Time-Resolved ESR Study of Spin Exchange Processes in the

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J. Phys. Chem. 1996, 100, 1622-1629

Time-Resolved ESR Study of Spin Exchange Processes in the Photoreduction of 9,10-Anthraquinone-1,5-disulfonate D. Beckert* Max-Planck-Group “Time ResolVed Spectroscopy”, UniVersity of Leipzig, Permoserstr. 15, 04303 Leipzig, Germany

R. W. Fessenden Radiation Laboratory and Department of Chemistry and Biochemistry, UniVersity Notre Dame, Notre Dame, Indiana 46556 ReceiVed: April 17, 1995; In Final Form: October 11, 1995X

The photoreduction of 9,10-anthraquinone-1,5-disulfonate by 2,2,6,6-tetramethylpiperidine in aqueous solution was studied on the nanosecond and microsecond time scales using time-resolved optical and ESR measurements. The primary electron transfer from the amine to the quinone triplet generates solvent-separated radical ion pairs which then diffuse apart. The lifetime of the 9,10-anthraquinone-1,5-disulfonate triplet in aqueous solution was determined to be 135 ns and the electron transfer rate constant from 2,2,6,6-tetramethylpiperidene to be kN ) 5.7 × 108 M-1 s-1. The corresponding rate constant for quenching by 2-propanol is lower by 2 orders of magnitude at 1.4 × 106 M-1 s-1. This system allowed both radicals of the pair, the anthraquinone anion and (for the first time) the aminyl radical, to be studied by ESR. The radicals are spin polarized (CIDEP) by both the triplet and geminate radical pair mechanisms. Time-resolved ESR experiments were carried out with the transient nutation and Fourier transform techniques. Because of steric hindrance, the recombination reaction in the quinone-piperidine system is suppressed and, therefore, the spin dynamics are dominated by spin polarization, relaxation, and spin exchange. A quantitative analysis by modified Bloch equations allowed polarization factors (triplet mechanism and radical pair mechanism), spin relaxation times (T1 and T2), and the spin exchange rate constants between the anthraquinone anion and aminyl radicals to be obtained. The spin exchange rate constants between quinone-aminyl radical pairs and between aminyl-aminyl radical pairs are identical and are in the diffusion-controlled limit (kex ) 4.5 × 109 M-1 s-1).

1. Introduction Chemically induced dynamic electron polarization (CIDEP) investigations have been established as a method to study radical-radical interactions in solution.1 Time-resolved ESR studies on transient radicals exhibiting CIDEP effects have proven invaluable for radical identification and for obtaining structural and kinetic information on free radicals occurring in fast chemical reactions. The kinetic behavior of time-resolved ESR signals gives insight into the interactions affecting polarization and relaxation of radicals. The recent experimental advances2 in time-resolved ESR techniques and pulsed UV lasers have given the possibility for measuring radical polarization and relaxation behavior at very short times. Nonequilibrium magnetization of free radicals (CIDEP) is generated mainly by the triplet mechanism (TM) and the radical pair mechanism (RPM). The triplet mechanism produces a net polarization by spin-selective intersystem crossing (S1 f T1) of optically excited molecules whereas the radical pair mechanism changes the population of the two electron spin levels by the combined effect of hyperfine mixing between S and T0 and exchange interaction within radical pairs. The RPM operates both during the initial separation of a geminate pair of radicals and during random subsequent encounters in which the radicals react. In a radical-radical collision there is always a competition between RPM polarization, spin exchange, and chemical reac* To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, December 15, 1995.

0022-3654/96/20100-1622$12.00/0

tion. Whereas recombination reactions occur only in S-pair states and in strong collisions, spin exchange takes place in each encounter of two radicals (both S-pairs and T-pairs). Depending on the strength of the exchange interaction J(r) in a radical pair collision, relaxation will be dominant (J(r)τe . 1, where τe denotes an effective encounter time) or CIDEP-RPM polarization will be generated (J(r)τe ) 1) whereby a second condition for CIDEP is the phase correlation in the encounter of previously paired radicals (cf. ref 9). Hence, the strength of a radical pair collision is measured by the exchange interaction J(rc) times the encounter time τe at the collision distance rc, and therefore, the diffusion and impact parameters for radical pairs play an important role in the dynamics of the radical magnetization detected by time-resolved ESR. Therefore, the analysis of timeresolved ESR experiments has to include the influence of RPMCIDEP, relaxation, spin exchange, and chemical recombination. The phenomenon of Heisenberg spin exchange was initially observed in through line-broadening effects under ESR steady state conditions with stable nitroxyl radicals.3,4 The first qualitative observations of effects ascribable to Heisenberg spin exchange between reactive radicals were in time-resolved ESR experiments on the hydrated electron generated by pulse radiolysis.5 The first quantitative measurements were in similar experiments an small alkyl radicals in aqueous solution.5,6 It could be concluded from the latter experiments that the “effective” distance of spin exchange is 2-3 times larger than the reaction distance. The theoretical aspects of the influence of spin exchange on radical pair polarization and spin-lattice relaxation are reviewed in refs 7 and 8, whereas a complete © 1996 American Chemical Society

