9130
J . Phys. Chem. 1991, 95, 9 130-9 134
Spin Polarizatlon Generated in the Triplet-Doublet Interaction: Hyperfine-Dependent Chemically Induced Dynamic Electron Polarization Akio Kawai, Tetsuo Okutsu, and Kinichi Obi* Department of Chemistry, Tokyo Institute of Technology, Ohokayama, Meguroku, Tokyo 152. Japan (Received: April 3, 1991; In Final Form: June 24, 1991)
We studied CIDEP (chemically induced dynamic electron polarization) generated by the interaction between doublet radicals and triplet molecules. ClDEP signals showed significant hyperfine dependence in addition to net emissive signals. Net emissive ClDEP was explained by the avoided crossing of 1Q-3/2) and ID1/2) states of a tripletdoublet encounter complex on the potential surfaces followed by the vanishing of the doublet spin states of this system through triplet quenching. The hyperfine dependence of ClDEP was interpreted by the mixing of 1Q1/2) and ID1/2) states and that of (Q-1/2) and ID-1/2) states in the region of zero exchange interaction. This mixing is due to the hyperfine interaction between triplet and doublet molecules followed by the exchange interaction by the reencounter. The observed spectrum of the free radical was well reproduced by the simulated spectrum assuming those two mechanisms.
Introduction
ClDEP has been widely studied by time-resolved ESR (TRESR), leading to the evolution of the CIDEP generation mechanism.' ClDEP is a useful phenomenon in which to study photochemical and photophysical processes and much work has successfully been carried out in order to assign intermediate species and to research photochemical reaction and energy transfer mechanisms.* There are two main mechanisms to generate CIDEP on free radicals: one is the triplet mechanism (TM) in which the electron spin polarization of a reaction precursor, triplet state, is preserved in produced radicals and the other is the radical pair mechanism (RPM), which is caused by the mixing of spin states of a radical pair, mainly between S and To states. Most CIDEP spectra are interpreted with a blend of these two mechanisms. Generation of ClDEP is not peculiar to photochemically produced radicals from the excited state, but it is also seen in the interaction between doublet radicals and short-lived triplet molecules in the liquid phase. Imamura et aL3 observed emissive electron spin polarized 4-amino-2,2,6,6-tetramethyl-lpiperidinyloxyl (ATEMPO) radical in a benzene solution of benzophenone and ATEMPO by laser flash photolysis and suggested that the CJDEP of ATEMPO was produced by electron spin polarization transfer (ESPT) from the initial spin-polarized triplet molecules to ATEMPO, which is a similar mechanism to the TM. On the other hand, a treatment similar to RPM was proposed for the tripletdoublet complex as the radical triplet pair mechanism (RTPM) by Blattler et aI.$ where CIDEP of radicals was generated by the mixing of quartet and doublet spin states of triplet-doublet encounter complexes through the zero-fieldsplitting (zfs) interaction of the triplet molecule. They predicted the generation of net emissive electron spin polarization for the free radicals by RTPM. These two mechanisms predict only net polarization for free radicals, even if both mechanisms contribute to ClDEP signals. In this paper, we report the hyperfine-dependent ClDEP signals of free radicals generated by the quartet-doublet mixing in tripletdoublet complexes. These signals are superimposed on net electron spin polarization. As ESPT and RTPM cannot interpret the hyperfine-dependent CIDEP, we propose a new mechanism; the hyperfine interaction between triplet and doublet molecules, which also causes the mixing of quartet and doublet spin states. This treatment is similar to the S-To mixing of RPM. By introducing this interaction, we succeeded in reproducing the hy( I ) Adrian, F. J. Reo. Chem. Intermed. 1979, 3, 3 . Muss, L. T.; Atkins, P. W.;McLauchlan, K . A.; Pedersen, J. B. Chemically Induced Magnetic Polarization; Reidel: Dordrecht, 1977. (2) Thurnauer, M. C.: Meisel, D. Chem. Phys. Lett. 1982,92,343. Emori. S.;Colpa, J. P.; Wan, J. K. S. Chem. Phys. Lett. 1983, 98, 142. (3) Imamura. T.; Onitsuka, 0.; Obi, K. 1.Phys. Chem. 1986, 90, 6741. (4) Blattler. C.; Jent, F.; Paul, H. Chem. Phys. Lett. 1990, 166, 375.
