Time-Resolved Detection of Magnetic Field Effects on Radical Pairs in

Aug 6, 2015 - magnetic field effects (MFEs) on radical pairs (RPs). In the photoinduced hydrogen abstraction reaction of benzophenone (BP) in sodium ...
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Time-Resolved Detection of Magnetic Field Effects on Radical Pairs in Micelles: Two-Step Two-Laser Fluorescence Spectroscopy of Transient Radicals Tomoaki Yago, Ayuto Takashino, and Masanobu Wakasa* Department of Chemistry, Graduate School of Science and Engineering, Saitama University, 255 Shimo-ohkubo, Sakura-ku, Saitama-shi, Saitama 338-8570, Japan

ABSTRACT: A two-step two-laser fluorescence spectroscopy method was employed to enable time-resolved detection of magnetic field effects (MFEs) on radical pairs (RPs). In the photoinduced hydrogen abstraction reaction of benzophenone (BP) in sodium dodecyl sulfate (SDS) micellar solution, fluorescence from the BP ketyl radical (BPH•) was observed under various magnetic fields; BPH• forms RPs with hydrogen-abstracted SDS radicals (•SDS) in the micelles. Kinetic parameters of the RP dynamics such as the spin relaxation rate, the generation rate, and the escape rate were determined from the simple analysis. The MFEs on BPH• observed from the fluorescence measurements were explained by the spin relaxation mechanism proposed by Hayashi and Nagakura. In this study, we demonstrate that two-step two-laser fluorescence spectroscopy in combination with a magnetic field provides valuable information about photochemical reactions in which RPs play important roles.

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liquids.15,16 Transient absorption spectroscopy, in which the absorption of transient radicals can be observed with high time resolution, is surely the first choice for the direct observation of RP dynamics under magnetic fields. In transient absorption measurements, however, the absorption of the photoexcited states, which are precursors of the radicals, is often overlapped with the absorption of the radicals. In such situations, it is difficult to distinguish the RP dynamics from the excited-state ones. To measure complete RP dynamics, it is necessary to choose an adequate photochemical reaction in which the absorption of the precursor states dose not overlap with that of the radicals. To overcome the above limitation of transient absorption spectroscopy, a two-step two-laser fluorescence spectroscopy is most convenient, in which radicals generated by photochemical reactions are observed by measuring the fluorescence of their photoexcited states. This technique has been utilized to develop new chemical processes and to identify intermediates in complex photochemical reactions.17−20 Ito et al. reported two-step two-laser fluorescence spectra of the tautomer produced by intramolecular proton transfer in 7-hydroxyquinoline.19 The rise and decay of fluorescence were analyzed to clarify the mechanism of the complex photochemical reaction.

INTRODUCTION Radicals and radical pairs (RPs) are common short-lived intermediates in various photochemical reactions. A magnetic field can alter the reactivity of a RP, thereby affecting the yields of photochemical products. A unique aspect of such magnetic field effects (MFEs) on RPs is that the magnetic field can change the rate of RP reactions that proceed via the activated states of the reactions, although the magnetic energy of the RP is much smaller than the thermal energy. For this reason, MFEs on photochemical reactions involving RPs have attracted considerable attentions since the mid 1970s and have been studied by various quantitative measurements such as product analysis, steady-state and transient absorption spectroscopy, and fluorescence spectroscopy.1−4 The mechanisms of MFEs including the hyperfine coupling mechanism, the Δg mechanism, the level-crossing mechanism, the triplet mechanism, the spin relaxation mechanism, and low-field effects have been well established by reliable experimental measurements and through the development of theory of spin dynamics, which are also associated with the generation of chemically induced magnetic polarizations.1,4 It has been suggested and demonstrated that RP dynamics in the absence and presence of magnetic fields are rich in information not only regarding the mechanisms of MFEs5−7 but also regarding spatial RP motions in various media such as uniform solutions,8,9 micelles,10−13 proteins,14 and ionic © 2015 American Chemical Society

