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Solvent Viscosity Effect on Triplet−Triplet Pair in Triplet Fusion Kana Yokoyama,† Yusuke Wakikawa,‡ Tomoaki Miura,† Jun-ichi Fujimori,§ Fuyuki Ito,§ and Tadaaki Ikoma*,†,⊥,∥ †

Graduate School of Science and Technology, Niigata University, 2-8050 Ikarashi, Nishi-ku, Niigata 950-2181, Japan Advanced Instrumental Analysis Center, Shizuoka Institute of Science and Technology, 2200-2 Toyosawa, Fukuroi 437-8555, Japan § Institute of Education, Shinshu University, 6-Ro Nishinagano, Nagano 380-8544, Japan ⊥ Core Research for Evolutionary Science and Technology, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi 332-0012, Japan ∥ Center for Instrumental Analysis, Niigata University, 2-8050 Ikarashi, Nishi-ku, Niigata 950-2181, Japan ‡

S Supporting Information *

ABSTRACT: The effect of the solvent viscosity dependence of time-resolved magnetoluminescence (ML) on the delayed fluorescence of 9,10-diphenylanthracene (DPA) sensitized by platinum octaethylporphyrin has clarified the structure and dynamics of the triplet−triplet pair (TT), i.e., the transition state of triplet fusion. Phase inversion of the ML effect with time provides evidence for the recycle dynamics of the excited triplet state for DPA in triplet fusion. The electron spinrelaxation by random molecular rotation causes intersystem crossing among the different spin states of the triplet−triplet pair and allows the 3,5TT to engage in triplet fusion. Therefore, slow-down of the molecular diffusion by an increase in the solvent viscosity can enhance the triplet fusion yield. However, the reduction of the ML effect observed in quite high viscosity solvents suggests that the substantially slow rotational motion decreases the triplet fusion yield due to steric factors in electron exchange from the triplet−triplet pair.

1. INTRODUCTION Triplet fusion, also known as triplet−triplet annihilation, is one of the fundamental reactions of electron exchange with two molecules in the lowest excited triplet (T1) state: formation

originated from the triplet fusion due to diffusion of T1 molecules in fluid solution were observed.20−23 These studies in solution phase point out that mutual orientation and molecular rotation in the triplet−triplet pair bring about different dynamics of the transition state from that in solid phase. For clarifying a causal relation between the transition state and the overall fusion efficiency in solution phase, it is desired to investigate systematically the solvent viscosity dependence of the ML effect. Here we show how the rotational diffusion as well as translational diffusion influence the dynamics in the triplet−triplet pair, which determines the fusion efficiency, by means of time-resolved measurement of the delayed fluorescence of 9,10-diphenylanthracene (DPA) in various solvents. The ML effect is defined in percentage figures by

fusion

T1 + T1 XooooooooooY TT ⎯⎯⎯⎯⎯→ S1 + S0 dissociation

(1)

which can occur when the total energy of the reactants (2T1) is higher than that of the products of excited singlet (S1) and ground singlet (S0) states. In recent years, triplet fusion has received much attention in developing the performance of organic electronic devices because it can solve difficult issues, such as the harvesting energy of dark triplet excitons in lightemitting diodes1 and the utilization of the red and near-infrared regions of the solar spectrum for photovoltaic cells.2−4 The photosensitized triplet fusion system is also applied for upconversion with low optical power5−11 and bioimaging with low risk of photodamage.12,13 Thus, clarification of factors that determine the triplet fusion efficiency contributes greatly toward broad field of application. In the late 1960s and 1970s, studies on the effect of magnetic field (B) on luminescence, the magnetoluminescence (ML) effect, from the S1 product in polyacene crystals indicated the importance of the triplet−triplet pair (TT), which may be recognized as a transition state in bimolecular triplet fusion reactions.14−19 After the earliest findings of ML effect in organic molecular solids, many different types of the ML effects © 2015 American Chemical Society

