → O2(X3Σg−) transition. In our earlier study on the effect of temperature on the nonradiative deactivation of O2(a1Δg), we addressed this issue in the form of a linear combination of different solvent properties.7 Carrying this perspective over to the present work on kr results in eq 3, where the respective importance of a given

integrated absorbance as the temperature was raised from 20 to 60 °C (see Supporting Information for the spectra and method of correction). Most importantly, making the appropriate correction in eq 2 for this temperature-dependent change in the PN absorbance yielded data that were identical to those independently recorded using BP. An analogous experiment indicated a ∼2.5% decrease in the absorbance of PNS in D2O. 1.7. Correction for Temperature-Dependent Changes in the O2(a1Δg) Lifetime. Under conditions in which the intensity of the O2(a1Δg) phosphorescence signal, IΔ, is obtained as the integral of the time-resolved O2(a1Δg) phosphorescence trace, it is necessary to normalize the data by the O2(a1Δg) lifetime, τΔ (vide supra). When IΔ is obtained by extrapolating the timeresolved O2(a1Δg) signal to t = 0, this extrapolation inherently accounts for τΔ. Data recorded from toluene, benzene, and acetonitrile were independent of the method used to obtain IΔ, thus confirming the expectations on this point. The time-resolved O2(a1Δg) traces recorded from D2O solutions, however, have a comparatively slow rising component reflecting a slower rate of O2(a1Δg) formation (see example in the Supporting Information). The latter is due to the lower oxygen concentration in air-saturated water and the corresponding slower rate of oxygen-dependent sensitizer deactivation.42 As a consequence, values of IΔ from D2O can only accurately be obtained by integrating the time-resolved O2(a1Δg) trace and then normalizing by τΔ values independently obtained using a kinetic fitting routine that also accounts for the rate of O2(a1Δg) formation.3 The temperature-dependent values of τΔ obtained and used in the present work were all consistent with data previously published.7 1.8. Correction for Possible Temperature-Dependent Change in the O2(a1Δg) Quantum Yield. A key aspect in the design of this study is the choice of BP and PN as sensitizers; both have solvent-independent values of ϕΔ ∼1.0 (vide supra).30,32 The question remains, however, as to whether these values of ϕΔ deviate from ∼1.0 as the temperature is changed. Indeed, there is a report that ϕΔ for PN decreases with an increase in temperature.43 However, this conclusion was obtained by assuming that kr does not change with temperature.43 Given the principal point of the present study on kr, this latter conclusion regarding PN is invalid, and it is incumbent upon us to independently ascertain whether ϕΔ for our chosen sensitizers is independent of a change in temperature. To avoid a cyclical argument about the effect of temperature on ϕΔ and kr, we need to quantify ϕΔ using an approach that does not involve the direct detection of O2(a1Δg) phosphorescence. To this end, we designed an experiment that uses DPBF to trap the O2(a1Δg) produced by the sensitizer and then used the resultant spectroscopic changes in DPBF as a measure of the amount of O2(a1Δg) produced. This test for ϕΔ was performed using BP because its spectroscopic properties ideally complement the pertinent spectra of DPBF and its oxygenated products. Experiments were performed in toluene in 1-cm path length cuvettes. The concentration of BP used (7.8 × 10−5 M) was such that the sample absorbance at the irradiation wavelength of 510 nm was 0.26. At this wavelength, DPBF is transparent, and light is absorbed only by BP. DPBF irreversibly reacts with O2(a1Δg) with a rate constant of ∼9 × 108 s−1 M−1.16,44 The resultant endoperoxide has a distinctly different absorption 16230



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Figure 3. Plot of relative kr values against the solvent temperature for BP-sensitized data recorded from toluene. The data are normalized against the kr value obtained at room temperature (dashed lines). Although the solid line is a linear fit to the data, the intent is only to serve as a guide for the eye.