Received: August 3, 2015 Published: August 6, 2015 20217

DOI: 10.1021/acs.jpcc.5b07524 J. Phys. Chem. C 2015, 119, 20217−20223

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1.7 T were provided by a TOKIN SEE-10W electromagnet. The applied magnetic fields were measured with a Lake-Shore Model 425 gauss meter placed immediately adjacent to the quartz sample cell. Benzophenone (BP, Kanto Kagaku) was recrystallized from methanol. Sodium dodecyl sulfate (SDS, Tokyo Kasei) was recrystallized from a 1:1 (v/v) mixture of methanol and ethanol. Deionized water was used as a solvent. The concentrations of BP and SDS in aqueous micellar solutions used were 6 × 10−4 and 8 × 10−2 mol dm−3, respectively. The sample solution was deoxygenated by bubbling with nitrogen gas and was pumped through the quartz sample cell. All measurements were performed at 298 K.

Wasielewski et al. showed that the charge generated by a photoinduced electron-transfer reaction can be transferred to a neighboring molecule by irradiation with a second laser pulse.20 Majima et al. reported a series of two-step two-laser excitation studies on carbonyl compounds. In those reports, highly excited states of the carbonyl compounds and the excited states of the generated radicals were examined.21−25 Recently, we constructed a two-step two-laser fluorescence measurement system with an electromagnet to observe RP dynamics directly in the presence of various magnetic fields. In our two-step two-laser fluorescence measurement system, the first laser pulse (266 nm) triggers the photochemical reaction and generates intermediate radicals. The subsequent second laser pulse (532 nm) excites the radicals, and the resultant fluorescence from the excited state of the radicals can be detected. Tanimoto et al. first applied two-step two-laser fluorescence measurements to MFE studies.26−28 However, they did not observe fluorescence directly from an RP but from recombination products or escaped products. Thus, the generation dynamics of the RP in that study could not be obtained. When the rate constant for the generation of an RP is comparable with the rate constant for the RP’s decay, an analysis that includes the generation process of the RP is needed to clarify RP dynamics. In the present study, to clarify the RP dynamics in detail, the hydrogen abstraction reaction of benzophenone (BP) in sodium dodecyl sulfate (SDS) micellar solutions was studied by means of two-step two-laser fluorescence spectroscopy and MFEs measurements. This reaction, which generated RPs of BP ketyl radicals (BPH•) and hydrogen-abstracted SDS radicals (•SDS), is a representative photochemical reaction that exhibit extremely large MFEs; the MFE of this particular photochemical reaction has been extensively studied by transient absorption spectroscopy.29−31 In the transient absorption spectra, however, the absorption of BPH• is seriously overlapped by the triplet−triplet absorption of BP. Therefore, the complete RP dynamics have not yet been fully elucidated for this reaction. In the present study, the time profiles of the yield of the RPs were obtained by monitoring the fluorescence from BPH• using two-step two-laser fluorescence spectroscopy. The results were analyzed by a simple kinetic model in which two distinct RP decays from T0 and T±1 were considered. Our analysis revealed that the observed MFEs are consistent with the relaxation mechanism proposed by Hayashi and Nagakura.32 The kinetic parameters of the RP, such as the rate constants for spin relaxation, generation and escape, were determined by fitting the complete time profiles of RP dynamics obtained from the fluorescence measurements.

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RESULTS AND DISCUSSION Reaction Scheme. The primary photochemical reactions of BP in the SDS micellar solution during the two-step two-laser fluorescence measurements are summarized in Figure 1. Most

Figure 1. Reaction scheme for the photochemical reaction of benzophenone (BP) in sodium dodecyl sulfate (SDS) micellar solutions. The RP states in which the two radicals interact within an SDS micelle are illustrated in the black-outlined box.