0022-3654/91/2095-9130$02.50/0
TABLE I: Electron Spin Polarization of Free Radicals Generated by the Interaction of Triplet and Doublet Molecules CIDEP spin of the polarization of
triplet molecule benzophenone phenanthrene naphthalene 1-nitronaphthalene 4-aminoacetophenone phenazine biacetyl benzil
radical Em Em Em Em Em Em Em Em 9,lO-acenaphthenequinone Em acetone Em pyruvic acid Em
the triulet state Em Ern Em Em Em Em Abs Abs
ref ~
5, 6 3 8 9
10 I1
Abs
11 12 13
Abs Abs
3, 7
13, 14
perfine dependence in CIDEP spectra. Experimental Section
TR-ESR spectra were obtained by a conventional ESR system (Varian E-I 12) without field modulation. Transient ESR signals obtained in the photolysis were acquired by a boxcar integrator (Stanford SR-250) with a gate time of typically 0.5-1.5 ps. Photolysis was carried out by a XeCl excimer laser (308 nm, Lambda Physik LPX 100) or an N2 laser (337 nm, Molectron UV24). ATEMPO (Eastman Kodak), 4-0~0-2,2,6,6-tetramethyI-lpiperidinyloxyl (OTEMPO) (Wako Pure Chem. IND), 2,2,6,6tetramethyl- 1-piperidinyloxyl (TEMPO), and galvinoxyl (Aldrich) were used as received. Benzophenone and 4-aminoacetophenone were recrystallized from n-hexane or ethanol. The other chemicals were used as supplied. In the experiments in triplet-doublet systems, benzene solution including samples was flowed through a cavity during photolysis at room temperature. The solution was deoxygenated by passage of nitrogen gas. Results and Discussion Net Polarization in Triplet-Doublet Systems. Figure 1 a shows
the TR-ESR spectrum of TEMPO obtained by the 308-nm laser photolysis of the benzophenone-TEMPO system in benzene. The observed spectrum shows a triplet hyperfine structure with total emissive ClDEP signals. The hyperfine structure is the same as that of the CW-ESR spectrum of TEMPO (Figure IC) with three peaks of equivalent intensity corresponding to the nuclear spin states of nitrogen atoms. Therefore, the observed TR-ESR spectrum is attributed to TEMPO radicals. Traces of the emissive ClDEP signals of TEMPO were obtained by irradiation without benzophenone, which were neglected in the following analysis. The triplet benzophenone is known to have emissive spin polarization from TP-ESR at low temperatureS and CIDEP at room
0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 23, I991 9131
Hyperfine-Dependent CIDEP
T Y
5z W
W
-
0
R (trip(et radical )
Figure 2. Energy diagram and state mixing of spin states of the triplet-doublet encounter complex assuming J < 0.
2 mT
Figure 1. TR-ESR spectra of TEMPO (0.60 mM) in (a) TEMPO and benzophenone ( 5 5 mM) mixture and (b) TEMPO and pyruvic acid (72 mM) in benzene by 308-nm excitation. (c) CW-ESR spectrum of
TEMPO. temperature.6 Figure 1b shows the TR-ESR spectrum obtained in the pyruvic acid-TEMPO system of benzene solution, where total emissive CIDEP signals of TEMPO are also seen. The TR-ESR’ and CIDEP’ measurements showed that pyruvic acid had an absorptive spin polarization in the triplet state. Table I summarizes the CIDEP signals generated in systems containing nitroxide radicals and many kinds of triplet molecules. The radicals used were TEMPO, ATEMPO, and OTEMPO. Electron spin polarizations of triplet states cited from refs 3 and 5-14 are also listed in Table I. The spin polarization of triplet acetone was reported to show different phases: absorption by TM in CIDEP at room temperature” and emission in ODMR at 4 K.I4 We adopted the polarization by TM. The spin polarization of the radicals is always emissive regardless of the spin polarization of the triplet states. Imamura et al? proposed ESPT in doublet-triplet systems. The results obtained here cannot be interpreted by this mechanism; all spin polarization would be lost due to spin lattice relaxation within the triplet state at the radical concentration used here. Actually, the triplet molecules with absorptive polarization yield emissive CIDEP radicals. Recently Blattler et a1.4 reported that emissive polarization was induced in benzyl radicals in the presence of triplet molecules and discussed spin interaction between doublet and triplet species, which resembles RPM for F pairs. We try to interpret the emissive ( 5 ) Murai. H.; Imamura. T.;Obi, K. Chem. Phys. Lett. 1982, 87, 295. (6) Miyagawa, K.;I’Haya, Y. J.; Murai, H. Nippon Kagaku Kaishi 1989,
1365.