For our present experiments and discussion, the rate constant krem refers only to the radiative deactivation channel. Note that, for all solvents examined, knr ≫ kr and the absolute magnitude of the sum knr + kr characterizes a process at the so-called preequilibrium limit (i.e., k−diff ≫ krem).7,49 As such, the following expression represents our system: kr = (kdiff /k−diff) krem. Within the context of this model, we first consider the possible effect of a temperature-dependent increase in the collision frequency between oxygen and M (i.e., increase in kdiff) combined with the possibility that krem could be an activated process7 and, as such, would likewise be favorably influenced by an increase in temperature. The net result would be an increase in the magnitude of kr with an increase in temperature. This is clearly not what is observed for three of the four solvents examined (benzene, toluene, and acetonitrile). We next consider the arguably more complicated effect of a temperature-dependent change in solution viscosity. It has previously been established that, for processes of O2(a1Δg) removal by an added quencher Q that occur at the preequilibrium limit, an increase in the viscosity of the surrounding medium causes an increase in the bimolecular rate constant for O2(a1Δg) removal.50,51 Admittedly, this effect is slight and was only observed at the limit of going from a liquid solution to glassy polymers. It was interpreted to reflect a viscositydependent increase in the number of collisions within the Q− O2(a1Δg) encounter complex, thereby facilitating krem at the expense of k−diff. Applying this argument to the present experiments could be somewhat tenuous since, in part, the temperature-dependent viscosity changes are not as great as those observed in the transition from a liquid to a glassy polymer. Nevertheless, if such a temperature-dependent viscosity change played a significant role in influencing the present data, we would expect to see a decrease in the magnitude of kr with an increase in temperature. This is indeed observed for three of the four solvents examined (benzene, toluene, and acetonitrile). However, the increase in kr with an increase in the temperature of D2O is difficult to accommodate in this model since, as with the other three solvents, the viscosity of D2O likewise decreases with an increase in temperature.52

Figure 2. (A) Absorption spectra of DPBF recorded as a function of the elapsed time of BP irradiation at 510 nm. Experiments were performed in toluene at 22 °C (solid lines) and 60 °C (dashed lines), and the arrow denotes spectra recorded as the elapsed irradiation time increased. (B) Normalized change in DPBF concentration plotted against the elapsed irradiation time of BP for the data recorded at 22 °C (open circles) and 60 °C (filled squares). This plot reflects the total amount of O2(a1Δg) produced as a function of time. The temperaturedependent differences in the rate of BP-sensitized DPBF bleaching (±1.2%) do not exceed the uncertainty in the value of ϕΔ for BP (ϕΔ = 0.96 ± 0.05).

parameter/property is embodied in the magnitudes of the coefficients a, b, c, etc. Temperature Effect on k r = a[Solvent Property #1] + b[Solvent Property #2] + c[Solvent Property #3] + ···

(3)

In the discussion that follows, we now consider selected parameters and properties of the solvent that might contribute to the observed temperature-dependent change in kr. 2.2. Possible Effects of Changes in Viscosity and Collision Frequency. For this discussion, we invoke a standard kinetic model to illustrate sequential events in the collision-dependent, solvent-mediated deactivation of O2(a1Δg) (Figure 4).7,49 The first step involves the diffusion-dependent encounter of O2(a1Δg) with a given solvent molecule M to form an encounter complex. Events that occur within this encounter complex then lead to the removal of O2(a1Δg) from the system. 16231



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Table 1. Temperature-Dependent Changes in the Solvent Refractive Index, n, the Solvent Concentration, [S], and the FullyCorrected Bimolecular Rate Constant for O2(a1Δg) Radiative Deactivation, kr solvent

ΔTa

n1b

n2b

[S]1c

[S]2c

D2O acetonitrile benzene toluene

40 40 40 40

1.328 1.344 1.501 1.496

1.323 1.326 1.475 1.473

55.2 19.1 11.3 9.4

54.5 18.3 10.7 9.0

[kr(1)−kr(2)]/kr(1)d 4.5 −1.8 −10.0 −10.7

± ± ± ±

3.9 2.5 6.8 1.4

T2 − T1 where T1 was always 20 °C and T2 was always 60 °C. bRefractive indices for the corresponding values of T1 and T2 using n recorded at 589 nm. cSolvent concentrations in mol L−1 where the numbers 1 and 2 correspond to T1 and T2. dThe numbers 1 and 2 correspond to T1 and T2, and the quotient shown has been multiplied by 100 to yield a percent change in the normalized value. a