of BP molecules are situated in the micelles by means of hydrophobic interactions.34,35 Upon irradiation of the first laser pulse, BP is excited to its excited singlet state (1BP*). 1BP* is converted to the excited triplet state (3BP*) by fast intersystem crossing. 3BP* abstracts a hydrogen atom from an SDS molecule, forming an RP consisting of a BP ketyl radical (BPH•) and a hydrogen-abstracted SDS radical (•SDS). In the present system, the RP is born in the triplet spin state (3(BPH• •SDS)). In Figure 1, the RP states in which the two radicals interact within an SDS micelle are illustrated in the blackoutlined box. During the RP’s lifetime, spin conversion occurs within the RP, depending on the nature of magnetic interactions, such as exchange interactions, hyperfine interactions, dipole−dipole interactions, and g-values in combination with Zeeman splitting. Thus, magnetic fields (B) influence the rate of spin conversion, generating a MFE on the RP. The singlet RP (1(BPH• •SDS)) reacts and gives recombination products. Both BPH• and •SDS can depart from the micelle, yielding escaped radicals from 1,3(BPH• •SDS). The second laser pulse excites BPH•, and the resultant fluorescence can be observed. The time dependence of the fluorescence intensity is interpreted by the mixed dynamics of the RPs and the escaped radicals. Transient Absorption and Fluorescence Spectra of Benzophenone Ketyl Radical. Time profiles of the transient absorption were measured in the wavelength range of 350−650 nm. Figure 2 shows the transient absorption spectra obtained at delay times of 0 ns, 200 ns, 500 ns, and 1 μs after the first laser irradiation. Here the second laser (for fluorescence measurement) was not applied. A transient absorption peak due to the triplet−triplet (T-T) absorption of 3BP* was observed at 520−

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EXPERIMENTAL SECTION A two-step two-laser fluorescence measurement system was developed on the basis of the laser flash photolysis apparatus described elsewhere.33 The fourth harmonic (266 nm) of a nanosecond Nd:YAG laser (Quanta-Ray, INDI; 7 ns fwhm) was used to initiate photochemical reactions. The second harmonic (532 nm) of a nanosecond Nd:YAG laser (QuantaRay GCR-130; 6 ns fwhm) was used to induce fluorescence from the generated radicals. The two lasers were synchronized by using delay generators (Stanford Research Systems, DG535 and DG645), and the laser beams were coaxially guided to a quartz sample cell. The fluorescence from the radicals was recorded by a LeCroy WavePro 960 digitizing oscilloscope with a Hamamatsu R636 photomultiplier. Magnetic fields of up to 20218

DOI: 10.1021/acs.jpcc.5b07524 J. Phys. Chem. C 2015, 119, 20217−20223

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Figure 4 shows the time profiles of the transient absorption (A(t)) observed at 550 nm in the absence and presence of

Figure 2. Transient absorption spectra observed at delay times of 0 ns (red circles), 200 ns (green circles), 500 ns (blue circles), and 1 μs (purple circles) after the laser excitation (266 nm) of SDS (8 × 10−2 mol dm−3) micellar solution containing benzophenone (6 × 10−4 mol dm−3).

Figure 4. Time profiles of transient absorption observed at 550 nm in SDS (8 × 10−2 mol dm−3) micellar solution containing BP (6 × 10−4 mol dm−3) in the absence (red line) and presence of magnetic fields of 0.05 T (blue line), 0.2 T (green line), and 1.7 T (black line).

530 nm.36 Following the disappearance of the T-T absorption, transient absorption attributed to BPH• is expected to be observed at 540−550 nm.30 Since the absorptions of 3BP* and BPH• are overlapped, the dynamics of BPH• dose not appear immediately in the transient absorption measurements. Next, the fluorescence spectrum of BPH• was observed in the wavelength range of 470−700 nm by means of the two-step two-laser fluorescence measurement system. Here, the second laser pulse, with a wavelength of 532 nm, was applied at various delay times (t) of 0−10 μs after the first laser pulse. Since the lifetime of the excited state of BPH• is within the laser pulse length,23 the integrated fluorescence intensity (I(t)) observed at a delay time t is proportional to the yield of BPH• (Y(t)). In Figure 3, the I(0.3 μs) values are plotted against the observed