( 7 ) Grant, A. 1.; McLauchlan, K. A. Chem. Phys. Lett. 1983, 101, 120. (8) El-Sayed. M. A.; Moomaw, W. R.;Chodak, J. B. Chem. Phys. Lett.
1973, 20, 11. (9) Shioya, Y.; Yagi, M.; Higuchi, J. Chem. Phys. Lett. 1989, 154, 25. (10) Akiyama, K.;Tero-Kubota, S.;Ikoma, T.;Ikegami, Y. Nippon Kugaku Kaishi 1989, 1463. (11) Yamauchi, S.; Hirota. N. J . Phys. Chem. 1984, 88, 4631. (12) Chan, I. Y.; Nelson, B. N. J. Chem. Phys. 1975, 65,4080. (13) Basu, S.; Grant, A. L.; McLauchlan, K. A. Chem. Phys. Lett. 1983, 94, 517. (14) Gehrtz, M.; Brauchle, Chr.; Voitlander, J. Chem. Phys. Lett. 1982, 91, 217.
CIDEP of radicals by introducing a triplet-doublet interaction. Triplet-doublet encounter complexes show quartet and doublet spin states. In this system, hyperfine interaction between triplet and doublet molecules and zfs interaction of triplet molecule are considered as effective perturbations. When a radical encounters a triplet molecule and enters the region of nonzero J interaction, the encounter complex becomes doublet or quartet spin state weighted with spin statistics. As the doublet state results in a separated pair of a singlet molecule and a doublet radical,I6 a triplet molecule is quenched through the encounter complex with a doublet state. On the zeroth-order potential surface, no electron spin polarization is generated by this triplet quenching. On the other hand, on the first-order potential surface, electron spin polarization of the radical is generated by perturbations, which resembles S-T-, mixing in RPM. Zfs interaction causes the state mixing, even in the nonzero J interaction region. Effective state mixing in RPM is hardly observed in the nonzero J region except in highly viscous solvent^'^ or at low temperature,” because the normal hyperfine interaction is too weak to cause S-T-I mixing. However, in the quartet-doublet mixing, the magnitude of a typical zfs interaction is estimated to be about 100 mT, corresponding to a state mixing rate of 3 X IO9 s-l, which is about 100 times faster than a typical hyperfine interaction. Hence, state mixing in the nonzero J region is expected. According to the zfs interaction, state mixing is allowed within )Q-3/2), 1Q1/2), and ID1/2) states and is also allowed within (Q3/2), lQ-1/2), and lD-1/2), where D and Q denote the doublet and quartet spin states of the encounter complex, respectively, and the number represents the spin magnetic quantum number. Therefore, the mixing between (Q-3/2) and ID1/2) for J < 0 and lQ3/2) and ID-1/2) for J > 0 adequately occurs in the nonzero J region of the triplet-doublet encounter complex. The energy diagram and the state mixing are illustrated in Figure 2, assuming J < 0. In the course of random encounters between triplet and doublet molecules, the T-l D-,/? state of the separated pair correlating to the 1Q-3/2) spin state IS efficiently converted to the ID1/2) spin state due to the avoided crossing of the 1Q-3/2) and (D1/2) states. According to the same mechanism, TI + D-1/2 and To + Dl states correlating to the (Dl/z)state are forced to the IQ-312) state. The other states of separated pairs remain on the zeroth-order surface without state mixing. All quartet and doublet spin sublevels are equally populated, but the reversible separation of encounter complexes on the same potential surface occurs only on the quartet surfaces because the doublet spin state of the encounter complexes disappears into singletdoublet separated pairs leading to the triplet quenching. Hence, after separation of triplet-doublet pairs, free radicals with an a spin state are enhanced more than those with a p spin state and net emissive CIDEP of the radical is observed.