decrease in n. Thus, the data obtained from these three solvents are consistent with the model that the extent to which O2(a1Δg) is perturbed scales with the electronic polarizability of the solvent. However, the data obtained from D2O are again not as straightforward. Although the temperature-dependent change in n for D2O is admittedly very small, nD2O nevertheless decreases slightly with an increase in temperature, as is the case with the other solvents examined (i.e., dn/dT is a negative number for D2O). Values of kr in D2O, however, increase with an increase in temperature. Thus, if the observed temperature effect on kr depended solely on the solvent polarizability, then our D2O data again point to an apparent inconsistency. 2.4. Considering the Molecular Parameter of “Polarizability Volume”. Carrying the discussion in the previous section further, it has also been shown that solvent-dependent values of kr recorded at room temperature correlate quite well with the molar refractivity.5,6,11−13 This parameter is readily obtained through the Lorenz−Lorentz formula in which the bulk polarizability is normalized by the solvent density ρ and, as such, focuses on the molecular property of polarizability volume, α.54 The latter would arguably be more pertinent with respect to a model of a 1:1 complex between a given solvent molecule M and O2(a1Δg). Thus, given the above-mentioned limitations of considering the bulk solvent polarizability, we need to consider if our kr data are better explained using the temperature dependence of the volume polarizability. Using published temperature-dependent values of both n and ρ, we calculated values of the volume polarizability α for our four solvents over the range of temperatures examined (see Figure 6, with further details in the Supporting Information). The results show that values of α vary only slightly as a function of temperature (e.g., ± 0.5%, at maximum, for toluene over the range 20 °C − 60 °C). This is, in fact, an expected conclusion based on work that has appeared over the years.55−57 We cannot discount this model on the sole basis that α changes only slightly with a change in temperature; we are unable to state how much of a change in α would be required to see the corresponding change in kr. On the other hand, we find that α systematically increases with an increase in temperature in toluene, benzene, and acetonitrile, whereas α decreases with an increase in temperature in D2O. These changes go against what is expected for the perturbation of O2(a1Δg) by M as manifested in the temperature-dependent values of kr. Thus, on the basis of this latter observation, it certainly appears that it is not appropriate to use the polarizability volume in the model to account for the perturbation of O2(a1Δg) by M. If this last statement is indeed true, then the observed isothermal correlation of kr with molar refractivity5,6,11,13 may just be a fortuitous extension of a more meaningful and

Figure 4. Kinetic scheme for the deactivation of O2(a1Δg) by a solvent molecule M.

Thus, it appears that we need to consider other factors in interpreting our kr data. 2.3. Perspective Based on Solvent Electronic Polarizability. In previous room temperature studies of the effect of solvent on kr, the kr values thus obtained were shown to correlate well either with the refractive index of the solvent, n, or specific functions of the solvent refractive index (e.g., (n2 − 1)/(n2 + 2)).5,6,11−13,15,16,18,53 Because kr increases with an increase in n, these correlations suggest that increasing the optical (i.e., electronic) polarizability of the solvent plays an important role in increasing the extent to which oxygen is perturbed and the otherwise forbidden O2(a1Δg) → O2(X3Σg−) transition is promoted.5,6 If the magnitude of kr indeed scales according to the electronic polarizability of the solvent, as reflected in the magnitude of n, then it is incumbent upon us to see if the temperature-dependent changes in kr correlate with the temperature-dependent changes in n. To this end, we have plotted values of [kr(T1) − kr(T2)]/kr(T1) against dn/dT for our present data recorded from four solvents (Figure 5). Upon increasing the temperature in benzene, toluene and acetonitrile, the decrease in kr is indeed accompanied by a

Figure 5. Plot of [kr(T1) − kr(T2)]/kr(T1) against -dn/dT for the four solvents studied. In Table 1, the corresponding numbers on the y-axis have been multiplied by 100 to yield a percent change in the normalized value of kr. 16232



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Temperature Effect on k r = a[Solvent Polarization Dependent Perturbation] + b[Oxygen Polarization Dependent Perturbation] + c[H‐Bonding Effect in Water] + ···

(4)

2.7. An Ensemble of Solvent Molecules is Better. Considering all aspects of the preceding discussion, it seems that our temperature-dependent data are best explained using a model through which the perturbation of O2(a1Δg) is achieved by a collection of solvent molecules M. The available data are simply not consistent with a model in which the perturbation occurs solely through a 1:1 complex between M and O2(a1Δg). This ensemble-based model is illustrated in Figure 7. The key aspect of this model is that O2(a1Δg) “sees” solvent molecules Figure 6. Plots of relative changes in the volume polarizability, α, as a function of temperature for three of the four solvents used: acetonitrile (ACN), toluene (TOL), and D2O. The plot for benzene is very similar to that for toluene. The data are normalized to the value of α at 20 °C. The dashed line is a guide for the eye and indicates what would be observed if α was temperature independent.