Photoreduction of 9,10-Anthraquinonedisulfonate theoretical treatment of the time evolution of the magnetization of exchanging radicals with modified Bloch equations is given in ref 9. Furthermore, the dependence of radical pair S-T0 polarization PST and exchange rate constant kex on molecular parameters, specifically the distance of closest approach rd, the diffusion coefficient D, and the collision time τe, are treated in detail in ref 10. In this paper, we report time-resolved ESR experiments on a pair of radicals which can undergo spin polarization and spin exchange but their chemical recombination is suppressed by steric hindrance. The photolysis of quinones produces strongly polarized triplet states and, by fast triplet quenching, this triplet polarization can be transferred to the doublet radical products. The triplet quenching of quinones by alcohols and amines has been widely investigated by optical, ESR, and CIDEP methods.11-13 From these investigations it was found that the first step in the triplet quenching is an electron transfer in the quinone triplet-amine encounter pair which generates a solventseparated ion pair. Proton transfer may occur as a second step to produce neutral radicals which escape from the solventseparated radical pair. If a hydrogen atom is present on an R-carbon, then the N-centered radical can transform to a C-centered R-amino alkyl radical which is a good reducing agent. This radical can then disappear by reducing another quinone. Up to now only semiquinone radicals have been observed because the amine radical cations or the neutral amine radicals disappear by secondary reaction with the solvent or react with the quinone too rapidly to detect by time resolved transient nutation ESR methods. In this study of the photoreduction of 9,10-anthraquinone1,5-disulfonate (AQDS) by 2,2,6,6-tetramethylpiperidine (TMPIP) in aqueous solution, the AQDS radical anion and the TMPIP aminyl radical are observed as long-lived radicals with strong CIDEP and spin exchange effects. Results from both steady state and time-resolved ESR experiments (transient nutation ESR and FT-ESR) as well as optically detected nanosecond laser photolysis experiments were included in these studies in order to understand the primary chemical reaction and the CIDEP and spin exchange effects quantitatively. 2. Experimental Section In the steady state ESR experiments, radicals were produced by photolysis of aqueous solutions with a 1 kW Hg-Xe lamp in a housing with an elliptic mirror. To reduce heating effects of the sample, the visible and IR wavelengths were removed by a CoSO4-NiSO4 filter solution. The ESR spectrometer was described elsewhere in detail.14 The time-resolved ESR equipment was the same as described in ref 15. The sample was excited by a Lumonics HyperEx400 excimer laser operating with XeCl (308 nm) at 25 Hz. The laser pulse length was about 20 ns, the energy was typically 25-50 mJ per pulse, and the beam cross section was 0.9 cm2. ESR time profiles typically represent the average over 1002000 repetitions. The ESR cavity used was a Varian V-4531 multipurpose cavity with a 0.4 mm thick silica flat cell. The solution flowed through this cell at about 20 mL/min. and the solution temperature at the exit from the cell was about 28 °C. The Fourier transform ESR experiments were done with the equipment described in ref 16. The photolysis of anthraquinone1,5-disulfonate was with an excimer laser (Lambda Physik, LPX 105ESC) using a pulse energy of 10-15 mJ at 308 nm. The microwave cavity used was the Bruker split-ring module ER 4118X-MS-5W and the energy of the microwave pulse was 20 W (τ(π/2) ) 80 ns). In order to improve the base line of the FT-ESR spectra the experimental free induction decays (fid) were extrapolated into the dead time by a LPSVD procedure.17

J. Phys. Chem., Vol. 100, No. 5, 1996 1623 The nanosecond laser flash photolysis equipment has been described in detail elsewhere.18 Briefly, pulses (308 nm, 15 ns, 5 mJ) from a Lambda Physik EMG 101-MSC excimer laser were used for excitation in a rectangular cross-beam geometry. The rectangular quartz cell used has a path length of 5 mm. The transient absorbances in the reaction at a preselected wavelength were monitored by a detection system consisting of a monochromator and a photomultiplier tube. The signal from the photomultiplier was processed by a 7912AD Tektronix transient digitizer controlled by a Digital Equipment Corp. LSI11/2 microcomputer. 9,10-Anthraquinone-1,5-disulfonate disodium salt, 1,5-AQDS (Aldrich) and 2,2,6,6-tetramethylpiperidine, TMPIP (Aldrich) were used as received. Some experiments with freshly distilled TMPIP gave exactly the same results as without distillation. The water used was from a Millipore Milli-Q system. Normally, no extra base was added; the amine caused the pH to be about 11. 3. Reaction Scheme and Theoretical Model The photoreduction of 9,10-anthraquinone-1,5-disulfonate (AQDS) by 2,2,6,6-tetramethylpiperidine (TMPIP) in water can be described by the following general reaction scheme:19,20

excitation and intersystem crossing: hν

ISC

AQDS 98 AQDSS1 98 AQDST1*

(1)