magnetic fields. In the present photochemical reaction, the A(t) curves have fast (0 < t ≤ 1.0 μs) and slow (1.0 μs < t) decay components. The former mainly corresponds to the decay of the triplet and the latter to the decay of BPH•. As was reported previously, the yield of escaped BPH• is dramatically increased by the application of magnetic fields due to magnetic field dependent spin relaxation.29−31 The MFEs observed by transient absorption and two-step two-laser fluorescence measurements were compared at various delay times from the first laser pulse. Figure 5 shows the relative MFEs on the yield of BPH• observed by transient absorption (R(B) = Y(B)/Y(0 T) = A(B)/A(0 T)) and fluorescence measurements (R(B) = Y(B)/Y(0 T) = I(B)/I(0 T)). The MFEs observed by transient absorption were always underestimated, except at the delay time of 2.5 μs, because the absorption of 3BP* overlaps with that of BPH• at 550 nm and 3 BP* shows no MFE. At a delay time of 2.5 μs, the MFEs observed by transient absorption were almost the same as those observed by fluorescence measurements. The lifetime of 3BP* was estimated to be 400 ns from the analysis of RP dynamics (see next section). At a delay time of 2.5 μs, therefore, almost all of 3BP* is quenched. Thus, we concluded that one can directly evaluate MFEs generated in the hydrogen abstraction reaction of BP in SDS micellar solution using two-step twolaser fluorescence measurements. In contrast, as shown in Figure 5, transient absorption measurements failed to evaluate MFEs at earlier times (≤2 μs) owing to absorption of the precursor state. Time Profile of the Yield of the Radical Detected by Two-Step Two-Laser Fluorescence Measurements. Time profiles of the yield of BPH• (Y(t)) were evaluated by means of the two-step two-laser fluorescence measurements. Since the integrated fluorescence intensity (I(t)) is proportional to the yield of BPH•, I(t) observed at 600 nm is used to discuss the yield of BPH•. The I(t) curves observed for 0, 0.05, 0.2, and 1.7 T are shown in Figure 6. For each magnetic field, the rise and decay of BPH• are clearly observed. At 0 T, BPH• quickly decays owing to geminate recombination in the micelle. Applications of the magnetic fields decelerated the geminate recombination and drastically increased the yield of escaped BPH•. Though MFEs on BP in SDS micellar solutions were reported 30 years ago,29−31 to the best of our knowledge, this

Figure 3. Fluorescence spectrum of benzophenone kety radical in the SDS micellar solution obtained by two-step two-laser fluorescence measurements. The hydrogen abstraction reaction occurred by the first laser pulse (266 nm), generating benzophenone ketyl radical (BPH•). The second laser pulse (532 nm) at the delay time of 0.3 μs after the first laser pulse excited BPH•, generating fluorescence from the excited state of BPH•.

wavelength. This figure shows the fluorescence spectrum obtained by two-step two-laser excitation of BP in SDS micellar solution at a delay time of 0.3 μs. From the peak wavelength of 600 nm and the spectral shape,17,23 the observed fluorescence spectrum can be safely assigned to fluorescence from BPH• only. In the following experiments, I(t) observed at 600 nm was used to discuss the yield of BPH• (Y(t)) in various magnetic fields. MFE on the Yield of Benzophenone Ketyl Radical. The MFE on the yield of BPH• was evaluated by means of transient absorption and two-step two-laser fluorescence measurements. 20219

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Figure 5. Relative MFEs of the yield of BPH•, R(B) = Y(B T)/Y(0 T), evaluated by the transient absorption observed at 550 nm (blue circles) and by the fluorescence at 600 nm (red circles) with the various delay times from the first laser pulse. 3

kHA

BP* + SDS ⎯⎯→ 3(BPH • •SDS)

(1)

(BPH • •SDS) ⇄ 1(BPH • •SDS)

(2)

3

1,3

kesc

(BPH • •SDS) ⎯→ ⎯ BPH • + • SDS

1

k rec

(BPH • •SDS) ⎯→ ⎯ recombination products

(3) (4)