+
(15) Trifunac, A. D. Chem. Phys. Lett. 1977, 49, 457. (16) Schulten, K. J . Chem. Phys. 1984,80, 3668.
9132 The Journal of Physical Chemistry, Vol. 95, No. 23, 1991
Kawai et al.
f
a)
I
2’5
-
1
BenzoDhenone
75
u
s
2.0 -
X v
1.5
-
1.0
-
%
C W
!I 2.00586-
( Triplet Mdecules
( Radicals )
2.00410 ( g values 1
Figure 3. (a) TR-ESR spectrum of galvinoxyl (0.59 mM) in the system benzil (48 mM)-galvinoxyl in benzene. (b) CW-ESR spectrum of galvinoxyl and (c) CW-ESR spectrum of TEMPO. In the case of J > 0, the net absorptive ClDEP of the radical should be observed with the same mechanism. Our experimental results show net emissive CIDEP and, thus, the J value should be negative. According to the mechanism discussed above, the magnitude of the ClDEP generated should depend on the efficiency of triplet quenching process. The rate of triplet quenching drastically changes depending on the relative energy between TI and Dl, and two quenching mechanisms are considered in triplet-doublet systems: one is energy transfer from triplet molecules to doublet radicals, which is possible in the system where the TI energy is higher than the DI energy, and the other is the enhanced intersystem crossing of the triplet state” by the perturbation of radicals, which is often observed in the system where the TI energy is lower than the DIenergy. The latter process is too slow to explain the rise time of CIDEP (51 ps). Considering that a typical rate constant of this process is about 106 M-I s-l and the concentration of TEMPO is about IO-’ M, the lifetime of triplet states determined by this process would be about 1 ms. On the other hand, energy transfer is considered to occur under diffusion controlI8 and the lifetime estimated is about 0.1 ps, which is fast enough to generate a CIDEP with a rise time of about 1 ps. To clarify the role of energy transfer in the generation of the net emissive CIDEP, we examined the spin polarization in several tripletdoublet systems where the energy between TI and DI was varied. Triplet molecules used were benzophenone, benzil, phenazine, and anthracene and radicals were TEMPO and galvinoxyl. Galvinoxyl is known as an efficient triplet quencher. Figure 3a shows spinpolarized galvinoxyl in the benzil-galvinoxyl system. Galvinoxyl has a hyperfine structure in a narrow magnetic field region compared to TEMPO and its gvalue is estimated to be 2.00410 from the center of its hyperfine structure. Figure 4 shows an energy diagram of these molecules.19 We estimated the D, energies of TEMPO and galvinoxyl to be higher than 18 OOO and 11 OOO cm-I, respectively, from their absorption spectra. TR-ESR spectra were measured for various triplet molecules in the presence of TEMPO and galvinoxyl, whose concentrations were kept (17) Gijzeman, 0.L. J.; Kaufman, F.; Porter, G. J. Chem. Soc., Faraday Trans. 2 1973,69, 727. (18) Kuzumin,V. A.; Tatikolov, A. S.Chem. Phys. Lerr. 1978, 53,606. (19) Murov, S. L. Handbook of Photochemlstry; Marcel Dekker Inc.: New York, 1973.
