5334
J. Phys. Chem. 1996, 100, 5334-5342
Photoionization of N,N,N′,N′-Tetramethylphenylenediamine Studied by Q-Band Time-Resolved EPR Spectroscopy. Separation of Singlet and Triplet Ionization Channels Nikolai I. Avdievich, Antony S. Jeevarajan,† and Malcolm D. E. Forbes* Venable and Kenan Laboratories, Department of Chemistry, CB# 3290, UniVersity of North Carolina, Chapel Hill, North Carolina 27599 ReceiVed: August 8, 1995; In Final Form: October 25, 1995X
The photoionization of N,N,N′,N′-tetramethylphenylenediamine (TMPD) in alcohols at room temperature was studied by time-resolved electron paramagnetic resonance (TREPR) spectroscopy at Q-band (35 GHz). Direct photolysis of TMPD in 2-propanol led to spectra of the solvated electron (e-solv) and the cation radical of TMPD (TMPD•+). The spectra show emission due to the triplet mechanism of chemically induced dynamic electron spin polarization, along with an E/A pattern due to the radical pair mechanism, consistent with the existence of a triplet precursor. It is found that the exchange interaction (J) in this radical pair has a negative sign. The light intensity dependence of the e-solv signal shows that the triplet-state ionization pathway is biphotonic. Photoionization through the singlet state, considered to be dominant in alcohol solution from flash photolysis studies, does not appear in the TREPR spectra without an acceptor for e-solv. By use of 2-bromo-2-methylpropionic acid as electron acceptors and 1,3-cyclohexadiene as a triplet quencher, the photoionization pathway through the excited singlet state was isolated. The TREPR signal from singlet photoionization is found to increase approximately linearly with increasing light intensity until it saturates due to biphotonic ionization processes. The light intensity dependence for both ionization channels is simulated and discussed using a kinetic model. The consequences of exciplex formation in the singlet pathway are also discussed.
Introduction
SCHEME 1
The photoionization of N,N,N′,N′-tetramethyl-p-phenylenediamine (TMPD) has been under investigation for more than 3 decades. Many different techniques have been used to study this reaction, including photoconductivity,1-4 fluorescence and transient absorbance,5-7 Raman spectroscopy,8,9 and magnetic field dependence measurements.10 The extremely complex behavior of TMPD has led to conflicting reports concerning the spin multiplicity of the excited-state precursor and also concerning the number of photons necessary for photoionization. Scheme 1 summarizes the sequence of reactions leading to TMPD photoionization in liquid alcohols, including both singlet and triplet channels. The first step is the excitation of TMPD with rate constant k1. After this, deactivation of the first excited singlet can occur by intersystem crossing to the triplet state (step 2, with rate constant kisc), direct ionization (step 3, with rate constant kion), or ionization caused by absorption of another photon (step 4, with rate constant k2). We show the decay of the triplet in Scheme 1 occurring by ionization induced by a second photon (step 5 with rate constant k3). We have omitted from consideration the direct ionization of the triplet, and reasons for this will be presented below. Flash photolysis experiments on alcoholic solutions of TMPD at room temperature were first carried out by Tsubomura and co-workers.11-13 They found that (1) TMPD radical cation (TMPD•+) was not detected in aerated solutions and (2) the yield of TMPD•+ was proportional to the square of the excitation light intensity. The conclusion was made that biphotonic ionization proceeded through the triplet state. In work by Ottolenghi14,15 the triplet channel was ruled out, in contrast with Tsubomura’s results. They concluded that biphotonic ionization occurred * Author to whom correspondence should be addressed. † Current address: Department of Chemistry, University of Alabama, Tuscaloosa, AL 35487. X Abstract published in AdVance ACS Abstracts, March 1, 1996.
0022-3654/96/20100-5334$12.00/0
through the singlet channel involving an intermediate “semiionized” state. The general opinion of most of the papers published in the past decade6-10,16,17 is that photoionization of TMPD in liquid alcohols is monophotonic and proceeds predominantly through the singlet channel. However, Hirata and Mataga7 reported evidence for biphotonic ionization through the singlet state in the reaction of TMPD in 2-butanol. © 1996 American Chemical Society
Photoionization of TMPD
J. Phys. Chem., Vol. 100, No. 13, 1996 5335
The photoionization of TMPD has recently been studied by time-resolved electron paramagnetic resonance (TREPR)16,17 and fluorescence detected magnetic resonance (FDMR).18,19 These two techniques can give complementary information because the former favors the observation of triplet-born radical ions, whereas the latter allows observation of the singlet-born pairs. In a TREPR study by Murai et al.,16,17 it was suggested that the exchange interaction, J, in the radical pair (RP) of TMPD•+ and the solvated electron (e-solv) has a positive sign. The determination of the correct sign of J is critically important in analysis of TREPR spectra, especially if the spin multiplicity of the precursor is to be unambiguously determined. This is an important issue which we will address in detail below for the TMPD photoionization process. There are other reports which contradict the general opinion about monophotonic ionization. Bakker and Trifunac,19 using FDMR, confirmed the results of Ottolenghi regarding biphotonic photoionization of TMPD in 2-propanol from the singlet state. They used a sophisticated computer simulation of the light intensity dependence that included the spatial characteristics of their laser pulse. Strong evidence for biphotonic ionization through the triplet route has also been observed in electron spinecho experiments by Shkrob and Trifunac20 during photoexcitation of TMPD in different alcohols. The photoexcitation of TMPD in solid alcohols has been studied by Bernas et al.21 The results of that work showed that the ionization pathway (monophotonic or biphotonic) may also depend upon the excitation wavelength. Hirata and Mataga6,7 measured the fluorescence lifetime and quantum yield of formation for the TMPD triplet state. From those results we can estimate the intersystem crossing rate constant at 107 s-1 for reaction in methanol and at 108 s-1 for 2-propanol, 2-butanol, tert-butyl alcohol and a few other alcohols. Biphotonic triplet ionization under their experimental conditions would not be expected, because of the very short laser pulse duration (7 ps). However, in many of the other experiments described above, lasers with 15-20 ns pulses have been used, and therefore triplet photoionization within the laser flash is quite possible and should be taken into account. Separation of the singlet and triplet channels is difficult using many of the experimental techniques mentioned above (except magnetic resonance spectroscopies), since those methods are insensitive to the multiplicity of the RP precursor (triplet or singlet). Also, absorption spectra of intermediate species such as triplet TMPD, TMPD•+, and e-solv have overlapping bands. This makes interpretation of optical results more difficult. In this paper we present the results of our studies of the photoionization of TMPD by TREPR (direct detection) using a 35 GHz (Q-band) spectrometer. In spite of the rather poor sensitivity of this method in comparison with flash photolysis, TREPR can be useful for two reasons. First, it is well-known that the multiplet polarization pattern from the radical pair mechanism (RPM)22 of chemically induced dynamic electron spin polarization (CIDEP) depends on the multiplicity of the radical pair precursor and the sign of the exchange interaction J,23 according to eq 1.