ML(B , t ) =

ΔI(B , t ) I(B , t ) − I(0, t ) × 100 = × 100 I(0, t ) I(0, t ) (2)

where I(B, t) is the delayed fluorescence intensity under a magnetic field (B) at a delay time after photoexcitation (t). Although there is no fusion probability in eight out of nine spin Received: November 16, 2015 Revised: December 3, 2015 Published: December 3, 2015 15901

DOI: 10.1021/acs.jpcb.5b11208 J. Phys. Chem. B 2015, 119, 15901−15908

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2. EXPERIMENTAL SECTION DPA (Tokyo Chemical Industry), was purified by several recrystallization processes with toluene prior to use. PtOEP (Sigma-Aldrich) was used without further purification. Commercially available organic solvents with various coefficients of viscosity (η) at room temperature were utilized, such as 3-chloropropene (η = 0.330 mPa·s),26 dichloromethane (η = 0.442 mPa·s),26 chlorobenzene (η = 0.753 mPa·s),27 and odichlorobenzene (η = 1.324 mPa·s).27 The concentration of DPA ranged from 1.0 × 10−2 to 1.0 × 10−4 mol·dm−3, while that of PtOEP was kept constant at 6.0 × 10−5 mol·dm−3. The solutions with well-dissolved solutes were sealed in quartz tubes with inner diameter of ca. 3.5 mm after being degassed with several freeze−pump−thaw cycles using a vacuum line with a pressure of 10−3 Pa in order to prevent oxygen molecule, which dissolved in solvent under atmospheric conditions, from quenching 3PtOEP and 3DPA. Figure 1 shows a schematic diagram of the apparatus used to measure the time-resolved ML effect. The second harmonics

sublevels of the triplet−triplet pair due to spin conservation, i.e., the rule of spin statistics, fast intersystem crossing (ISC) among the spin states, i.e., the spin dynamics, provides an opportunity for fusion of the triplet−triplet pairs initially populated in the eight spin-forbidden states, which results in an enhancement of the total triplet fusion efficiency. Molecular rotation was determined to be a key for control of the spin dynamics and the fusion of the triplet−triplet pair. The transition state dynamics clarified by the viscosity dependence of the ML effect provides a new concept for dynamic spin engineering in the development of organic optoelectronics with respect to the triplet harvesting. In this study, we adopt a triplet fusion system in a solution phase that is known as a photosensitized up-conversion, as illustrated in Scheme 1, to effectively produce DPA in the T1 Scheme 1. Molecular Structures of Fluorescent DPA and Phosphorescent PtOEP, and Reaction Scheme for Triplet Fusion by Triplet Sensitization

a

I: photoexcitation. II: intersystem crossing. III: energy transfer. IV: triplet fusion. V: radiative decay. ki represents the rate constant of stepi. kTD and kTA are the intrinsic decay rate constants of the 3PtOEP and 3 DPA, respectively.

state (3DPA), even under excitation with low intensity light. Platinum(II) 2,3,7,8,12,13,17,18-octaethyl-21H,23H-porphine (PtOEP), which has a high quantum yield of ISC (ϕII ≈ 1.0),24 was used as a triplet sensitizer. The fluorescence quantum yield of the S1 state of DPA (1DPA) is also very high (ϕV = 0.97).25 The first step (step-I) is the generation of the S1 state of PtOEP (1PtOEP) by irradiation with light of which the energy is lower than that of 1DPA. In the second step (step-II), 1 PtOEP undergoes ultrafast ISC, which results in generation of the T1 state of PtOEP (3PtOEP). 3PtOEP is then quenched by energy transfer to DPA, which forms 3DPA in the third step (step-III). The fourth step (step-IV) is triplet fusion, in which the encounter of two 3DPA molecules results in the formation of 1DPA and the S0 state of DPA. 1DPA finally decays with fluorescence (step-V). Using this photosensitized up-conversion system, the fluorescence spectrum from 1DPA and the phosphorescence one from 3PtOEP appear in different wavelength ranges as shown in Figure S1 of the Supporting Information. The fluorescence of 1DPA due only to the triplet fusion can be detected without interference from the prompt one. In addition, the kinetics for the generation of 3DPA can be monitored by using the phosphorescence from 3PtOEP.