C)
d)
and TR-ESR spectra of TEMPO (0.61 mM) and galvinoxyl (0.23 mM) mixtures containing (a) benzophenone (37 mM), (b) benzil (63 mM), (c) phenazine (56 mM), and (d) anthracene (56 mM). Figure 5. CW-
constant in each system. Emissive ClDEP spectra of TEMPO and galvinoxyl are observed in benzophenone and b e n d systems (Figure 5a,b), where energy transfer is possible for both radicals. On the other hand, in the phenazine and anthracene systems (Figure 5c,d), the relative CIDEP intensity of TEMPO to galvinoxyl became weak in comparison to that of benzophenone and benzil. Since energy transfer is only operative to galvinoxyl but not to TEMPO in these systems, the CIDEP signals of TEMPO whould be generated through enhanced intersystem crossing, diminishing the TEMPO signals of the energy transfer channel. These results suggest that energy transfer makes a major con-
-
The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 9133
Hyperfine-Dependent CIDEP
A
2 mT
a)
A 0.35ps
4
1.75 ps
Q
C)
Figure 6. Hyperfine-dependent ClDEP spectra of OTEMPO (0.60 mM) in the systems of OTEMPO and triplet molecules in benzene. The systems are (a) phenazine (8.3 mM)-OTEMPO and (b) acetone (0.68 M)-OTEMPO.
TABLE 11: Hypefine Dependence of ClDEP Intensity triplet molecule benzophenone 4-aminoacetophenone 4-benzoylbiphenyl bend
I-naphthol 1-chloronaphthalene phenazine I -nitronaphthalene biacetyl 9, IO-acenaphthenequinone acetone
ratio of the CIDEP intensity for each hyperfine peak (M-,:Mo:M+,)' 1.00:0.95:0.92 1.00:0.93:0.78 1.00:0.89:0.79 1.00:0.89:0.78 I .00:0.89:0.69 1.00:0.76:0.42 1.00:0.70:0.50 1.00:0.65:0.44 I .00:0.59:0. I8 1.00:0.500.14 1.00:0.41:-0.24
" M ,represents the hyperfine peak due to the M I= i nuclear spin state of the nitroxide radical. A positive sign indicates emissive polarization, while a negative sign indicates an absorptive one. The ratio of CIDEP intensity include about 5% experimental error. tribution to CJDEP generation in triplet-doublet systems. Hyperfine Dependence of CIDEP in a Triplet-Doublet System.
Figure 6 shows the TR-ESR spectra of phenazine-OTEMPO and acetone-OTEMPO systems. It is noteworthy that the relative intensity of the three hyperfine lines is different, especially the phase of the CIDEP signal, which changes from emission at MI = -1 and 0 to absorption at M I = 1 in the acetone-OTEMPO system. Hyperfine-dependent ClDEP was observed in various systems. The most intense line is the hyperfine peak at the Mr = -1 nuclear spin state of the nitrogen atom. The emissive CIDEP intensity diminishes with an increase in quantum number MI. Several examples in triplet-OTEMPO systems are summarized in Table 11. We measured the ClDEP in many other tripletdoublet systems not shown in Table 11, but the hyperfine dependence is not so strong for most triplet molecules: the typical ratio (M-l:M,,:M+l)of the CIDEP intensity is about 1:0.9:0.8 and acetone is only one example showing polarity inversion in the hyperfine structure. Generally, the decay profile of the CIDEP signal depends on the magnetic relaxation time and microwave power as well as the decay of radicals themselves. Of course, decay of radicals does
2.25~s
Figure 7. TR-ESR spectra of OTEMPO (0.60 mM) in the system acetone (0.68 M)-OTEMPO in benzene.