Γmultiplet ) µ sign(J)
(1)
The spin multiplicity factor µ is assigned a value of 1 for triplet precursors and -1 for singlet precursors. J is negative for RP’s in which singlet lies lower than the triplet and positive if the triplet lies below the singlet. The sign of Γmultiplet determines whether the spectrum will appear with low-field lines in emission and high field in absorption (E/A, Γmultiplet ) -1) or vice versa (A/E, Γmultiplet ) +1). Although J is normally
negative in radical pairs, we need to be concerned about the possibility of a positive J coupling in charged radical ions. This is not only because of Murai et al.’s results on TMPD but also because evidence for positive exchange interactions has appeared in other radical ion pair systems where CIDEP has been observed.24,25 The Q-band Zeeman splitting is large enough to provide a substantial chemical shift difference (∆g) between e-solv and most carbon-centered free radicals, and this can lead to net polarization from the RPM.23 The phase of this net polarization (positive Γnet for absorption, negative Γnet for emission) is determined by eq 2.
Γnet ) µ∆g sign(J)
(2)
The sign conventions for µ and J are the same as for eq 1, and ∆g, by definition, is negative for the radical at higher field. For example, e-solv from a triplet precursor with a negative J would, in most cases, show absorption from this mechanism. Information about both µ and J can be determined in most cases directly from the experimental TREPR spectrum. The sensitivity of the TREPR technique to the multiplicity of precursor (singlet or triplet) provides an excellent way to separate both photoionization pathways. A second advantage of the TREPR technique over optical methods is that the identification of the reactive intermediates is easier because of the high structural resolution, especially that available at high magnetic field as in the Q-band TREPR experiment. The Q-band apparatus also has superior time response to X-band, allowing well-resolved spectra to be obtained at delay times as short as 10 ns after the laser flash under optimal conditions. Experimental Section Unless otherwise indicated, all experiments were run by using TMPD from Aldrich that was sublimed once in vacuo. The 2-bromo-2-methylpropionic acid (BMPA), 1,3-cylohexadiene, and all solvents were used as received from Aldrich. The Q-band (35.1 GHz) TREPR experiments were carried out by using a boxcar integrator on an apparatus described previously,26-28 at concentrations of TMPD ranging from 1 to 3 mM. The excimer laser was a Lambda-Physik LPX-100i operating at 308 nm with a maximum pulse energy of 200 mJ. The gate width of the boxcar integrator in all experiments was 100 ns. The delay times specified are not corrected for a 40 ns propagation delay in the signal preamplification circuit. All experiments were performed at room temperature. After a very short time of irradiation, solutions of TMPD show an intense blue color due to generation of Wurster’s blue salt.29 To exclude the possibility of interference from photoproducts, every experiment reported here was performed by using a single-pass flow system. Solutions were purged with dry nitrogen during the entire experiment. The effect of flow rate was investigated because it can affect the shape and intensities of TREPR spectra, due to the fast rate of creation of photoproducts. Increasing of the flow rate led to an increase in the intensities of all lines in the spectra but did not change the observed polarization patterns. The sample cell was a flat cell with a path length of 0.2 mm and a sample volume in the active area of the microwave cavity of 3 µL. The laser beam was conditioned prior to entry into the cavity by focusing using a cylindrical lens. An aperture the same size as the opening in our home-built TE103 optical transmission microwave cavity (approximately 3.5 mm × 1.8 mm) blocked the light not passing through the sample cell. This was done to prevent heating of the cavity exterior walls. The beam dimensions at the sample cell were measured using heat-
5336 J. Phys. Chem., Vol. 100, No. 13, 1996
Avdievich et al. TABLE 1: Parameters Used in the Simulation Shown in Figure 1Aa radical
g factor
TMPD•+
2.0028
e-solv
2.002
hyperfine coupling constants, MHz 19.0 (4 CH3) 19.6 (2 N) 5.6 (4 H)
line width, G
ref
3.0
33
3.0
16, 34
a
The ratio of TM to RPM polarization is 0.7, obtained by best fit to the experimental spectrum.