Figure 1. Block diagram of the apparatus used for time-resolved ML measurements: S, sample solution; PMT, photomultiplier tube; PC, personal computer.

(wavelength (λ): 532 nm) from a nanosecond YAG laser (FDSS 532−150-I, CryLas) with a pulse width of 2 ns and a repetition frequency of 20 Hz was used for selective excitation of PtOEP in the sample solution. The incident light intensity was controlled in the range of 1013−1015 photons·pulse−1 cm−2 using a glan-laser prism (GL-prism; Sigmakoki). Emission from the sample solution was captured by an optical fiber and directed to detectors equipped with appropriate filters. Spectra were obtained with a multichannel spectrometer (PMA C10027, Hamamatsu) with a notch filter (NF-532.0-E-25.0M, Melles Griot). To detect time profiles of the emissions, luminescence was passed through appropriate band-pass filters (MX0430; MX0640; MX0650, Asashi Spectra) and supplied into a photomultiplier tube (PMT; R7400U-01, Hamamatsu). The signals were then monitored with a digital oscilloscope (DPO7104, Tektronix). Static magnetic fields were applied to the sample fixed in the center of an electromagnet (TMYSV5410−061.5, Tamagawa Factory). The magnetic field strength was measured with a gauss meter (HGM-8201−8R15902

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seconds. When the initial concentration of 3 PtOEP ([3PtOEP]0) was increased by increasing the incident photon density, the decay of 1DPA fluorescence became fast with no change of its rising rate (Figure S2a of Supporting Information). In contrast, when the concentration of DPA was increased, both the rise and decay of 1DPA fluorescence became fast (Figure S2b of Supporting Information). The dependence of the 1DPA fluorescence decay on the incident photon density and [DPA] is interpreted by the bimolecular reaction of two 3DPA molecules, of which the initial concentration [3DPA]0 increases with the excitation power or [DPA]. The dependence of the 1DPA fluorescence rise on the DPA concentration is understood by the intermolecular energy transfer from 3PtOEP to DPA. According to Scheme 1 and the elementary processes eq 1 for the step-IV, rate equations for the concentrations of 3 PtOEP, 3DPA, 3DPA3DPA, and 1DPA are expressed by

10 V, Tamagawa Factory). The temperature of the sample was controlled with an in-house-built flow system of cold nitrogen gas using a quartz dewar. The transient absorption of 3DPA was measured using an inhouse-built spectrometer equipped with a nanosecond YAG laser (SLII-10, Continuum) that irradiates the third harmonic of λ = 355 nm as a pump light and a continuous wave Xe lamp probe light (UXL153-o, Ushio), of which the spectrum is appropriately shaped with high and low cut-filters. The probe light passing through the sample solution was dispersed by a monochromator (SG-80, Koken Kogyo) and then detected with a PMT (R955, Hamamatsu). The output signal from the PMT was recorded with a digital oscilloscope (DPO4104, Textronix). The magnetic fields at the sample were generated by an electromagnet (SEE-16, NEC TOKIN). The temperature of the sample was controlled with the same flow system of cold nitrogen gas used for measurement of the ML effect.

d[3PtOEP] = − k TD[3PtOEP] − kIII[3PtOEP][DPA] dt

3. RESULTS AND DISCUSSION Time and Temperature Dependences. Figure 2a shows time profiles for 3 PtOEP phosphorescence and 1 DPA