not affect relative intensity in hyperfine structure but only the integrated intensity of CIDEP. Magnetic relaxation time may depend on MI. If the decay rate of the CIDEP signal of the M I = 1 peak is faster than that of the MI = -1 peak, the CIDEP signal of M I= 1 would be weaker than that of MI = -1. Figure 7 shows CIDEP signals obtained with different delay times. The ratio of signal intensities of three hyperfine peaks does not change significantly in all gate times and hence it is concluded that magnetic relaxation time has no effect on the ratio of the CIDEP signal intensities in our system. CIDEP signals are reported to decay with beat where emissive and absorptive signals recur with time.20 However, as seen in Figure 7, no phase modulation with time was observed for all three hyperfine peaks within the first 2 ps after laser pulse. Thus, the hyperfine dependence of CIDEP signals must result from triplet-doublet interaction. These hyperfinedependent CIDEP spectra are very similar to the E*/A (emission/absorption) signal pattern of CIDEP in typical RPM.' Thus, we conclude that this E*/A-type signal consists of a total emissive signal due to RTPM and an E/A signal generated by some type of hyperfine-dependent interaction. Next, we will discuss this hyperfine-dependent interaction. Mechanism for the H y p e r f i i Dependence of the CIDEP Signal. The hyperfine interaction could yield the hyperfine-dependent CIDEP spectra. If the hyperfine interaction acts on the mixing of )Q-3/2) and ID1/2) states in addition to a zfs interaction, hyperfine lines of net emissive CIDEP have different relative intensity. However, the matrix element of the hyperfine interaction between )Q-3/2) and JD1/2) states is zero and hence the hyperfine interaction does not contribute this state mixing. As for the mixing of (Q-1/2) and ID1/2) and that of 1Q-3/2) and lD-l/2), hyperfine interaction is effective but its magnitude is thought to be small because the encounter pair exists for a short time in the crossing region compared to the mixing time due to the hyperfine interaction. Therefore, we should examine another mechanism. It is well-known that spin polarization by RPM' results from S-To mixing followed by a fast electron exchange interaction. We consider the similar process for a triplet-doublet system. The hamiltonian in this system is represented as (20) Hore. P. J.; McLauchlan,
K. A. J . Mogn. Reson.
1980, 36, 129.
The Journal of Physical Chemistry, Vol. 95, No. 23, 1991
9134
Kawai et al.
+ Mho + H(ZfS) where is the exchange interaction, Mho is the hyperfine interaction including Zeeman splitting, and MdS)is the zero-field H = Mex)
Sim.
splitting. They are given by
Mex) = -2J(sR*&)
(1)
+ gRSR)'HO + xATiIl(k)'ST+ ~Ap.,I)'& M"s) = D(&$ - 1 / 3 & 2 ) + E(S,,Z - S J )
Mho = p(g&
(2)
J
I
(3)
where subscripts R and T represent the radical and triplet molecule, respectively. S is the electron spin angular momentum operator, g is the g tensor, @ is the Bohr magneton, and Ho is the external magnetic field. AT, and AR, are the hyperfine tensors of the ith and jth nuclei. IT, and I are the nuclear spin angular momentum operators of the ith anvjth nuclei. k and I represent nuclear spin states of triplet and doublet molecules, respectively. D and E are the zero-field splitting constants of the triplet molecule and ti is the zero-field-splitting axis of the triplet molecule. First, we consider the mixing of IQI /2) and (Dl/ 2 ) states and also that of 1Q-1/2) and (D-1/2) states by the perturbation of eqs 2 and 3. In RPM, if J is constant for the period of S-To mixing with its rate of wab,$aired radicals must exist at a separation of J = @ab for lO-'-IO s, which is highly improbable. Mixing rates of IQ1/2)-JDI /2) states and lQ-l/2)-lD-l/2) states were estimated to be the same order of wab as discussed above. Therefore, in analogy with RPM, we assume that the triplet-doublet pair experiences an initial period of Q D mixing by Mho+ HCds) from t = 0 to t , followed by an exchange interaction flex) during the reencounter of the pair caused by diffusion in the period from t , to t2. We omitted the anisotropic terms of g tensors and hyperfine tensors because the rapid free rotations of doublet and triplet molecules in the period of slow Q-D mixing would average the effect of anisotropic interaction and hence the anisotropic terms did not contribute to the state mixing. The effect of Mds) would also be averaged to zero during Q-D mixing and, therefore, does not contribute to this mixing. The mixing among different &man levels is considered to have a much smaller mixing rate compared to IQ1/2)-)D1/2) and [Q-l/2)-[D-l/2) mixing because of the large energy difference of the states under our experimental condition of high magnetic field (about 340 mT). Thus, we also neglected the mixing among Zeeman levels. As discussed before, the doublet pairs mainly disappear through triplet quenching and the quartet pairs return to the initial spin state. The time evolution of the wave function is given as * ( t ) = cQ(t)lQ1 / 2 M ) + cD(t)lD1/2,kl) with CQ(0)= 1 and CD(0) = 0. The perturbations described above mix the IQ1/2) and ID1 /2) states as follows: CQ(f2) = cos (wkltl) cos ( J ( t z - t , ) ) + i cos (wkirl)sin ( J ( t 2- t , ) ) (4) cD(t2) = -sin ( w k p I )sin (2J(r2- tl)l - i sin ( w k l t l )cos 1241, - r , ) ] ( 5 ) where wkl is the rate of the IQ1/2)-(D1/2) mixing. The value of wk/ is obtained as matrix elements of Mho. w&/ = (Ql/2,kllMh"Dl/2,kl) = (2'/'/3)1(gT - gR)BHO + zaTiMTi(k)- zaRjMR~(')l i
I
where a, is the isotropic hyperfine coupling constant and M,is the magnctic quantum number of the ith nucleus. Electron spin polarization of separated doublet radicals pR+ is obtained by
=
(*(t2)lsRzl*(t2)) = ( 1 /6)(C~*(t2)Cq(t2)CD*(rZ)CD(t2)1 - (21'2/3)lCQ*(t2)CD(tZ) + CD*(r2)CQ(t2)] (6) Consequently, we obtained the magnitude of pR+ from eqs 4-6 as follows
pR+
PR+ =
(1/6) cos (2wkltl)+ (2II2/3) sin (2wkltI)sin 13J(t2 - t , ) ]
Obs.