triplet deactivation by the solvent: kL

AQDST1* + H2O 98 {AQDS‚‚‚H2O} f AQDSOH• + AQDS•- + H+ (2) electron transfer: kN

AQDST1* + R1-NH-R2 98 {AQDS•-*‚‚‚R1-NH•+*-R2} (3) In eq 1 the ISC preferentially populates the upper triplet level of AQDST1 (emissive polarization) which is then depopulated by the competition of triplet spin relaxation 3T1 and chemical deactivation by the solvent and the amine scavenger with rate constants kL and kN, respectively (see section 4.2). The mechanism of reaction of AQDS triplet with water (eq 2) is not clear21 but is not important for the following discussion. The first step in the photoreduction of the AQDS triplet is an electron transfer from the amine to the quinone yielding a solvent separated radical ion pair. Depending on the concentration of TMPIP these radicals are emissively polarized by the TM (denoted by *) and during interaction in the radical pair an RPM polarization can also be generated. The escaped radicals with both TM and RPM polarization are denoted by **. The g factors of the two radicals are very similar so that the quinone radical anion is dominated by triplet polarization with a small contribution of RPM polarization in its spectrum (cf. section 4.4). In the quantitative analysis of the AQDS•-** time profiles only TM polarization must be considered because RPM polarization can be neglected in the central line. From optical measurements it is known that the lifetime of solvent-separated radical ion pairs in water is less than 10 ns.22 With the escape of the radical ion pair from the solvent cage, the amine radical cation will lose the amine proton and escape as a neutral aminyl radical:

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escape from solvent-separated radical ion pair: kesc

{AQDS•-*‚‚‚R1-NH•+*-R2} 98 •+ AQDS•-** + R1-NH **-R2 (4) (a)

After the escape of the radical ions from the solvent cage, the CIDEP is developed in the radical pair by S-T0 mixing (high field approximation) and at some subsequent time the amine cation will lose a proton to become the neutral radical. Spontaneous loss of the proton should be slow but a basecatalyzed loss is possible.23 The amine can act as the base and, at 50 mM concentration, a pseudo-first-order rate constant of about 2.5 × 108 s-1 would be expected. Thus the amine cation radical R1-NH•+**-R2 is expected to have a lifetime of 4 ns and most of the geminate pair polarization would be developed by this form of the radical together with the semiquinone radical anion.

loss of proton: R1-NH•+-R2 + B f R1-N•-R2 + BH+ (b)

(5)

The lifetimes of a and b are of the order of 0.5 ms because of the steric hindrance of the aminyl radicals and the Coulomb repulsion of the semiquinone radical anions. Therefore, recombination reactions and F-pair polarization need not be considered in the analysis of the time behavior of both radicals. In steady state ESR spectra of quinone radical anions the line width is often determined by degenerate electron transfer27 in eq 6: ket

AQDS•- + AQDS 98 AQDS + AQDS•-

(6)

This degenerate electron transfer could also be studied by timeresolved ESR experiments at high microwave detection field as a change in the saturation behavior of the time profiles.28,29 In the experiments described here this process need not be included in the kinetic analysis because at a concentration of 0.5 mM AQDS the exchange time constant is in the order of 100 µs (ket ≈ 108 M-1 s-1). Furthermore, the small RPM polarization that is observed in the AQDS•- spectrum shows that the degenerate electron transfer can be neglected on our time scale.30 In the following, the concentration of radicals is controlled by both AQDS and TMPIP. The concentration of triplets is determined by the concentration of AQDS (through the amount of light absorbed) and the efficiency of reactive quenching is determined by the concentration of TMPIP. The TM polarization will depend on the triplet AQDS lifetime: a higher TMPIP concentration will produce radicals more rapidly before the polarization of the triplet states has time to relax. In order to simulate the time profiles of both radicals an important assumption must be introduced. The ESR spectrum of AQDS•- consists of a splitting pattern of a triplet of triplets of triplets with an overall extension of 0.33 mT whereas the R1-N•-R2 spectrum is divided into a 1.56 mT triplet, each line of which has a multiline splitting of 0.0845 mT (cf. Figure 1). To allow a mathematical modeling of the ESR time profiles we divide the AQDS•- spectrum in the central line to a part in resonance (mar(t) with a degeneracy Ma) and the rest of the lines which are nonresonant (man(t) with the degeneracy (1 - Ma)). The R1-N•-R2 spectrum consists of three lines groups with an 1.56 mT splitting with the same center as AQDS•- (the small g value difference can be neglegted). To calculate the time

Figure 1. Steady state ESR spectrum with UV excitation of an aqueous solution of 0.5 mM 1,5-AQDS and 10 mM TMPIP. The modulation amplitude for recording the low- and high-field lines of the aminyl radical is enhanced by a factor of 16.

TABLE 1: g Values and Hyperfine Splitting Parameters of the AQDS•- Radical Anion and the R1-N•-R2 Radical radical

g value

hfs coupling (mT)

AQDS•-

2.004 28

R1-N•-R2

2.004 38

a(2H, 4,8) ) 0.129 a(2H, 2,6) ) 0.037 a(2H, 3,7) ) 0.006 a(N) ) 1.56 a(12H, CH3) ) 0.0847