(3)

d[3DPA] = kIII[3PtOEP][DPA] + kdis[3DPA3DPA] dt − k TA[3DPA] − 2k for[3DPA]2

(4)

d[3DPA3DPA] = 2k for[3DPA]2 − (kdis + k fus)[3DPA3DPA] dt (5) 1

d[ DPA] = k fus[3DPA]2 − k V[1DPA] dt

(6)

as described in detail in part S3 of Supporting Information. kfor and kdis represent the rate constants of formation and dissociation due to the diffusional motion in solvent. kfus is the rate constant of fusion. Under the condition of [DPA] ≫ [3PtOEP], eq 3 can be solved as a pseudo-first order decay and the intensity of 3PtOEP phosphorescence per unit time (Ip(t)) is proportional to kTD[3PtOEP]; therefore, Ip(t ) = Ip0 exp{−(k TD + kIII[DPA])t }

(7)

The decay rate constant of the 3PtOEP phosphorescence is kTD + kIII[DPA]. On the other hand, since the intensity of the delayed fluorescence for 1DPA at time t (If(t)) is proportional to [1DPA], the fluorescence intensity is given by I f (t ) ∝ Figure 2. (a) Time-profiles for the intensities of DPA fluorescence at 430 nm and 3PtOEP phosphorescence at 640 nm measured in a dichloromethane solution of DPA (1.0 × 10−3 mol·dm−3) and PtOEP (6.0 × 10−5 mol·dm−3) at room temperature. The black lines indicate simulation curves calculated on the basis of bimolecular kinetics (see main text). (b) Difference time profile of the 1DPA fluorescence at 430 nm obtained by subtracting the profile in the absence of the external B field from that measured at 500 mT. (c) Time profile for the ML effect on the 1DPA fluorescence measured at 500 mT.

2k forpfus kV

[3DPA]2

(8)

1

∵ pfus =

k fus kdis + k fus

(9)

under steady-state approximation for the short-lived species of 3 DPA3DPA and 1DPA. The Ip and If obtained from [3PtEOP] and [3DPA] calculated using the rate equations reproduce the observed kinetics of the 3PtOEP phosphorescence and 1DPA fluorescence as shown in Figure 2a, which confirms that the triplet fusion initiated by triplet sensitization proceeds. In the simulations the next four constants are adopted: [3PtOEP]0 of 5 × 10−6 mol·dm−3 estimated from incident photon density, extinction coefficient and triplet yield of PtOEP; kTD of 2.6 × 105 s−1 and kIII of 1.4 × 109 mol−1 dm3 s−1 which are determined by Stern−Volmer analysis (see part S4 of Supporting Information); kTA of 1.7 × 104 s−1 obtained by

fluorescence after laser flash to selectively excite PtOEP at λ = 532 nm observed in a dichloromethane solution with a low η of 0.442 mPa·s at room temperature. The 3PtOEP phosphorescence decays within a few hundred nanoseconds and the 1 DPA fluorescence increases simultaneously. The 1DPA fluorescence gradually decreases within several tens of micro15903

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quenching of the 3PtOEP phosphorescence with DPA (see part S4 in Supporting Information). ϕIV was calculated with kTA, kIV, and [3DPA]0 determined from time-resolved measurements for the delayed fluorescence of 1DPA and the absorption of 3DPA (see part S5 in Supporting Information). Both ϕIII and ϕIV were almost constant at the measured temperatures. The bimolecular rate constants of kIII and kIV decrease due to the slow translational diffusion motion in viscous solvents at low temperature; however, a reduction of kTD and kTA due to diminishment of the nonradiative processes of 3PtOEP and 3 DPA at low temperature compensates the quantum yields of ϕIII and ϕIV. The temperature dependence of the overall yield ϕDF observed in low viscosity solvents, which cannot be interpreted in terms of the simple five steps, suggests the significance of the triplet−triplet pair in the course of the triplet fusion reaction, which can be influenced by the solvent viscosity. Magnetic Field Dependence. According to the multiplicity of electron spin, the generation of the triplet−triplet pairs with the low, middle or high angular momentum of electron spin (1TT, 3TT, or 5TT, respectively) obeys the spin statistics as 1:3:5;