appropriate correlation of kr with the bulk polarizability. Indeed, mechanistic conclusions that have been drawn using a model based on the polarizability volume5,6,19 can equally be drawn using a model based on the bulk polarizability. In any event, the data shown in Figure 5 indicate that, thus far, a model based on the bulk polarizability appears to best account for our temperature-dependent data. We carry this point further in the following sections. 2.5. Likely Contribution of H-Bonding Effects. It is wellestablished that, for water, changes in temperature alter the extent to which hydrogen-bonding plays a role in defining the system.37−39 As such, for our experiments in D2O, it is quite likely that “H”-bonding effects could play a role in influencing the magnitude of kr. Indeed, with an increase in temperature, it is expected that intermolecular D2O−D2O “H” bonding will become less pronounced,37−39 thus possibly making an individual D2O molecule a more effective perturber of a solute oxygen molecule. In this way, we can rationalize an increase in the magnitude of kr with an increase in the D2O temperature, despite the corresponding temperature-dependent decrease in the solvent polarizability as manifested in n. 2.6. Returning to the Multiparameter Model. We now return to the model expressed in eq 3 where the magnitude of kr in a given solvent is presumed to depend on a number of different parameters. Although the overall temperature dependent change in kr may be principally driven by one property of the solvent (e.g., the electronic polarizability), other factors must play a role. We have indicated that, in water, the extent to which H-bonding determines water−water interactions could influence the water−oxygen interaction. In an analogous way, temperature-dependent changes in London dispersion interactions in a solvent such as toluene could likewise influence the extent to which oxygen is perturbed. Finally, it is reasonable to consider that the temperature-dependent polarizability of both the O2(a1Δg) and O2(X3Σg−) states must also contribute to the solvent−oxygen interaction.58 Thus, as shown in eq 4, we can now be a bit more explicit with respect to the terms in our linear combination.

Figure 7. Attempt to illustrate the fact that the perturbation of solvated oxygen is best interpreted by considering an ensemble of interacting solvent molecules M rather than a single molecule M in a 1:1 M−O2 complex.

that interact with each other. These M−M interactions thus account for (1) a better correlation with the bulk electronic polarizability as opposed to the polarizability volume, as shown in Figures 5 and 6, and (2) H-bonding interactions between M molecules. This model is also consistent with the kinetic scheme shown in Figure 4; because we are at the so-called preequilibrium limit, multiple M−M and M−O2(a1Δg) collisions within the solvent cage provide an “averaging effect” that allows us to think more in terms of bulk properties. The ensemble-based model illustrated in Figure 7 is also consistent with independent ab initio calculations that model the effect of solvent on spectroscopic transitions of a solute, including those that involve O2(a1Δg).59−61 These calculations specifically show that modeling the solvent perturbation through a 1:1 complex does not accurately represent experimental data. Rather, one also needs to consider a bulk solvent effect (e.g., a dielectric continuum or a molecularmechanics-based representation of longer range solvent perturbations). Further confirmation that the correlation of kr with the bulk solvent electronic polarizability is the most accurate way to envision the perturbation of O2(a1Δg) by M is found in an experiment in which O2(a1Δg) phosphorescence was used to quantify ϕΔ for a sensitizer in a glassy polymer.33 In this study, the correlation between kr and n for a large number of liquid solvents was used to estimate the expected kr for a glassy polymer of a known n. This value of kr for the polymer was then used to normalize O2(a1Δg) phosphorescence data acquired from the polymer to yield a value of ϕΔ. Most 16233