By hydrogen abstraction of 3BP* from SDS, the triplet RP (BPH• •SDS) is produced in the micelle with a rate constant of kHA (eq 1). For the generation of the MFE, the diffusion from close RP to separated RP generally plays an important role. In the present photochemical reaction, the lifetime of the RP is on the order of hundred nanoseconds, while the time of the diffusion from the close RP to the separated RP is estimated to be ∼20 ns from the radius (∼2 nm) and the viscosity (∼20 cP) of the micelle. This diffusion process is much faster than the other kinetics of the RP such as escape and recombination rates. Thus, the diffusion process of RP in the micelle is not readily observed in the RP dynamics measured here. The triplet RPs are converted to the singlet RP 1(BPH• •SDS) by the magnetic interactions (eq 2) and this process is affected by the magnetic fields. Some of BPH• or •SDS radicals, or both, escape from the micelle with a rate constant of kesc (eq 3). BPH• in the singlet RP decays with a rate constant of krec owing to geminate recombination in the micelle (eq 4). Figure 7 shows the kinetic scheme of RP used in the analysis. The 3

Figure 6. Time profiles of the yield of BPH• observed at 600 nm by two-step two-laser fluorescence measurements of the hydrogen abstraction reaction of BP (6 × 10−4 mol dm−3) in SDS (8 × 10−2 mol dm−3) micellar solution at 0 T (red circles), 0.05 T (blue circles), 0.2 T (green circles), and 1.7 T (black circles). Solid lines indicate the time dependence of the concentrations of BPH• calculated by eqs 5−9. The parameters used in the calculations are listed in Table 1. In the calculation, initial concentration of the excited triplet state of BP ([3BP0*]) is set to be 1 for simplicity.

study provides the first observation of the complete time profile of the yield of BPH• in magnetic fields. The time dependence of the MFEs observed in the present study was analyzed by fitting the decay of the transient absorption signal with multiexponential functions. We observed both the rise and decay of Y(t). Since the rise and decay of Y(t) overlapped, the magnetic field also would have affected the rise component of Y(t), suggesting that analysis of only the decay components of Y(t) is not sufficient for qualitative analysis of RP dynamics. The two-step two-laser fluorescence measurements enable us to analyze RP dynamics in detail in the present photochemical reaction, in which the rate of radical generation is comparable with the rate of radical decay and the transient absorption bands corresponding to radical generation and decay are overlapping. To analyze the time profiles of the yield of BPH•, the following reaction scheme is considered:

Figure 7. Schematic diagram of spin relaxation pathways for the singlet (S) and triplet (T+1, T0, T−1) states of radical pair and rate constants for the concerning states. 20220

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analysis of RP dynamics in the transient absorption study. However, the two-step two-laser fluorescence measurements performed here provide full RP dynamics, and one can analyze RP dynamics in detail by means of this method. In addition to the above conclusion, we also found that even in the absence of the magnetic field, the use of the different kr and kST0 give the better fitting results. It has been assumed that the three triplet spin states are degenerate and kST0 = kr in the absence of the magnetic field. In the analysis, on the other hand, we used the values of kST0 = 1.5 × 107 s−1 and kr = 2.5 × 106 s−1 in the absence of the magnetic field. This suggests that the dipole− dipole coupling gives the energy gap between the T±1 and T0 states and also between the T±1 and S states in the SDS micellar solution. The high viscosity in the SDS micelle suppresses the RP rotation and prevents the triplet state from averaging of dipole−dipole interaction. The three triplet states are not degenerated in the absence of the magnetic field and the different kr and kST0 values are presented. The parameters estimated from the fitting are listed in Table 1. Kitahama et al. reported the kinetic parameters for the same

scheme was originally proposed by Hayashi and Nagakura to account the MFE due to the spin relaxation mechanism.32 Initially the T±1 and T0 states are populated by the hydrogen abstraction reaction from the photoexcited triplet state. RPs in T±1 states interconvert to the RPs in T0 and S states with a rate constant of kr. The kr value is dependent on the magnetic field and is the origin of MFE. Here we assume that kr for the T±1−S transitions is the same with kr for the T±1−T0 transitions. RPs in S and T0 states interconvert with a rate constant of kST0. Since the small contribution of the Δg effects to the RR dynamics in the present photochemical reaction, the kST0 value is assumed to be independent of the magnetic field. From the kinetic scheme in Figure 7, the following differential equations can be obtained for the concentrations of T±1 state ([T±1]), T0 state ([T0]), singlet state ([S]), and escaped free radicals ([FR]): d[T±1] dt