Figure 1. (A) Experimental (top) and simulated (bottom) Q-band TREPR spectra of TMPD•+ (broad multiple lines) and e-solv (broad single line indicated by arrow). The experimental spectra were obtained upon photolysis of a 3 mM solution of TMPD in 2-propanol at a delay time of 0.05 µs after the laser flash. In this and all subsequent spectra, lines below the baseline are in emission and those above the baseline are in enhanced absorption. Parameters used in the simulation are listed in Table 1. (B) Laser pulse energy dependence of the e-solv TREPR signal obtained at a delay time of 0.05 µs. The solid line is a calculated curve using eq 11 from the kinetic model described in Section D of the text.
sensitive paper. The pulse energy of this beam was measured with no sample present immediately after exiting the cavity by using a Laser Probe Model RM-6600 UV radiometer. Variation of pulse energies was accomplished by using stainless steel mesh on a rotating optical mount. The attenuation was calibrated by using the radiometer. Steady-state absorption spectra were obtained on a HewlettPackard 8452A spectrophotometer, and steady-state emission spectra were obtained by using a SPEX Fluoromax emission spectrometer. Reduction potentials were measured by using a Bioanalytical Systems 100W electrochemical analyzer with 2-propanol as solvent and lithium perchlorate as added electrolyte. Results and Discussion A. Isolation of the Triplet Ionization Channel and the Sign of J. The Q-band TREPR spectrum obtained at several delay times after photoexcitation of a solution of TMPD in 2-propanol is shown in Figure 1A. The light intensity depen-
dence is shown in Figure 1B. It is clearly nonlinear, and this will be discussed in detail below. In the spectra shown in Figure 1A and all subsequent EPR spectra, lines above the baseline exhibit enhanced absorption, while those below the baseline are in emission. From the simulation shown immediately below the experiment spectra we can assign the signal carriers to the TMPD•+ and e-solv. The TMPD•+ signal shows significant uncertainty broadening at this delay time, but careful simulations of later time delay spectra confirmed all hyperfine splittings to be equal to literature values for this radical ion. To confirm that the single line is due to e-solv, we performed the experiment using different quenchers and acceptors. For example, if the experiment is run using a solution that is saturated in nitrous oxide, N2O, the e-solv signal is not observed. Experiments with other acceptors and quenchers are described below. In the absence of N2O, the e-solv signal seen in Figure 1A decays during the first 100 ns at this level of purity of the starting materials. It is known to have a long spin-lattice relaxation time (4-6 µs in aqueous solution),30,31 but the chemical lifetime can be shortened considerably by the presence of impurities, even in minor quantities, or by the presence of deliberately added trapping agents. Even though the materials used in our system are very pure, there can be small amounts of impurities present in the solvent, and also there are products formed during the laser pulse of 17 ns. We have also observed the TREPR spectrum of e-solv in 1-octanol, but all attempts to observe it in methanol failed. The signals of TMPD•+ and e-solv in Figure 1A both show net emission, which means polarization was created by the triplet mechanism (TM)23 in the excited triplet TMPD molecule and then transferred to both radicals. According to Scheme 1 this confirms that at least some of the RPs are created through the triplet state (step 5). The generation of strong TM polarization is probably a consequence of running the TREPR experiment at Q-band instead of the conventional X-band microwave frequency. From previous work we have seen that in some systems it is possible to get an order of magnitude increase in the TM at the higher frequency.32 The simulation at the bottom of Figure 1A, using the parameters listed in Table 1,33,34 shows that there is also RPM multiplet E/A polarization23 in the TMPD•+ spectrum, with a weight of about 70% of the TM polarization. According to eq 1 this E/A pattern means that we have one of two situations: (1) there is a triplet precursor and J is negative, or (2) there is a singlet precursor and J is positive for the RP of TMPD•+ and e-solv.24,25 Even though the spectrum shows TM polarization, it is difficult to make conclusions about the multiplicity of the RP precursor because the sign of J is not known with absolute certainty, so the possibility of competing triplet and singlet pathways cannot be ruled out based on this one spectrum. Attempts to remove the triplet ionization channel using 1,3cyclohexadiene as a quencher were performed. The intensity of the spectrum in Figure 1A was lower at 10 mM and disappeared completely at 30 mM concentration of quencher. These results confirm that the observed E/A polarization was