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(4) Cló, E.; Snyder, J. W.; Ogilby, P. R.; Gothelf, K. V. Control and Selectivity of Photosensitized Singlet Oxygen Production: Challenges in Complex Biological Systems. ChemBioChem 2007, 8, 475−481. (5) Schweitzer, C.; Schmidt, R. Physical Mechanisms of Generation and Deactivation of Singlet Oxygen. Chem. Rev. 2003, 103, 1685− 1757. (6) Ogilby, P. R. Solvent Effects on the Radiative Transitions of Singlet Oxygen. Acc. Chem. Res. 1999, 32, 512−519. (7) Jensen, R. L.; Arnbjerg, J.; Ogilby, P. R. Temperature Effects on the Solvent-Dependent Deactivation of Singlet Oxygen. J. Am. Chem. Soc. 2010, 132, 8098−8105. (8) Minaev, B. F. Solvent-Induced Emission of Molecular a1Δg Oxygen. J. Mol. Struct. (THEOCHEM) 1989, 183, 207−214. (9) 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. (10) 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. (11) Hild, M.; Schmidt, R. The Mechanism of the Collision-Induced Enhancement of the a1Δg → X3Σg− and b1Σg+ → a1Δg Radiative Transitions of O2. J. Phys. Chem. A. 1999, 103, 6091−6096. (12) 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. (13) Schmidt, R.; Shafii, F.; Hild, M. The Mechanism of the Solvent Perturbation of the a1Δg → X3Σg− Radiative Transition of O2. J. Phys. Chem. A. 1999, 103, 2599−2605. (14) Minaev, B. F.; Mikkelsen, K. V.; Ågren, H. Collision-Induced Electronic Transitions in Complexes between Benzene and Molecular Oxygen. Chem. Phys. 1997, 220, 79−94. (15) 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. (16) 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. (17) 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. (18) Poulsen, T. D.; Ogilby, P. R.; Mikkelsen, K. V. Solvent Effects on the O2(a1Δg) → O2(X3Σg−) Radiative Transition: Comments Regarding Charge-Transfer Interactions. J. Phys. Chem. A 1998, 102, 9829−9832. (19) Dzhagarov, B. M.; Jarnikova, E. S.; Stasheuski, A. S.; Galievsky, V. A.; Parkhat, M. V. Effect of Medium Dielectric Properties on Spontaneous Emission of Molecular Singlet Oxygen. J. Appl. Spectrosc. 2013, 79, 861−867. (20) Pimenta, F. M.; Jensen, R. L.; Holmegaard, L.; Esipova, T. V.; Westberg, M.; Breitenbach, T.; Ogilby, P. R. Singlet-Oxygen-Mediated Cell Death Using Spatially Localized Two-Photon Excitation of an Extracellular Sensitizer. J. Phys. Chem. B 2012, 116, 10234−10246. (21) Silva, E. F. F.; Pedersen, B. W.; Breitenbach, T.; Toftegaard, R.; Kuimova, M. K.; Arnaut, L. G.; Ogilby, P. R. Irradiation- and Sensitizer-Dependent Changes in the Lifetime of Intracellular Singlet Oxygen Produced in a Photosenstized Process. J. Phys. Chem. B. 2012, 116, 445−461. (22) Abdel-Shafi, A. A.; Worrall, D. R. Photosensitized Production of Singlet Oxygen and Factors Governing its Decay in Xenon and Carbon Dioxide Supercritical Fluids. J. Photochem. Photobiol. A. 2007, 186, 263−269. (23) Worrall, D. R.; Abdel-Shafi, A. A.; Wilkinson, F. Factors Affecting the Rate of Decay of the First Excited Singlet State of Molecular Oxygen O2(a1Δg) in Supercritical Fluid Carbon Dioxide. J. Phys. Chem. A 2001, 105, 1270−1276. (24) van Houten, J.; Watts, R. J. Temperature Dependence of the Photophysical and Photochemical Properties of the Tris(2,2′-

importantly, an independent chemical trapping experiment that did not involve the detection of O2(a1Δg) phosphorescence was used to validate the value of ϕΔ thus obtained for the polymer. This experiment is thus particularly informative in that the correlation of kr with n is valid in solvents as disparate as a liquid and a glassy polymer; changes in solvent viscosity cannot play a significant role in influencing kr. Given the ensemble-based model shown in Figure 7, experiments on kr for the O2(a1Δg) → O2(X3Σg−) transition performed as a function of both temperature and pressure in Xe or CO2 supercritical fluids could provide interesting and useful further insight.22,23

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CONCLUSIONS Experiments have been performed to indicate that the solventspecific radiative rate constant for the transition O2(a1Δg) → O2(X3Σg−) can depend significantly on temperature. This observation is unique in that, to our knowledge, there is little precedence for temperature-dependent changes in radiative rate constants. Although our results can have important practical ramifications for a wide range of experiments that rely on O2(a1Δg) → O2(X3Σg−) phosphorescence, particularly those that use the phosphorescence intensity to quantify relative yields of O2(a1Δg) production, our data are arguably more significant with respect to developing a better model for the mechanism by which solvent perturbs O2(a1Δg). Specifically, we conclude that a model based on a 1:1 complex between O2(a1Δg) and a solvent molecule M does not accurately represent the perturbing interaction. Rather, one must consider an ensemble of mutually interacting molecules M that surround O2(a1Δg).

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ASSOCIATED CONTENT

* Supporting Information S

Temperature-dependent solvent properties; temperature-dependent near IR absorption spectra for D2O; temperaturedependent absorption spectra for BP and PN in the solvents studied; details of the corrections used to obtain values of kr; results of individual experiments used to obtain average values of kr. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions ‡

R.L.J. and L.H. contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Danish National Research Foundation. REFERENCES

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