transient absorption spectroscopy (see part S5 in Supporting Information). The best fit simulation yields an apparent fusion rate constant kIV ∼ 2kforpfus of 1.3 × 1010 mol−1 dm3 s−1, which is in order of the diffusion limited rate constant, kdif, in DCM at room temperature (8 × 103RT/(3η) = 1.7 × 1010 mol−1 dm3 s−1). If the encounter of two 3DPA is assumed to be diffusionlimited as kfor = kdif, fusion probability pfus is calculated to be pfus ∼ 0.38. This value is larger than the value of 1/9 = 0.11 expected from the spin statistics, which indicates that spin and molecular dynamics of the triplet−triplet pair plays an important role on enhancing fusion efficiency over the spinstatistics limit. Figure 3 shows dependence of the 1DPA fluorescence spectrum intensity detected in dichloromethane on the

Figure 3. Temperature dependence of the 1DPA fluorescence (red) intensity, and of ϕIII and ϕIV, which correspond to the quantum yields for the energy transfer and triplet fusion reactions (black), respectively, measured in a dichloromethane solution. The concentrations of DPA and PtOEP in the solution were 1.0 × 10−3 and 6.0 × 10−5 mol·dm−3, respectively.

The 1,3,5TT have individual fusion pathways, according to the conservation rule of the spin angular momentum. Only the 1TT contributes to the fusion to yield the fluorescent S1 state with a rate constant kS (S-ch). The 3TT gives a highly excited triplet state (Tn) with a rate constant kT (T-ch). The fusion pathway from the 5TT (Q-ch) is usually closed due to the extremely high energy of the excited quintet state. On the other hand, the spin conversion among the spin states with a rate constant kISC occurs by the local magnetic interactions. Time profiles for the 1DPA fluorescence were measured in the presence of external magnetic field to detect the triplet− triplet pair, because the magnetic field can modulate the ISC rate among the different spin states due to the Zeeman interaction.14−18,28,29 The Zeeman energy is much smaller than the thermal energy, so that it does not influence the spin statistics, but the Zeeman splitting changes the ISC resulting in changes in the final product yields due to the spin conservative fusions from the triplet−triplet pairs. Figure 2b shows the typical difference between the time profiles detected at B = 500 and 0 mT in dichloromethane at room temperature. In the presence of a magnetic field, the fluorescence intensity becomes weaker in the early time range and stronger in the later time range, in comparison with that at 0 mT. At zero-cross time (tcr), when the intensity difference of ΔI crosses the zero level, is 12 μs. The ML value is initially maintained at a certain negative level in the nanosecond region, then increases monotonically and switches to positive at tcr, as shown in Figure 2c. Observation of ML effect originated from the magnetic field dependent ISC among the different spin states of the triplet− triplet pair confirms the importance of the spin dynamics for the triplet fusion yield. The negative ML effect at the early times can be explained by reduction of ISC efficiency by the external magnetic field and reduction of S-ch efficiency, of

temperature. The intensity at 240 K increases by 20% from that at room temperature. In 3-chloropropene solution with a small η of 0.330 mPa·s, the delayed fluorescence intensity of DPA sensitized by 3PtOEP also increased with decreasing temperature (Figure S6a in Supporting Information). The rise and decay of the delayed fluorescence, which reflect the energy transfer and triplet fusion reactions respectively, became slower with a decrease in temperature, as shown in Figure S5b of Supporting Information. A similar effect on the rise and decay of delayed fluorescence was observed with an increase in the solvent viscosity at room temperature (Figure S7 in Supporting Information). Therefore, it is considered that the increase of viscosity at low temperature is the main reason for the significant enhancement of the delayed fluorescence intensity. The quantum yield for delayed fluorescence (ϕDF) is expressed as the product of the yields for all the steps in Scheme 1 (ϕI, i = I − V) as V

ϕDF =

∏ ϕi i=I

(10)

The absorption spectra of PtOEP at low temperatures are the same as that at room temperature. Both ϕII and ϕV are almost unity even at room temperature. Therefore, there is no reason why ϕI, ϕII, and ϕV increase at low temperatures. The temperature dependences of ϕIII and ϕIV are represented in Figure 3. ϕIII was measured by a Stern−Volmer analysis with 15904