Photoionization of TMPD formed in triplet RPs and support the hypothesis that J is negative in the RP consisting of TMPD•+ and e-solv. To determine whether the presence of water or other impurities in the alcohol solution were affecting the photochemistry, we performed these experiments with a solution consisting of TMPD that was sublimed three times in vacuo and dissolved in 2-propanol that had been distilled from calcium oxide. The sample preparation procedure for this experiment was performed in a drybox under a nitrogen atmosphere. Following these purification procedures led to an increased chemical lifetime of the signal due to e-solv, which could be observed at delay times as long as 1 µs. At 0.05 and 0.1 µs delay times, we obtained the same EPR spectra as we obtained without the extended purification procedures. It is interesting to note that at the later delay time of 0.5 µs, the signal of e-solv has changed from emission to absorption (Figure 1A), while the TMPD•+ signal has completely disappeared (presumably by spin-lattice relaxation). This change to absorptive polarization is created by diffusive RPs of TMPD•+ and e-solv (F-pairs). In these RPs there is a large ∆g of 10 G at the Q-band external magnetic field of 12.5 kG.16,33,34 For F-pairs, µ ) +1, and ∆g is negative for e-solv. According to eq 2, to get an absorptive net RPM signal for the high field radical (e-solv), J must be negative. Combined with the quenching experiment described above, these spectra provide conclusive evidence that J is negative in the RP of TMPD•+ and e-solv. This contradicts Murai and Kuwata’s previous X-band TREPR results.16,17 B. Isolation of the Singlet Ionization Channel. The RPs from the singlet channel, which are supposed to be dominant in this reaction, do not appear in the spectra shown in Figure 1. The absolute value of the RPM polarization in singlet-born RPs might be small compared to that generated by triplet-born pairs, because of the generally shorter lifetime of the former ones. Also, E/A polarization from the triplet precursor and A/E polarization expected from the singlet precursor will cancel. The resulting spectrum then depends on the number of radicals produced from each precursor, plus the absolute polarization magnitude. The dominance of the polarization from the tripletborn RPs in these spectra gives us the opportunity to investigate the triplet ionization channel exclusively, which is an advantage over optical absorption spectroscopy or FDMR. The quenching experiment described above, however, clearly shows that >95% of the observed TREPR signal in Figure 1A is of triplet origin. In order to observe the singlet-born RPs, we attempted to trap e-solv using a variety of electron acceptors. With high concentrations of acceptors, we might also expect to see direct photoinduced electron transfer (ET) from TMPD excited states (singlet or triplet) on the time scale of the TREPR experiment. If this is the case we need to be concerned about the possibility of exciplex formation in either the ground or excited state of TMPD, in both the presence and absence of quenchers. This possibility and its role in the kinetics will be discussed in detail below. Scheme 2 outlines the expected trapping and ET reactions. Fortunately, the spin history of the trapped/transferred electron is identical for each reaction. Previously, Murai and co-workers attempted to do this using maleic anhydride, but the spin polarization patterns they obtained were unusual. They explained their observations by invoking S-T-mixing in the radical ion pair state.35,36 Such an effect would then be sensitive to the magnetic field at which the EPR experiment is performed. We have repeated the TMPD/maleic anhydride experiment at Q-band and found the same polarization pattern as they did at X-band.37 This seems to rule out S-T-mixing as the cause of the unusual polarization pattern observed at X-band in this
J. Phys. Chem., Vol. 100, No. 13, 1996 5337
Figure 2. Q-band TREPR spectra observed during the photolysis of a 2-propanol solution that was 1 mM in TMPD and 15 mM in BMPA at the delay times indicated.
SCHEME 2
system. Electron-hopping, cross-relaxation, or radical-triplet pair mechanism (RTPM) polarization are all possible alternative explanations for the unusual appearance of those spectra, a complete discussion of which is outside the scope of this paper. We have therefore sought out electron acceptors other than maleic anhydride, with the following criteria: The acceptor should have (1) a high bimolecular rate constant for reaction with the solvated electron, (2) a smaller number of hyperfine coupling constants of the radical adduct formed (to minimize the distribution of the transferred polarization), (3) a long (several microseconds) T1 relaxation time, and (4) relatively slow (107-108 M-1 s-1) bimolecular chemical decay. In this regard, 2-bromo-2-methylpropionic acid (BMPA) was chosen as the best acceptor38 for this study (Scheme 2, bottom). The 2-methylpropionic acid-2-yl radical (MPA•) is the paramagnetic species actually observed in the TREPR experiment. It is generated via loss of Br- from the anion radical of BMPA. MPA• contains large hyperfine coupling constants (21.6 G for six identical protons), leading to a well-resolved seven line EPR spectrum. Figure 2 shows the time dependence of the TREPR spectra of TMPD•+ and MPA• observed after the photoionization reaction in 2-propanol. The TREPR signal at 0.1 µs shows the presence of A/E multiplet polarization together with TM
5338 J. Phys. Chem., Vol. 100, No. 13, 1996
Figure 3. (A) Q-band TREPR spectra observed during the photolysis of a 2-propanol solution that was 3 mM in TMPD, 10 mM in BMPA, and 30 mM in 1,3-cyclohexadiene at a delay time of 0.1 µs and with a laser pulse energy of 70 mJ. The arrow indicates the transition monitored for the light intensity dependence. (B) Laser pulse energy dependencies of the TREPR signal obtained during the photolysis of a 2-propanol solution that was 1mM (2) or 3 mM (4) in TMPD, 15 mM in BMPA, and 30 mM in 1,3-cyclohexadiene at a delay time of 0.1 µs. The solid line is a calculated curve using eq 3 from the kinetic model described in section C of the text.