= −(4k r + 2kesc)[T±1] + 2k r[T0] + 2k r[S] +

2 kHA e−kHAt 3

(5)

Table 1. Parameters Used for Fitting of Time Profiles of Fluorescence Intensities Obtained by Two-Step Two-Laser Fluorescence Measurements: Hydrogen Abstraction Reaction Rate (kHA), Escape Rate from Micelle (kesc), Recombination Reaction Rate for Singlet Radical Pair (krec), S-T0 Mixing Rate (kST0), and Spin Relaxation Rate (kr) in Radical Pair

d[T0] = 2k r[T±1] − (k ST0 + 2k r + kesc)[T0] + k ST0[S] dt 1 + kHA e−kHAt (6) 3 d[S] = 2k r[T±1] + k ST0[T0] − (2k r + k ST0 + kesc + k rec) dt [S]

d[FR] = 2kesc[T±1] + kesc[T0] + kesc[S] dt

(7)

(8)

The above differential equations were numerically solved by using the Runge−Kutta method. The time profiles (C(t)) of the concentration of BPH• were obtained by the summation of the time profile of each state C(t ) = [T±] + [T0] + [S] + [FR]

B/T

kHA/s−1

0 0.05 0.1 0.2 0.5 1.7

2.5 × 10

kesc/s−1 6

krec/s−1

1.2 × 10

5

kST0/ s−1

1.5 × 10

7

1.5 × 10

7

kr/s−1 2.5 5.5 3.5 2.2 1.2 7.5

× × × × × ×

106 105 105 105 105 104

reaction using optically detected EPR with a pulsed microwave.37 The kesc and krec values determined in the present study are consistent with their reported values (kesc = 1.3 × 105 s−1 and krec = 1.9 × 107 s−1), demonstrating the validity of the fitting analysis in the present study. The kHA value determined in the present study is somewhat different from the value (kHA = 5 × 106 s−1) reported from optically detected EPR. Since we directly observed the fluorescence from BPH•, we believed that the kHA value determined in the present study should be closer to the true value. The magnetic field dependence of kr estimated from the analysis is plotted in Figure 8. The kr values steeply decrease with increasing B in the range of 0 < B ≤ 0.2 T, but at higher fields, change of the value becomes gradually. Here we attempt to fit part of the experimental data using the longitudinal spin relaxation rate (1/T1), which is generally accepted as a spin relaxation rate associated with the anisotropy (δA) of the hyper fine interaction:2

(9)

The experimentally observed I(t) curves were fitted with eqs 5−9. In the fitting, the kr value was varied to reproduce the magnetic field dependence of experimental data, while the kHA, kesc, krec, and kST0 values were fixed at the same values for all calculations. In Figure 6, the blue, green, and black solid lines indicate the time dependence of the calculated concentrations of BPH•. As shown in the figure, the experimental results were reproduced fairly well by this calculation, which included two recombination pathways. The calculation with only one recombination pathway failed to fit the time profiles of the RP dynamics in the presence of the magnetic field. The fitting gave either higher populations of RPs at early times (t < 2 μs) or quicker decay in the time range of a few microseconds. These findings suggest that recombination from the triplet RP state in the presence of magnetic fields consists of the two pathways predicted by Hayashi and Nagakura; these two pathways are based on the relaxation mechanism.32 Though these two recombination pathways are predicted by theory, the transient absorption signals observed in the present photochemical reaction have been analyzed by means of only one pathway for recombination, because the overlap of the transient absorption of 3BP0* with BPH• does not allow for detailed

kr =

(δA × gμB )2 1 1 τ 1 + = × + T1 TSR TSR 5ℏ2 1 + ω 2τ 2 (10)

where τ is a rotational correlation time for the radical and ω is the energy splitting between the spin states. We assumed that 20221

DOI: 10.1021/acs.jpcc.5b07524 J. Phys. Chem. C 2015, 119, 20217−20223

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yield of BPH• generated by photochemical reaction of BP in SDS micellar solution were observed in the presence of various magnetic fields. The experimental results were reproduced fairly well by a simple kinetic model based on the spin relaxation mechanism proposed by Hayashi and Nagakura. These results demonstrate that two-step two-laser fluorescence spectroscopy in combination with magnetic fields provides valuable information about the dynamics of complex photochemical reactions involving paramagnetic intermediates with fluorescent excited states.