DOI: 10.1021/acs.jpcb.5b11208 J. Phys. Chem. B 2015, 119, 15901−15908

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tendency to saturate at a certain level with high magnetic fields. The ML effect decreases with the delay time and changes its phase to positive at tcr, due to the recycle kinetics of 3DPA mentioned above. The asymptotic negative behavior in the observed magneto-curve of the ML effect is the main characteristic for the magnetically affected reaction yield of the singlet channel (S-ch in eq 11) by the triplet−triplet pair mechanism. The reduction of the ISC rates under the external magnetic field leads to decrease of the S-ch fusion efficiency. Saturation of the reduction effect on the ISC rates in high fields is the origin for the observed asymptotic behavior. We calculated magneto-curve for the ML effect using Merrifield’s theory, which takes into account of only the coherent mixing among the different spin state induced by the zero-field splitting interaction at a fixed molecular orientation of the triplet states in crystal (see part S8 in Supporting Information for details).30,31 The theoretical curve indicated by the blue curve in Figure 4 shows an antiphase peak at low field and an asymptotic dependence at high field, from which the half line width is estimated to be ca. 120 mT, which is close to the zero-field splitting parameters (|D| + |E| = 84.7 mT) in the excited triplet state of anthracene.32 The main features of the theoretical curve agrees well with the ML effect observed for DPA solid.33,34 In the simulation, two sublevels of the 5TT can coherently mix with the 1TT by the zero-field splitting interaction, which is a cause of ISC, in the absence of a magnetic field. Therefore, three spin sublevels have the chance of S-ch fusion. Under low field where the Zeeman and zerofield interactions are comparable, all of the 5TT are mixed with the 1TT, which is the reason for the antiphase ML effect at the low magnetic field. However, the number of spin sublevels that enable S-ch fusion is reduced to two under high magnetic field, because only one sublevel of the 5TT couples with the 1TT under the large Zeeman interaction on the 5TT.18 The calculated negative ML effect in the high field arises from the decrease of number of the coupled states. The experimental results exhibit much broader line shape and no clear low field effect, indicating different mechanism for the field dependentISC e.g. spin relaxation. Solvent Viscosity Dependence. As depicted in Figure 4, fitting of the observed magneto-curve with a Lorentzian function gives a high-field saturation ML value (MLS) and a magnetic field at half MLS (B1/2). The B1/2 and MLS values at 500 ns, which is the earliest time that gives a reliable maximum |ML| value in dichloromethane, are 315 mT and −9.4%, respectively. B1/2 does not change with the time, while MLS shows the inversion. The incident laser intensity had no significant effect on B1/2 and MLS at 500 ns (see Figure S8 in the Supporting Information). The solvent viscosity dependence of the ML effect on the 3PtOEP-photosensitized fluorescence of 1DPA was examined by changing the temperature and using other solvents with various η, such as 3-chloropropene, chlorobenzene and o-dichlorobenzene. A broad ML effect and its phase inversion from negative to positive with time, similar to that shown in Figure 4, were observed in all cases. The characteristic parameters obtained by the fitting of magnetocurves for the ML effect detected at early times are summarized in Figure 5. tcr and B1/2 increased and decreased with increasing solvent viscosity, respectively. MLS reached a maximum at a particular viscosity around 0.7−0.8 mPa·s. tcr is an estimate for when the triplet molecules that undergo formation and dissociation of the triplet−triplet pair become a majority of the triplet molecules remaining in the solution.