emissive polarization. The net emission, as described above, can only originate from the triplet precursor. The A/E polarization can arise from the triplet state if J is positive or from the singlet state if J is negative for this RP. Spectra observed at later delay times show E/A multiplet polarization created in F-pairs of TMPD•+ and MPA• (step 4 of Scheme 2). The F-pair E/A polarization begins to decrease the A/E polarization starting at 0.2 µs, cancels it at 0.5 µs, and completely dominates the spectrum at 5.0 µs. Since F-pairs must have µ ) +1, J must be negative for this RP (see eq 1). Therefore, we can conclude that the A/E pattern observed at early delay times is due to singlet-born RPs. We have repeated this experiment using a solution of distilled 2-propanol containing BMPA which was recrystallized from distilled pentane and TMPD which was triply sublimed in vacuo. This sample was prepared in a nitrogen atmosphere. The spectra obtained using the specially purified sample were identical with those shown in Figure 2. There are two possible pathways for the singlet RP generation: (1) Photoionization through the singlet state with creation of 1(TMPD•+ and e-solv), followed by trapping of e-solv by BMPA, or (2) direct electron transfer from 1TMPD* to BMPA. Adding 30 mM of 1,3-cyclohexadiene, a triplet quencher, to the solution completely removes the triplet channel of photoionization and allows us to detect a pure A/E polarization pattern due to singlet-born RPs, as shown in Figure 3A. The use of BMPA as an electron acceptor therefore adds a new dimension to our understanding of the photochemistry of TMPD, by showing the exclusive contribution of the singlet state to the
Avdievich et al. photoionization process. However, the possibility of exciplex formation cannot be excluded, and because this can affect the energetics and lifetime of the TMPD excited state, we have made a thorough investigation of this process as it pertains to our acceptors and quenchers. We have measured steady-state absorption and emission spectra of TMPD in 2-propanol at room temperature in the presence of BMPA and 1,3-cyclohexadiene at different concentrations. There are no shifts in the absorption bands of any of these species at any concentration. This rules out the formation of any strongly-bound complex of BMPA or 1,3cyclohexadiene with the ground state of TMPD. However, in the steady-state emission spectra, two new bands appear upon addition of BMPA that are blue-shifted from those found without BMPA. This is solid evidence for exciplex formation between the excited state of TMPD and BMPA. This process will therefore be included in the kinetic model for the light intensity dependence presented below. No additional emission bands were observed in the presence of 1,3-cyclohexadiene. This is one of several reasons why 1,3cyclohexadiene was chosen as the triplet quencher for these studies. This quencher has been used in other electron transfer studies using donors and acceptors of similar energies.39 It has a triplet energy of 219.4 kJ mol-1,40 which is well below that of TMPD (approximately 260 kJ mol-1),41 so triplet energy transfer is likely to be very efficient in our photoionization reactions. Also, we have measured its reduction potential in 2-propanol to be -1.23 V vs SCE, compared to BMPA’s reduction potential, which we measured to be -0.8 V vs SCE. Since electron affinities track monotonically with reduction potentials,42 we can conclude that our direct electron transfer reaction will involve only BMPA and not our triplet quencher. One drawback is its rather poor solubility in 2-propanol, but we have been able to get almost complete quenching of the TMPD triplet state at concentrations of 30 mM of this quencher. C. Light Intensity Dependence for the Singlet Channel. To check if the singlet ionization channel is biphotonic or monophotonic, measurements of the laser pulse energy dependence of the singlet polarization were performed. Figure 3B shows the results of those experiments, which were obtained during the photolysis of TMPD in the presence of 15 mM of acceptor (BMPA) and 30 mM of triplet quencher (1,3cyclohexadiene) at a delay time of 0.1 µs. An arrow in Figure 3A marks the specific transition where the intensity was monitored. Using a single delay time and transition is important because the line width of the signal should remain constant during this experiment. At low laser pulse energies, this curve shows approximately linear behavior. This result is in accord with the monophotonic ionization pathway in alcoholic solution that seems to be generally accepted in the most recent literature. Another feature of the curve in Figure 3B is the saturation effect observed at a laser pulse energy of about 60 mJ. To check if this saturation might be caused by depletion of the sample due to the high pulse energy, we also performed these measurements at lower TMPD concentration. Both experimental curves show similar behavior, which rules out the former hypothesis. In the case of direct electron transfer from 1TMPD* to the acceptor molecule, the light intensity dependence curve should have a similar shape at low pulse energies, Vide infra. Since we could not observe the trapping process directly by observation of both e-solv and the acceptor radical anion in the same spectrum, it is difficult to separate these two reaction routes and make a final statement about a preference for the singlet ionization followed by trapping or direct ET from the singlet. Since spin is conserved in this process, our conclusions
Photoionization of TMPD
J. Phys. Chem., Vol. 100, No. 13, 1996 5339
regarding multiplicity of the precursor excited state and the sign of J are unaffected by our inability to resolve the kinetics of electron capture by the acceptor. However, there is a clue as to which is the dominant pathway given by the fact that the MPA• radical shows multiplet polarization. If the reaction sequence were sequential, net polarization from e-solv would have been transferred to each hyperfine line of the MPA• radical. This polarization, which is expected to be absorptive from our results in Figure 1, is not observed. The only way multiplet polarization can be observed at these early delay times is if there exists a geminate radical pair consisting of TMPD•+ and MPA•. So, direct electron transfer is most likely the dominant process for this donor-acceptor system. To understand the light intensity dependence in more detail we need to consider the overall kinetics of the reaction, which are described by eq 3.