profiles of the aminyl radicals, one line group of the main triplet is divided, in the same manner, into a resonant (mbr(t) with the degeneracy Mb) and an nonresonant part (mbn(t) with the degeneracy (1 - Mb)). To calculate the time profiles of AQDS•-** and of R1N•**-R2 we use a set of modified Bloch equations9 where the exchange is introduced with the exchange rate constants (kexaa[a]) for radical a-radical a collisions, (kexab[b]) for radical a-radical b collisions, and (kexbb[b]) for b-b encounters. Furthermore, we have to distinguish between the signal from radical a (1,5-AQDS•-) and radical b (R1-N•-R2) with their different resonant and nonresonant spectral parts. The complete set of equations to calculate the ma(t) and mb(t) is given in the Appendix. In eqs A1 spin exchange in {AQDS•-‚‚‚AQDS•-} encounters can be neglected because the Coulomb repulsion will prevent approach of both radicals close enough to enable overlapping of the wave functions. Therefore, in all calculations kexaa ) 0 is used. 4. Results and Discussion 4.1. Steady State UV ESR. The steady state ESR spectrum, under continuous UV photolysis, of a aqueous solution of 0.5 mM AQDS with 10 mM TMPIP is shown in Figure 1. The central part is the AQDS•- spectrum with a small contribution by the central group of the R1-N•-R2 spectrum. The lowfield and high-field groups of R1-N•-R2 are recorded with a modulation amplitude 16 times higher than the central part. The hfs splitting parameters and g values of both radicals are listed in Table 1 where the g values were determined by comparison that of SO3•- (g ) 2.003 1624). The spectrum in Figure 1 shows no indication of any spin polarization effects as a result of the long lifetime (≈0.5 ms) for both radicals and the rapid relaxation of the spin polarization after radical formation (microsecond time range). 4.2. Laser Photolysis Experiments. Nanosecond laser photolysis experiments with optical detection of the transients

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Figure 2. Transient absorption UV spectra of 1,5-AQDS in an aqueous solution following laser photolysis at λ ) 308 nm. (b) AQDS triplet in the time window of 20-35 ns, and (9) spectrum at 100 ns after the pulse (1 mM 1,5-AQDS with 10 mM TMPIP).

were also carried out in addition to time-resolved ESR on the microsecond time scale. The transient UV-vis spectrum of an aqueous solution of 1 mM 1,5-AQDS without any additional electron donor is shown in Figure 2 where the absorbance is taken for the time interval 20-35 ns after the laser pulse. The spectrum has only a broad band with the maximum at 380 nm with a shoulder from 440 to 480 nm. This band can be assigned to the 1,5-AQDS triplet in agreement with Loeff et al.25 With the addition of TMPIP (10-40 mM) to the solution, the decay becomes more rapid and a long-lived absorption is found which is attributed to AQDS•-. The spectrum of this component (Figure 2) shows peaks at 390 nm and about 500 nm in agreement with ref 25. The lifetime of the 1,5-AQDS triplet in pure water was determined as τ0 ) 135 ns (cf. eq 2, kL ) 7.4 × 106 s-1). The kinetics of triplet quenching by 2,2,6,6-TMPIP is shown in Figure 3. From the kinetic plots of τ-1 vs [TMPIP] and [2-PrOH] the triplet quenching rate constants were determined to be kN ) 5.7 × 108 M-1 s-1 and k2-PrOH ) 1.4 × 106 M-1 s-1. 4.3. Determination of the Radical Concentration. Spin exchange is a second-order process and the exchange rate is proportional to [a•] and [b•]. Therefore, to determine the rate constants kexab and kexbb, the concentrations of radicals a• and b• are needed. As usual in ESR spectroscopy, the ESR amplitude of the radical under consideration is compared with that of a known concentration of a stable radical. The experimental line shapes of the 1,5-AQDS•- central line groups measured point by point in field offset for a given time delays are shown in Figure 4. The line shape was also detected by the same method for the central component of the low- and high-field groups of R1-N•-R2. These experimental line-shape patterns were fitted by Gaussian (low concentration, field inhomogeneity) or Lorentzian functions (high concentration and large spin polarization of AQDS•-*) and included consideration of the overlapping tails of the nearest neighboring lines. The line widths obtained are listed in Table 2. Because of a baseline restoration function of the spectrometer the amplitude and line shape of the stable radical, Fremy’s salt, could be measured by the same procedure. The concentration of the Fremy’s salt could be determined from the optical absorbance ((242 nm) ) 1660 M-1 cm-1 26) independently. Hence, the concentration of each radical could be calculated from the areas of the absorption lines (amplitude and fitted line widths) by comparison to the values for Fremy’s salt. The concentrations so obtained are included in Table 2. The agreement of the concentrations of the two species is excellent.

Figure 3. Kinetic traces at 380 nm of the 1,5-AQDS triplet with 20 mM TMPIP. The inset shows the dependence of the first-order rate constant for quenching upon the concentration of TMPIP.

Figure 4. Line shapes of the central line groups of 1,5-AQDS•-* at low concentration (a, 0.25 mM 1,5-AQDS and 10 mM TMPIP) and at high concentration (b, 5.0 mM 1,5-AQDS and 50 mM TMPIP) determined from recordings at different field offsets. The time delay was 20 µs.