which the detailed mechanism is discussed later. The sign inversion of the ML effect in the later time range can be explained by the recycle kinetics of the triplet molecules. The reduction of S-ch probability induced by the external field results in an increase in the regeneration of 3DPA from the triplet−triplet pairs by escape and/or T-ch fusion. The recovered T1 molecules repeat the triplet fusion reaction because 3DPA has a sufficiently long lifetime (∼60 μs) to encounter another 3DPA. By this recycle kinetics of 3DPA survived more under a magnetic field, therefore, the delayed fluorescence intensity becomes stronger in the later time range than that under zero magnetic field. The observed phase inversion of ML effect can be interpreted in terms of a reduction of fusion probability, pfus, under the external magnetic field. The fluorescence intensity expressed by eq 8 can be approximated to ⎛ ⎞ 2k forpfus 3 1 ⎟∝ ([ DPA]0 )2 I f ⎜t ≪ 3 kV [ DPA]0 kIV ⎠ ⎝

(12)

⎞ ⎛ 1 1 ⎟∝ I f ⎜t ≫ 3 2 [ DPA] k 2 k p ⎝ 0 IV ⎠ for fus k Vt

(13)

under the conditions of kforpfus[3DPA] ≪ kTD + kIII[DPA] and kTD ≪ kfor, kdis (see part S3 in Supporting Information for details). The fluorescence intensity is normally and inversely proportional to pfus at early and late times, respectively. If the Zeeman interaction simply diminishes the ISC efficiency, the magnetic field effect appears as decrease of pfus in the shortlifetime regime of the triplet−triplet pair, where the ISC and fusion kinetics of the triplet−triplet pair can be isolated from the slow formation and dissociation kinetics. Thus, one can observe negative ML effect at early times, while the positive ML effect in late times. Figure 4 shows the magnetic field dependence of the ML effect on the 1DPA fluorescence intensity. For the early time range, the negative ML effect increases with B and has a

Figure 4. Magnetic field dependence of the ML effect on the 1DPA fluorescence intensity measured in dichloromethane at room temperature. The numbers indicate the delay times after flash for the excitation of PtOEP in the same solution. The concentrations of DPA and PtOEP in the solution were 1.0 × 10−3 and 6.0 × 10−5 mol·dm−3, respectively. The dashed black lines represent fitting with a Lorentzian function and the solid blue and green lines show simulations calculated using a density matrix formalism with zero-field splitting parameters of anthracene (see part S8 in Supporting Information). 15905

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ℏ is the reduced Planck constant. The random thermal molecular rotation gives rise to fluctuation of the local magnetic field of D plus E on the electron spins, which mainly arises from the magnetic dipolar interaction between the two spins in the triplet state. Figure 6 presents some model calculations of

Figure 5. Dependence of tcr (green), B1/2 (blue), and MLS (red) of the ML effect on the solvent viscosity due to the triplet−triplet pair mechanism in the 1DPA fluorescence observed by triplet-sensitization with PtOEP in solution. ●, ■, ▲ and ▼ symbols represent 3chloropropene, dichloromethane, chlorobenzene and o-dichlorobenzene solvents, respectively. The dotted lines are shown to indicate the trend. The dashed line indicates the size of zero-field splitting for the triplet sublevels of anthracene.

Figure 6. Magnetic field effect on the spin−lattice relaxation rate constant for a triplet molecule with D = +76.6 mT and E = −9.03 mT calculated for τc = 20, 50, and 150 ps. The line widths of the Lorentzian curves (black) fitting the simulations of τc = 20, 50, and 150 ps are 167, 68, and 22 mT, respectively.