d[TMPD]/dt ) -k1n0[TMPD] + kf[1TMPD*]
(3a)
d[1TMPD*]/dt ) k1n0[TMPD] - (kf + kisc + kion + k2n0 + kaS[A])[1TMPD*] (3b) d[3TMPD*]/dt ) kisc[1TMPD*] - (k3n0 + kaT[A])[3TMPD*] (3c) The notation in eq 3 corresponds to that used in Schemes 1 and 2. Other terms are defined as follows: n0 is the number of photons per laser pulse delivered to the sample cell, kf is the fluorescence rate constant, [A] is the acceptor concentration (if any), and kaT and kaS are reaction rate constants for direct electron transfer to an acceptor molecule from 3TMPD* and 1TMPD*, respectively. In order to simplify the kinetic equations, we have assumed that back electron transfer reactions are slow compared to our observation time of 50-200 ns. The possibility of exciplex formation needs to be discussed at this point because it matters whether or not the second photon ionizes the exciplex or the uncomplexed 1TMPD*. Since we know that there is little or no ground-state interaction between TMPD and BMPA, we only need to consider the possibility of collisions between 1TMPD* molecules and ground-state BMPA molecules on the time scale of the laser flash. In order to affect the light intensity dependence, these collisions need to occur within the lifetime of 1TMPD*, which we know from previous work to be 8 ns.7 It should be stressed that a collision involving direct contact with the correct geometry is required for exciplex formation, whereas the direct electron transfer process can occur from other geometries and from solvent separated species. From a Stern-Volmer analysis of the fluorescence intensity of TMPD versus BMPA concentration, we have determined that the reaction rate between 1TMPD* and BMPA is (4.6 ( 0.3) × 109 s-1; i.e., it is approximately diffusion-controlled. At our concentrations of BMPA, we calculate a collision time of 20 ns for the highest concentration of BMPA used in our TREPR experiments. Therefore, collisions to form the exciplex are unlikely to affect the shape of our intensity curves. Further support for this is provided by running the experiment shown in Figure 3B at lower concentrations of BMPA, but monitoring the TREPR signal at the same delay time. When this is done, a curve is obtained which has exactly the same shape as those shown in Figure 3B. Analysis of eq 3 can proceed by numerical integration, but this approach will not lead to expressions for the light intensity with functional forms that are easy to understand in terms of
physically meaningful parameters. It should also be noted that the most rigorous treatment of the kinetics of multiphoton processes should include the spatial profile of the laser pulse and consideration of screening effects by excited-state absorbance during the laser flash. From our laser pulse conditioning and testing for uniformity using thermally sensitive paper at the sample, we can say with some certainty that our laser pulse intensity is uniformly distributed over the sample active area in the microwave cavity. Also, from our analysis below we have obtained an approximate value for the extinction coefficient S1fSn for TMPD. Using the Beer-Lambert law we have determined that the absorbance of the excited state competes for photons with the ground state only at our very highest light intensities. For these reasons, we believe it can be instructive to make a few reasonable approximations that lead to equations that will reproduce the shape of the curve in Figure 3B, yet they will also provide insight into the reasoning behind the shape. To do this, we will need to know the values of a few variables such as the number of absorbed photons, n0, the rate constant for absorption of photons by the ground state molecule (k1 in Scheme 1), and others. We begin with the former quantity. In our experiments, the TMPD concentration was 3 mM, and the path length of the sample cell (lS) was 0.2 mm. Using an extinction coefficient at 308 nm for TMPD of 1.8 × 103 M-1 cm-1,36 the molar absorbance of our sample, [TMPD]lS, is calculated to be 0.1. This small value allows us to use the approximation that e-[TMPD]lS ≈ 1 - [TMPD]lS, and therefore the number of photons absorbed by the sample, nabs, can be approximately expressed as n0[TMPD]lS. Next we derive an expression for k1, the rate constant for production of 1TMPD*, which is given by eq 4, assuming that the quantum yield of formation for the singlet excited state of TMPD is 1.0.
k1n0[TMPD] ) )
∴ k1 )
nabs NAτVS
(4a)
n0[TMPD]lS NAτVS
(4b)
lS NAτVS
(4c)
The term VS is the sample volume, τ is the laser pulse duration, and NA is Avogadro’s number. We have assumed that kf is small compared to other rate constants in eq 3 and neglected it. This seems valid when it is considered that the quantum yield of formation for the triplet7 is 0.75, and we know we are seeing a large concentration of radicals due to kion, so kf must be only a few percent of the total decay of 1TMPD*. Note that eq 4c defines k1, and it can also be used to calculate k2 and k3 in Scheme 1 if the extinction coefficients can be estimated. Actually we will do the reverse, i.e., get k2 and k3 from our simulations of the light intensity dependence, and plug them into eq 4 to see if the extinction coefficients have reasonable values. This will help us to validate the kinetic model. Next we use eq 4 to estimate the product k1n0. In our experiments about 4% of the total laser pulse energy is transmitted to the sample cell. With n0 ∼ 1 × 1016 (at 200 mJ pulse energy, our maximum), the product k1n0 is about 1.5 × 107 s-1. We note that the inverse of this rate is longer than the laser pulse duration (17 ns) and the lifetime of 1TMPD* (∼8 ns).7 This allows us to make what is the most important assumption in the development of this model: We will consider
5340 J. Phys. Chem., Vol. 100, No. 13, 1996
Avdievich et al.
the rate of creation of 1TMPD* to be constant during the laser pulse. Our strategy is then to use the steady-state approximation for 1TMPD* in eq 3a and obtain the stationary value of [1TMPD*] during the laser flash, as shown in eq 5.