4.4. Time-Resolved ESR Profiles and Line-Shape Analysis. The ESR time profiles of the central line of AQDS•- and

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TABLE 2: ESR Line Widths and Concentrations of AQDS•- and R1-N•-R2 under Different Experimental Conditionsa R1-N•-R2

AQDS••-

sample

∆Bfwhh (µT)

[AQDS ] (µM)

I II

6 (Gaussian) 24 (Lorentzian)

16 370

∆Bfwhh (µT)

[R1-N•-R2] (µM)

not determined not determined lfl 50(5, L) 362 hfl 60(5, L)

a G ) Gaussian line shape, L ) Lorentzian line shape. Sample I: 0.25 mM 1,5-AQDS, 30 mM TMPIP in aqueous solution. Sample II: 5.0 mM 1,5-AQDS, 50 mM TMPIP in aqueous solution.

of the low- and high-field lines of R1-N•-R2 are represented in Figure 5. In each case the central line of the group was measured. The time profiles of the other lines in each line group are identical to that of the central line (only multiplied by a factor relating to the different degeneracy of the lines). The central line group of the aminyl radical R1-N•-R2 is covered by the strong emissively polarized quinone radical anion and could not be measured. The time-resolved spectrum of AQDS•is emissively polarized with a small RPM contribution (the total width of this spectrum is quite small) whereas the R1-N•-R2 spectrum has an E/A* pattern. These E/A* patterns are the result of the superposition of TM and RPM polarizations with a relatively strong contribution from RPM. In the low concentration range (Figure 5a-c) the polarization decays as a “single phase behavior” whereas the high concentration time profiles of R1-N•-R2 (Figure 5d-f) are characterized by a “two-phase behavior”. The fast decay is determined by the T1b relaxation and the slow change in the time profile is caused by the exchange of magnetization between AQDS•- and R1-N•R2. The influence of the spin exchange is minimized in Figure 5a-c by a low radical concentration (0.25 mM AQDS) and by a small triplet polarization of AQDS•- (30 mM TMPIP) whereas the time profiles in Figure 5d-f are very strongly influenced by the spin exchange process (high radical concentration, 5.0 mM AQDS; high TM polarization, 50 mM TMPIP). Note particularly the growing portion after 7 µs of Figure 5f. Even though the relaxation time of the aminyl radical is relatively short, the line is pushed toward emission by the inverse polarization in AQDS•-. This effect was only present at high concentrations of both AQDS and TMPIP and so must clearly come from the spin exchange process. In addition to the transient nutation ESR (Figure 5), Fourier transform ESR experiments1c,16 were carried out on the same system. With FT-ESR the mz component of the magnetization is detected and, therefore, the value of T1 could be determined more directly. Furthermore, the line shape of each line group of both radicals could be measured independently. In Figure 6 the time behavior of mz(AQDS•-*) is represented for a sample with 1 mM 1,5-AQDS and 50 mM TMPIP. The signal rise in the first 100 ns has no chemical origin and is caused by the experimental response time. Figure 7 shows the FT ESR spectrum of 1,5-AQSD•-* at a delay between laser pulse and π/2-microwave pulse ∆t ) 50 ns. This spectrum is emissively polarized and the broad background line belongs to the central group of the aminyl radical R1-N•*-R2. A separation of the two spectra was not tried. The mz(AQDS•-*)-time profile can be described by a simple exponential decay from the emissively polarized state to the thermal equilibrium magnetization with the time constant T1. From the quantitative analysis of mz(t,AQDS•-*) T1 and the triplet polarization factor could be determined (cf. Table 3). The quantitative analysis of the 1,5-AQDS•-* and R1-N•*R2 transient nutation ESR time profiles (Figure 5) was carried

out with the eqs A1 and A2 given in the Appendix. The spin polarization is considered as initial geminate polarization only. F-pair polarization was not included because recombination reactions are restricted by steric hindrance and the lifetimes of both radicals are in the millisecond range. In order to minimize the number of free parameters in the fitting procedure the following assumptions are introduced: 1. T1 values are taken from FT-ESR results (cf. Table 3). 2. The radical concentrations were determined independently by comparison with the steady state signal from Fremy’s salt (cf. section 4.3). Furthermore, the relative concentration of radicals was calculated by the optical absorbance at the 1,5AQDS concentration used. 3. The B1 field strength in the cavity was determined by the Torrey oscillations on the AQDS•-* central line at low radical concentration. 4. No magnetic field inhomogeneity was included in the calculations. In most cases the line width determined by spin exchange (AQDS•-) or the natural width (aminyl) is larger than the field inhomogeneity. 5. The scaling parameter between the calculated and observed curves was required to be the same for both radicals. The results of the fitting procedure are represented in Figure 5 where the lines show the simulated time profiles. In order to prove the significance of the fit parameters, the time profiles were calculated for experiments with various quinone concentrations (0.25-5.0 mM) to change the radical concentration and for the dependence on the amine concentration (10-80 mM) to change the initial polarization, respectively. The parameters obtained are listed in Table 3. The fitted curves with the parameters in Table 3 describe the experimental results in the expected manner. The relaxation times T1 and T2 of AQDS•-* decrease slowly with the radical concentration (T1 ) 3.2 µs, T2 ) 1.5 µs at 1 mM 1,5-AQDS to T1 ) 2.2 µs, T2 ) 1.1 µs at 5 mM 1,5-AQDS) and the relaxation times T1 and T2 of R1-N•R2 are independently of radical concentration. The origin of this decrease in relaxation times is not clear because spin exchange is explicitly included. The triplet polarization increases with the TMPIP concentration in agreement with the faster electron transfer rate from the amine to the quinone triplet (Figure 8) whereas the radical pair polarization in the low-field and high-field lines of R1-N•-R2 behaves differently. The RPM polarization of the low-field lines decreases with the TMPIP concentration whereas it increases for the high-field lines. A symmetrical RPM from the geminate separation is not necessarily expected at lower amine concentration because the radicals in the pair are the semiquinone anion (g ) 2.0043) and the amine cation radical (g ) 2.003523). Thus the lowfield line should have a larger polarization and this polarization would be preserved when the proton is lost. At higher amine concentration, the transformation from cation to aminyl radical would occur faster during development of polarization and more polarization would be from a pair of radicals with similar g factors. The experiments seem to behave in an opposite way. An experiment with 20 mM amine was done and the 0.1 M KOH added to increase the rate of conversion. The polarization increased somewhat for all lines (both TM and RPM) but the effect was not like that with more amine. The spin exchange rate constants kexab and kexbb could be determined with kexab ) kexbb ) 4.5 × 109 M-1 s-1. Because the exchange rate constants kexab and kexbb influence the ESR time profiles similarly the error limits of these rate constants are approximately 30%. The spin exchange process influences not only the time profiles but also strongly affects the line shape of AQDS•-. In order to estimate the line broadening effects of spin exchange,