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AUTHOR INFORMATION

Corresponding Author

Figure 8. Magnetic field dependence of spin relaxation rate (kr) in radical pairs estimated from fitting of the experimental data with eqs 5−9 (black circles). Solid and dashed lines show the kr values calculated by eq 10 with parameters of δA = 0.5 mT, 1/TSR = 1.5 × 105 s−1, and τ = 0.65 ns (η = 10 cP, blue solid line), τ = 1.3 ns (η = 20 cP, red solid line), τ = 2.6 ns (η = 40 cP, green solid line), and δA = 0.5 mT, 1/TSR = 1.0 × 105 s−1, τ = 0.65 ns (η = 10 cP, dashed line) respectively.

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by a Grant-in-Aid for Young Scientists (B) (No. 25870123) and by a Grant-in-Aid for Scientific Research on the Innovative Area of “All Nippon Artificial Photosynthesis for Living Earth” (Area No. 2406; No. 25107509) and “Stimuli-responsive Chemical Species for the Creation of Functional Molecules” (Area No. 2408; No. 15H00917) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan.

the spin relaxation induced by the anisotropy of the hyperfine interaction plays a major role in the generation of the MFEs observed in the present study. In eq 10, we also added the magnetic field independent spin relaxation rate (1/TSR) associated with the spin rotational relaxation.38 The kr values calculated from eq 10 are shown in Figure 8 together with the kr values obtained by fitting the experimental I(t) curves with eqs 5−9. As can be seen in Figure 8, in the low magnetic field range (0 < B ≤ 0.5 T), the experimental results can be reproduced with eq 10 using the parameters of δA = 0.5 mT and τ = 0.5−3 ns. From τ values obtained from the analysis and the radius of the radical (d = 4 Å), the viscosity (η) inside of the SDS micelle was estimated to be 10−40 cP from the equation τ = 4πηd3/3kBT. The estimated viscosities are consistent with the viscosities (9−36 cP) reported for the SDS micelle.39−43 This analysis of the RP dynamics suggests that the observed MFEs mainly originated from the magnetic field dependence of the spin relaxations, as we expected. These results indicate that the kinetic parameters of RP motions, such as η and kesc, as well as the spin conversion rates, are determined from the time profiles of the yield of the radicals under various magnetic fields. In the analysis, we focused on the MFE data obtained in the low magnetic fields. In the simulation with the abovementioned parameters, calculated data somewhat deviate from the experimental results in the high magnetic fields. The value of τ is related with saturation field for the kr values. When τ is longer, the kr value is saturated at the lower magnetic field while the shorter τ value gives the higher magnetic field for the saturation. The deviation of the calculated data from the experimental results found in the high magnetic field implies that fast molecular motions also contribute to the spin relaxation in RP in addition to the molecular rotations associated with the correlation time of τ = 0.5−3 ns. Obviously the molecular motions in the micelles are not uniform. It may be also possible that the molecular vibrations enhance the spin relaxations at the high magnetic fields. Such effects may cause the spin relaxations mildly even in the high magnetic fields.

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REFERENCES

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CONCLUSION A two-step two-laser fluorescence spectroscopy method was developed to observe the fluorescence from short-lived radical intermediates under magnetic fields. The time profiles of the 20222

DOI: 10.1021/acs.jpcc.5b07524 J. Phys. Chem. C 2015, 119, 20217−20223

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DOI: 10.1021/acs.jpcc.5b07524 J. Phys. Chem. C 2015, 119, 20217−20223