[1TMPD*] )
)
k1n0[TMPD] (kf + kion + kisc + kaS[A] + k2n0) (k1/keff)[TMPD] n0 (1 + k2n0/keff)
(5a)
(5b)
where
keff ) kf + kion + kisc + kaS[A]
(5c)
This is a coarse approximation, because the laser pulse duration (17 ns) is only about two times larger than the 1TMPD* lifetime (∼8 ns, which corresponds to keff-1 in the absence of acceptor),7 and this may not be enough time for [1TMPD*] to reach a true stationary state. However, it is good enough to allow us to understand the qualitative behavior of the experimental light intensity dependence. Note that eq 5b has been written in the functional form of y ) ax/(1 + bx), where x ) n0. Thus the stated objective of writing the light intensity dependence in terms of simple variables is beginning to be achieved. There are several points to make before the analysis continues. The observable plotted in Figure 3B is the intensity of a spinpolarized EPR signal and not for the concentration of 1TMPD* shown in eq 5b. To simulate the shape of the curve in Figure 3B it is necessary to show that these two intensities are directly proportional under our experimental conditions. First, we stipulate that the geminate RPM polarization intensity is linearly proportional to the concentration of singlet RPs, [1RP]. This statement is an elementary tenet of CIDEP theory. It is perhaps easier to see that this is true if one considers F-pairs, which do not have this linear relationship. For F-pairs, the number of random encounters increases in a square-law fashion with increasing concentration, therefore the polarization generated by diffusive encounters is not necessarily a linear function of concentration. For this reason, all light intensity variations were performed by using spectra taken at the very earliest delay times, when very little F-pair polarization is present in the signals. We must determine the conditions under which the functional form of the light intensity dependence of the singlet-born radical pair concentration [1RP] is the same as that which we will calculate for [1TMPD*] using eqs 3 (exact solution) or 5 (approximate solution). In addition, we must keep in mind that the signal intensity plotted in Figure 3B was obtained in the presence of added acceptor (BMPA). The equations we use to find the correct condition must now include kinetic processes involving the acceptor acting both as a trap for e-solv and as a direct electron acceptor. We will consider steps 1-4 of Scheme 1 and steps 1-3 of Scheme 2. Two types of singlet-born radical pair are involved in the observed CIDEP intensities. We designate them as 1RP′ (TMPD•+ and e-solv) and 1RP (TMPD•+ and MPA•). To describe their time dependence we write eq 6, which must be integrated over the time of the laser pulse.
d[1RP]/dt ) ka[A][1RP′] + kaS[A][1TMPD*]
(6a)
d[1RP′]/dt ) (kion + k2n0)[1TMPD*] - ka[A][1RP′] (6b) Substituting eq 5b for [1TMPD*] into both of these equations allows integration with terms in [1TMPD*] outside the integrand.
This shows the advantage of using the steady-state approximation above to obtain eq 5. Integration of eq 6b and substitution of [1RP′] into eq 6a, followed by another integration, lead to the eq 7 for [1RP], the total concentration of singlet-born radical pairs of TMPD•+ and MPA•.
[1RP] ) [1TMPD*]τ{kaS[A] + (kion + k2n0)B}
[
B) 1+
]
(exp(-ka[A]τ) - 1) ka[A]τ
(7a) (7b)
Equation 7 shows clearly that [1RP] and [1TMPD*] will have the same functional form with respect to the light intensity when the term containing B is small compared to the term containing kaS[A]. This inequality eventually simplifies to eq 8 as the final condition we need to consider.
ka < kaS
(8)
The relationship is then valid when the rate constant for trapping of e-solv by BMPA is slower than the rate constant for direct electron transfer from [1TMPD*] to BMPA. Trapping rates for several R-bromocarboxylic acids have been measured,39 but unfortunately BMPA was not included in that study. Also, the rate constants obtained in that study were for water as solvent, not 2-propanol. From analogous systems and the fact that an additional methyl group should slow down the rate somewhat, ka for our system is estimated to be slightly less than diffusion controlled, i.e., about 1 × 109 s-1. The light intensity dependence in eq 5b is carried by the term in the denominator, namely, (k2/keff)n0. When this term is much greater than 1, the 1 in the denominator can be ignored, and the n0’s cancel. In other words, when this condition is satisfied, there will be no light intensity dependence for [1TMPD*] and therefore none for [1RP]. This saturation effect is clearly seen as the light intensity increases in Figure 3B, so this simple model works well for the singlet ionization case. Since this condition requires the rapid absorption of photons by 1TMPD* with rate k2n0, our conclusion is that the behavior of the experimental curve in Figure 3B is evidence for biphotonic singlet ionization. Fitting the curve in Figure 3B allowed an estimate of k2, and then the extinction coefficient S1fSn could be obtained by using eq 4. Exact solution of eq 3b gave somewhat better agreement of the experimental and simulated (solid line in Figure 3B) curves. We know that the fluorescence lifetime of TMPD in 2-propanol (keff-1) is 8 ns.7 We have measured the upper limit for kaS is a diffusion-limited rate constant (∼5 × 109 s-1). Using these values in our exact solution and then backtracking to eq 4, we can estimate the singlet-singlet extinction coefficient S1fSn (at λ ) 308 nm) to be 2.5 × 104 M-1 cm-1, a very reasonable value. This further supports the validity of the kinetic model. D. Light Intensity Dependence for the Triplet Channel. To determine whether photoionization through the triplet channel is monophotonic or biphotonic, we have measured the laser light dependence of the signal intensity of e-solv at the 0.05 µs delay time (Figure 1A). The results are plotted in Figure 1B. The experimental curve shows nonlinear behavior at low pulse energies, and the beginning of signal saturation at very high pulse energies. Since the shape of the curve at low intensities is closer to a square-law dependence than a linear one, direct ionization from the triplet was ignored. The saturation effect begins at pulse energies of about 200 mJ, which corresponds to nabs of about 1.5 × 1015 (from eq 4). From the concentration and sample volume, we know that we have about 6 × 1015
Photoionization of TMPD
J. Phys. Chem., Vol. 100, No. 13, 1996 5341
TMPD molecules per sample. Comparison of these two values shows that saturation due to sample depletion is not responsible for the curve beginning to level off at high light intensities in Figure 1B. To explain the behavior of the curve in Figure 1B we need to calculate the concentration of triplet-born radical pairs, [3RP], of TMPD•+ and e-solv, during the laser pulse (eq 9).
d[3RP]/dt ) k3n0[3TMPD*] [ RP] ) ∫0 (d[ RP]/dt)dt ) τ
3
3
∫
τ k3n0 0 [3TMPD*](t)
(9a) dt
(9b)
The time dependence of [3TMPD*] is obtained after integration of eq 3c to give eq 10. Following similar arguments as we did in section C for the analysis of the singlet light intensity, the value of [1TMPD*] was calculated from eq 5.