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J. Phys. Chem., Vol. 100, No. 5, 1996 1627

Figure 5. Transient nutation ESR time profiles of the centre line of the 1,5-AQDS radical anion and of the centre line of the low-field (lfl) and high-field (hfl) line groups of the aminyl radical R1-N•-R2. Sample: (a, b, c) 0.25 mM 1,5-AQDS and 30 mM TMPIP and (d,e,f) 5.0 mM 1,5-AQDS and 50 mM TMPIP in aqueous solution. (a, d) lfl of R1-N•-R2; (b, e) AQDS•-; and (c, f) hfl of R1-N•-R2.

Figure 6. FT-ESR time profile of the 1,5-AQDS radical anion (central line) with 1 mM 1,5-AQDS and 50 mM TMPIP in aqueous solution. The fitted parameters that fit this exponential decay are T1 ) 2.6 µs and polarization factor P ) -12.2.

the line shapes were measured for the AQDS•- central line group in the low and high exchange range after relaxation of the initial polarization (∆t > 20 µs). Figure 4a,b shows the results

Figure 7. FT-ESR spectrum of 1,5-AQDS•-* at a delay time of 50 ns with the same sample as in Figure 6.

obtained for both concentration ranges with the point by point method (cf. section 4.3). At low concentration the triplet with the smallest coupling (a(2H) ) 6.0 µT) could be resolved with a line width ∆Bfwhh ) 5.0 µT. This Gaussian line shape represents the field inhomogeneity in this experiment. In the

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TABLE 3: Relaxation Times T1 and T2, Polarization Factors, and Spin Exchange Rate Constants of AQDS•- and R1-N•-R2 Determined by Fitting the ESR Time Profile with Eqs A1 and A2a R1-N•-R2 T1 (µs) T2 (µs) PTM PRPM kexab (M-1 s-1) kexbb (M-1 s-1)

AQDS•-

lfl

hfl

3.2-2.2 1.4-1.1 -2.8 to -12.5 0

1.2 0.20-0.14 -2.8 to -12.5 11.5-5.0 4.5 × 109 4.5 × 109

1.2 0.20-0.14 -2.8 to -12.5 11.5-15.5

Figure 9. FT-ESR spectrum of the low-field line group (lfl) of the aminyl radical R1-N•*-R2. Delay time τd ) 50 ns; field offset -1.6 mT; number of repetitions 1000; sample as in Figure 6.

Figure 8. FT-ESR spectrum of 1,5-AQDS•-* with the same conditions as in Figure 7 with triethylamine as triplet quencher.

high concentration case, the triplet with the hfs coupling a(2H) ) 0.037 mT could be resolved and the line-shape function is a Lorentzian with ∆Bfwhh ) 24 µT or T2 ) 0.47 µs. The value expected from a combination of the T2-1 value in Table 1 together with the product of the concentration and spin exchange rate constant is in excellent agreement at 0.47 µs. The influence of spin exchange on the line shape could be seen more clearly in Figures 7 and 8 where the FT-ESR of the central line groups of AQDS•-* are compared in experiments with the triplet quenchers TMPIP and triethylamine, respectively. With triethylamine as an electron donor for the 1,5-AQDS triplet the line-shape function is a Gaussian with a line width ∆B1/2 ) 2.0 µT whereas in the case of TMPIP as electron donor the line shape is a Lorentzian with a line width 3 times higher. That means the line width in Figure 8 is determined by the field inhomogeneity, and in the 1,5-AQDS/TMPIP system the line shape is caused by the influence of the spin exchange process. The line shapes of the low- and high-field line groups of the aminyl radical R1-N•-R2 are difficult to measure because the line width is large and the signal amplitude decreases strongly with time. Therefore, the low-field line group of the aminyl radical was recorded with FT-ESR using a large number of repetitions and the FID was extrapolated by the LPSVD method. The result is shown in Figure 9 for a delay time τd ) 50 ns. The 13-line splitting by the 12 methyl protons (a(12H) ) 0.0847 mT) is clearly seen and from a fitting calculation we obtain a line width of ∆Bfwhh ) 75 µT. The corresponding T2 value is 150 ns in good agreement with the value obtained from this analysis of the transient nutation time profiles (Table 3). A paper with more detailed results on the aminyl radical kinetics is in preparation. 5. Conclusions In the photoreduction of 1,5-anthraquinonedisulfonate with 2,2,6,6-tetramethylpiperidine, both radicals generated by an electron transfer from the amine to the quinone triplet could be