Figure 8. (a) Stimulated spectra of OTEMPO obtained by eq 7, (b) assuming net emissive polarization and (c) by a sum of (a) and (b) with a ratio of 7:l and observed spectrum of the acetone-OTEMPO system. The parameters used are aN = 1.65 mT and g (TEMPO) = 2.005 86. Acetone's g value is not reported and we assumed it to be 2.00300.
The positive sign indicates the emissive electron spin polarization. As for the state mixing of JQ-1/2)-)D-1/2), similar results were obtained for pR- by the same treatment. The total electron spin polarization pR is given by the sum of pR+ and pR- as follows: p R = pR+
+ PR-
[2(2'12)/3] sin {3J(t2- rl)l(sin (2wkltl)]
In the fluid system, molecular motions are described by the diffusion theory, and we must calculate the time averaged value of pR according to the diffusion theory. As the second term included the exchange interaction by the reencounter process, we obtained its time-averaged value employing the same treatment as diffusion-controlled RPM1 as follows: (PR)I = ( 1 / 3 ) 1 0m P ~ ( t ~ / 7 ) - 3d(f1/7) /2 =
[4(24"2/91 (sin
1314(t2- t l ) l ) ( ~ / ~ ~ ~ ) ~ k l ( ~ ~ (7) k l ~ ~ ) 1 / 2 / ~
where 7 is the time between diffusive displacement of the radical and the triplet molecule and (sin ( 3 M ( t 2 - t , ) ) )is the averaged value of sin {3J(tz- t , ) ] . This crude results predict that the magnitude of CIDEP intensity depends on each hyperfine line. Figure 8a shows the CIDEP spectrum of OTEMPO simulated with eq 7 assuming that the hyperfine structure of the triplet molecule is single peak at the g center. Observed spectra of OTEMPO are reproduced by a sum of this hyperfine-dependent CIDEP and net emissive CIDEP indicated in Figure 8b. The simulated spectrum shown in Figure 8c well reproduces the observed spectrum in acetone-OTEMPO. Acetone shows the strongest hyperfine dependence among the systems studied here. At the present stage, it is not clear why acetone gives such a strong hyperfine dependence, but the following discussion makes the same observations about the magnitude of hyperfine dependence. First, rapid rotation of small acetone molecules partially averages out triplet zero-field splitting and hence weakens the net emissive mechanism. Second, relatively low viscosity of the acetone-OTEMPO system due to a high concentration of acetone results in shortening of the interaction time in the avoided crossing region. This also attenuates the net emissive signals and thereby the hyperfine dependence stands out, which is similar to S-T-,mixing in RPM. Acknowledgment. We are grateful to the reviewer of this paper for his very kind comments and suggestions. Registry No. TEMPO, 2564-83-2; benzophenone, 1 19-61-9; benzil, 134-8 1-6; phenazine, 92-82-0 anthracene, 120- 12-7; galvinoxyl, 237018-5.