[3TMPD*](t) )
kisck1[TMPD](1 - exp(-k3n0t)) keff(1 + k2n0/keff)
(10)
Using eqs 9 and 10, we can obtain the number of 3RP′s created during the laser pulse, shown in eq 11. With this equation we can qualitatively explain the behavior of the curve in Figure 1.
[3RP] )
kisck1[TMPD]n0τ (1 + (exp(-k3n0τ) - 1)/k3n0τ) keff(1 + k2n0/keff)
(11)
At low pulse energies (k3n0τ < 1) this equation shows a quadratic dependence on n0, as expected if there is biphotonic ionization through the triplet state. The presence of the exponential function in eq 11 also explains the different behavior of the singlet- and triplet-born RPs (Figure 3B vs Figure 1B). We used eq 11 to simulate the curve in Figure 1B (solid line). The value of k2 used in the simulation was obtained from our previous simulation of Figure 3B. Also, from eq 4 we obtained a value for the extinction coefficient T1fTn (at λ ) 308 nm) of 6 × 103 M-1 s-1. Using the exact solution of eq 3 for the simulation of Figure 1B does not change the shape of the curve but makes a correction for T1fTn. The final value we have obtained for T1fTn is 4 × 103 M-1 s-1, again a very reasonable value. We can therefore conclude that our kinetic analysis leads to physically reasonable values for the extinction coefficients S1fSn and T1fTn (at λ ) 308 nm). The simulations in Figures 1B and 3B take into account biphotonic ionization processes for both channels and describe the shape of the experimental light intensity dependence curves very well. Good fits to such data can also be obtained by using a much more sophisticated computer program (cf. ref 19), but connections to physical parameters then become difficult. The fact that the extinction coefficients come out to reasonable values gives us confidence in the self-consistency of our simple-minded kinetic model. Figure 4 shows TREPR spectra obtained at two different laser intensities during the photolysis of TMPD with added BMPA. It shows that decreasing the laser light intensity causes an increase in the amount of A/E (singlet precursor) polarization. By comparing the shapes of the curves in Figures 1B and 3B, it is clear that this should happen. If the two curves are normalized and plotted on the same graph, the largest difference in signal intensities will occur at low to medium pulse energies, while at high laser power both signals saturate. Figure 4 is an additional piece of evidence that the light intensity dependence is different for each channel.
Figure 4. Q-band TREPR spectra observed during the photolysis of a 2-propanol solution that was 3 mM in TMPD and 10 mM in BMPA at the laser pulse energies indicated. All spectra were obtained at a delay time of 0.1 µs.
E. Solvent Dependence. Photoionization of TMPD in the presence of BMPA as an acceptor was performed in 1-octanol and methanol solutions. The spectra obtained in 1-octanol resemble those obtained in 2-propanol. At a delay time of 0.1 µs we have been able to observe both A/E (singlet channel) and E (triplet channel) patterns. In methanol at 0.1 µs, the spectrum is only of singlet origin (A/E multiplet polarization). Those results are in accord with measurements of the intersystem crossing rate constant made by Mataga et al.7 They found that the quantum yield for triplet TMPD formation in methanol is about 0.05 and the fluorescence lifetime is 4 ns. In this case the estimated intersystem crossing rate is 107 s-1, which is much longer than the laser pulse. At 1.0 µs, spectra in both of these solvents become pure E/A due to RPM polarization in the F-pairs. Conclusion Our results confirm that TMPD photoionization in liquid 2-propanol at room temperature is biphotonic if it occurs under our experimental conditions from the triplet state. However, we do not mean to imply by this statement that photoionization proceeds exclusiVely from the triplet state. The TREPR method is clearly biased toward triplet-born pairs unless traps and/or quenchers are used. The photoionization of TMPD in the presence of a good electron acceptor allowed us to observe competing singlet and triplet ionization routes. By adding enough triplet quencher, we observed the singlet photoionization pathway exclusively. Ionization from the singlet state is complex, but there is clear evidence for biphotonic behavior. The extent of monophotonic ionization from the singlet state is not ascertainable from our analysis. The observation of RPs from both precursors by using the same experiment demonstrates the utility of this technique. We can also conclude with certainty that the sign of the exchange interaction is negative in the radical pair of TMPD•+ and e-solv and that J is negative in the radical pair of TMPD•+ and MPA•. Acknowledgment. We thank G. R. Schulz for assistance with purification of the materials, H. van Willigen for helpful comments, I. A. Shkrob and A. D. Trifunac for providing a copy of ref 20 in advance of publication, L. D. Kispert for partial financial assistance, and H. Murai for introducing us to the unusual photochemistry of TMPD. This work was supported by the National Science Foundation through Grant CHE9522007 and through the NSF Young Investigator Award Program (Grant CHE9357108). References and Notes (1) Tamir, M.; Ottolenghi, M. Chem. Phys. Lett. 1970, 6, 369. (2) Holroyd, R. A.; Russell, R. L. J. Phys. Chem. 1974, 78, 2128. (3) Choi, H. T.; Sethi, D. S.; Braun, C. L. J. Chem. Phys. 1982, 77, 6027.
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