observed by time-resolved ESR and optical measurements. The ESR spectra of the radicals AQDS•- and R1-N•-R2 show strong CIDEP effects produced by both the triplet mechanism and geminate radical pair interactions. Furthermore, the time behavior of the ESR spectra is strongly influenced by a spin exchange process between the quinone radical anion and the neutral aminyl radical. With modified Bloch equations which consider spin polarization, relaxation, and exchange, all parameters included in the model could be determined. The dependence of these parameters on the concentration of both reactants is consistent with the proposed reaction model. Acknowledgment. The research described herein was supported by the Office of Basic Energy Sciences of the Department of Energy. This is Contribution No. NDRL-3767 from the Notre Dame Radiation Laboratory. D.B. is greatly appreciative of support by a grant from the Contract DE-AC02-76ER00038 with the U.S. Department of Energy. The financial support by the Deutsche Forschungsgemeinschaft is also acknowledged. Appendix A In order to calculate theoretical time profiles for the exchange model given in the text, Bloch equations are extended with additional terms which describe the transportation of magnetization from one radical to another in strong radical-radical collisions. Because of the different structure of the a and b radicals we have to consider two different cases depending on which radical is observed. Furthermore, for each radical we have to distinguish between the resonant and nonresonant parts of the spectrum because under our experimental conditions the B1 field is in the medium saturation case. Case 1: AQDS•- Is Observed (Radical a, [a]).

dmarx/dt ) -marx/T2a + ∆ωa mary - kexab[b]marx

(A1a)

dmary/dt ) -∆ωamarx - mary/T2a - kexab[b]mary - ω1marz (A1b) dmarz/dt ) ω1mary - {marz - mao*Ma}/T1a kexaa(1 - Ma)[a]marz + kexaaMa[a]manz - kexab[b]marz + kexab[a]Ma{mb1z + mb2z + mb3z} (A1c) dmanz/dt ) -{manz - mao*(1 - Ma)}/T1a - kexaaMa[a]manz + kexaa(1 - Ma)[a]marz - kexab[b]manz + kexab(1 - Ma)[a](mb1z + mb2z + mb3z)

Photoreduction of 9,10-Anthraquinonedisulfonate

dmbiz/dt ) -{mbiz - mbio}/T1b - kexabMa[a]mbiz + kexab[b]/3marz - kexab(1 - Ma)[a]mbiz + kexab[b]/3manz 2kexbb[b]/3mbiz + kexbb[b]/3{mbjz + mbkz} (A1d) where the indices i, j, and k fulfill the relations: {i,j,k} ) {1,2,3}; {2,3,1}, and {3,1,2}. 1 denotes the low-field line of R1-N•-R2, 2 the center line, and 3 the high-field line. Case 2: Line i of R1-N•-R2 Is Observed (Radical b, [b]/3).

dmaz ) {maz - mao}/T1a - kexab[b]maz + kexab[a](mbirz + mbinz) - 2kexbb[b]/3maz + kexbb[a]{mbjz + mbkz} (A2a) dmbirx ) -mbirx/T2b + ∆ωbmbiry - kexab[a]mbirx kexbb(1 - Mb)[b]mbirx - 2kexbb[b]/3 mbirx (A2b) dmbiry ) -mbiry/T2b - ∆ωbmbirx - ω1mbirz - kexab[a]mbiry kexbb(1 - Mb)[b]mbiry - 2kexbb[b]/3mbiry (A2c) dmbirz ) ω1mbiy - {mbirz - mbo*Mb}/T1b - kexab[a]mbirz + kexabMb[b]/3}maz - kexbb(1 - Mb)[b]/3mbirz + kexbbMb[b]/3mbinz - 2kexbb[b]/3mbirz + kexbbMb[b]/3(mbjz + mbkz) (A2d) dmbinz ) -{mbinz - mbo*(1 - Mb)}/T1b - kexab[a]mbinz + kexab(1 - Mb)[b]/3}maz - kexbbMb[b]/3mbinz + kexbb(1 - Mb)[b]/3mbirz - 2kexbb[b]/3mbinz + kexbbMb[b]/3 (mbjz + mbkz) (A2e) dmbjz ) -{mbjz - mbo}/T1b - kexab[a]mbjz + kexab[b]/3}maz - kexbb[b]/3mbjz + kexbb[b]/3(mbirz + mbinz) kexbb[b]/3mbjz + kexbb[b]/3mbkz (A2f) dmbkz ) -{mbkz - mbo}/T1b - kexab[a]mbkz + kexab[b]/3} maz - kexbb[b]/3mbkz + kexbb[b]/3(mbirz + mbinz) kexbb[b]/3mbkz + kexbb[b]/3mbjz (A2g) where the indices i, j, k fulfill the same conditions as in case 1. {marx(t), mary(t), marz(t)}, and {manx(t), many(t), manz(t)} designate the resonant and nonresonant magnetization components of 1,5-AQDS•- and {mbix(t), mbiy(t), mbiz(t)} those of R1-N•-R2. ∆ωa and ∆ωb designate their resonance offset, and ω1 is the microwave transition field; T1a, T2a, T1b, and T2b are the relaxation times of AQDS•- and R1-N•-R2, [a] and [b] the radical concentration [AQDS•-] and [R1-N•-R2], and kexaa, kexab, and kexbb the exchange rate constants of {AQDS•-‚‚‚AQDS•-}, {AQDS•-‚‚‚R1-N•-R2}, and {R1-N•R2‚‚‚R1-N•-R2} encounters, respectively.