magnetic field dependence of kISC due to the T1-relaxation using various τc. Because of the Zeeman term of ω in eq 15, kISC gradually approaches zero with an increase in the magnetic field, which can be fit by a Lorentzian function. The apparent Lorentzian shape agrees with the asymptotic behavior of the observed magneto-curve of ML effect (Figure 4). B1/2 for the simulated magneto-curve of the T1-relaxation rate decreases with increasing τc, which is also in agreement with the observed η-dependence of B1/2 as evidenced by the Stokes−Einstein− Debye relation between τc and η: τc = 4r3πη/(3kBT). Hence we performed simulation considering the incoherent spin dynamics according to Atkins’ theory (see part S8 in Supporting Information for detail).21 As shown by the green curve in Figure 4, a simulation based on the spin relaxation using τc = 20 ps estimated from the solvent viscosity with the Stokes− Einstein−Debye equation and two parameters of kS = 4.6 × 109 s−1 and kdis = 1.9 × 109 s−1 is in good agreement with the observed curve. In addition, τc-dependence of the spin relaxation rate at zero field shown in Figure 6 indicates that the ISC rate due to the spin relaxation increases with increasing η. Hence, the increase of the delayed fluorescence intensity observed in dichloromethane at low temperatures is interpreted in terms of the acceleration of the ISC in the triplet−triplet pair due to the slow rotational diffusion. The T1-relaxation time of 3DPA in dichloromethane with η = 0.78 mPa·s at 240 K, where the maximum delayed fluorescence intensity was observed as shown in Figure 3, is calculated to be ca. 200 ps. Within this period, each of the 3DPAs in the triplet−triplet pair can diffuse ca. 0.8 nm according to eq 14. Therefore, it should be noted that the triplet−triplet pair in such a distance works as the transition state in increasing the total triplet fusion efficiency. The spin and molecular dynamics of the transition state plays an essential role increasing the total triplet fusion efficiency by the incoherent ISC from the 3TT and 5TT to 1TT, which directly gives the S1 state. The branching ratio of kSr = kS/kdis

Therefore, this can be considered by a random walk of molecules with diameter r in a solution with η. According to the Stokes−Einstein law, the average time for two molecules that encounter each other after moving a distance d (ten) can be expressed by

ten =

3πr⟨d 2⟩η kBT

(14)

where T and kB represent temperature and the Boltzmann constant, respectively. ten for 3DPAs separated by d of ca. 70 nm in dichloromethane at room temperature35 is calculated to be 1.6 μs. Although the estimated ten is one order smaller than the observed tcr, the proportionality between tcr and η is also acceptable, considering the necessary time to re-encounter and the reduction of the 3DPA concentration with time. The B1/2 value much larger than that for coherent mixing due to the zero-field splittings of triplet molecule indicates the contribution of spin relaxations to the ISC among the spin sublevels of the triplet−triplet pair in solution.21,36,37 The anisotropic zero-field splittings are averaged out to zero by fast random molecular rotation in the solution, because the zerofield interaction is traceless. The rotational correlation time (τc) of DPA in the solvents used here ( 1 could also be a possible reason for the roll-off of MLS for large η. As τc increases in viscous solvents, the coherent ISC due to zero-field splittings becomes more effective. ML effect caused by the coherent ISC is observed in ordered and disordered solids, in which there is no fast molecular rotation of the triplet excitons.32,33 In either case, it is clear that the molecular rotation on the transition state dynamics plays a key role in the triplet fusion in liquid. The triplet fusion efficiency also monotonically increases with kSr. It should be noted, therefore, that the peak behavior of

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AUTHOR INFORMATION

Corresponding Author

*(T.I.) E-mail: [email protected]. Present Address

(K.Y.) Research Center for Ultra-High Voltage Electron Microscopy, Osaka University, Osaka, Japan. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS T.I. thanks Prof. Shozo Tero-Kubota (Tohoku Univ.), Prof. Kimio Akiyama (Tohoku Univ.), and Prof. Katsumi Tokumaru (AIST) for fruitful discussions and comments. This work was financially supported by a grant of Core Research for Evolutionary Science and Technology from the Japan Science and Technology Agency, a Grant-in-Aid for Scientific Research (No. 2610088), and the Nanotechnology Platform Program (Molecule and Material Synthesis) from the Japanese Ministry of Education, Culture, Sports, Science and Technology, a grant from Idemitsu Kosan Co., Ltd., and a grant from the Network Joint Research Center for Materials and Devices. 15907

DOI: 10.1021/acs.jpcb.5b11208 J. Phys. Chem. B 2015, 119, 15901−15908

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The Journal of Physical Chemistry B

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DOI: 10.1021/acs.jpcb.5b11208 J. Phys. Chem. B 2015, 119, 15901−15908