J. Phys. Chem., Vol. 100, No. 5, 1996 1629 The spin polarizations of the four lines are included in the initial conditions for the integration of the set of differential equations as

{maz(0), mb1z(0), mb2z(0), mb3z(0)} ) {PT([TMPIP]), PT([TMPIP]) - PRPM, PT([TMPIP]), PT([TMPIP]) + PRPM} (A3) where PT([TMPIP]) denotes the triplet polarization of the amine concentration and PRPM the radical pair polarization of geminate {QDS•-‚‚‚R1-N•-R2} encounter. References and Notes (1) For reviews of CIDEP studies see: (a) Muus, L. T.; Atkins, P. W.; McLauchlan, K. A.; Pedersen, J. B. Chemically Induced Magnetic Polarization; Reidel: Dordrecht, 1977, and references therein. (b) McLauchlan, K. A.; Stephens, D. G. Acc. Chem. Res. 1988, 21, 54. (c) van Willigen, H.; Levstein, P. R.; Ebersole, M. H. Chem. ReV. 1993, 93, 173. (2) Kevan, L.; Bowman, M. K. Modern pulsed and continous-waVe electron spin resonance; Wiley-Interscience: New York, 1990. (3) Plachy, W.; Kivelseon, D. J. Chem. Phys. 1967, 47, 3312. (4) Johnson, C. S., Jr. Mol. Phys. 1967, 12, 25. (5) Verma, N. C.; Fessenden, R. W. J. Chem. Phys. 1976, 65, 2139. (6) Bartels, D. M.; Trifunac, A. D.; Lawler, R. G. Chem. Phys. Lett. 1988, 152, 109. (7) Jenks, W. S.; Turro, N. J. Res. Chem. Intermed. 1990, 13, 237. (8) Adrian, F. J. Res. Chem. Intermed. 1991, 16, 99. (9) Syage, J. A. J. Chem. Phys. 1987, 87, 1022. (10) Syage, J. A. J. Chem. Phys. 1987, 87, 1033. (11) (a) Cohen, S. G.; Parola, A.; Parson, G. H. Chem. ReV. 1973, 73, 141. (b) Simon, J. D.; Peters, K. S. J. Am. Chem. Soc. 1981, 103, 6403. (c) Harriman, A.; Mills, A. Photochem. Photobiol. 1981, 33, 619. (d) Hamanoue, K.; Nakayama, T.; Yamamoto, Y.; Sawada, K.; Yuhara, Y.; Teranishi, H. Bull. Chem. Soc. Jpn. 1988, 61, 1121. (12) (a) Rao, P. S.; Hayon, E. J. Phys. Chem. 1973, 77, 2274. (b) Kavarnos, G. J.; Turro, N. J. Chem. ReV. 1986, 86, 401. (13) Hore, P. J.; McLauchlan, K. A. Mol. Phys. 1981, 42, 1009. (14) Davis, H. F.; McManus, H. S.; Fessenden, R. W. J. Phys. Chem. 1986, 90, 6400. (15) Madden, K. P.; McManus, H. J. D.; Fessenden, R. W. ReV. Sci. Instrum. 1994, 65, 49. (16) Sa¨uberlich, J.; Beckert, D. J. Phys. Chem. 1995, 99, 12520. (17) Stephenson, D. S. Prog. NMR Spectrosc. 1988, 20, 515. (18) Jeevarajan, A. S.; Fessenden, R. W. J. Phys. Chem. 1992, 96, 1520. (19) McKellar, J. F. Radiat. Res. ReV. 1971, 3, 141. (20) Bruce, J. M. In The Chemistry of Quinoid Compounds; Patai, S., Ed.; Wiley: New York, 1974. (21) Clark, K. P.; Stonehill, H. I. J. Chem. Soc., Faraday Trans. 1 1977, 73, 722. (22) Weller, A. Z. Phys. Chem. N.F. 1982, 130, 129. (23) The pK of (CH3)2NH•+ is reported to be approximately 7 (Fessenden, R. W.; Neta, P. J. Phys. Chem. 1972, 76, 2857) so that spontaneous loss of the proton would occur with a rate constant of only about 103 s-1. (24) Jeevarajan, A. S.; Fessenden, R. W. J. Phys. Chem. 1989, 93, 3511. (25) Loeff, I.; Treinin, A.; Linschitz, H. J. Phys. Chem. 1983, 87, 2536. (26) Rakintzis, N. Th.; Stein, G. J. Phys. Chem. 1966, 70, 727. (27) Meisel, D.; Fessenden, R. W. J. Am. Chem. Soc. 1976, 98, 7505. (28) Hore, P. J.; McLauchlan, K. A. Mol. Phys. 1981, 42, 1009. (29) Beckert, D.; Schneider, H. Chem. Phys. 1987, 116, 421. (30) The argument with the RPM polarization was given by one of the referees which is gratefully acknowledged.

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