J. Phys. Chem. 1995, 99, 248
248
Magnetic Field Effect in the Recombination Reaction of Radical Ion Pairs: Dependence on Solvent Dielectric Constant U. Werner? and H. Staerk” Max-Planck Institut fiir Biophysikalische Chemie, Abteilung Spektroskopie und Photochemische Kinetik, Am Fassberg, 0-37077 Gottingen, Gemzany Received: June 7, 1994; In Final Form: September 13, 1994@
The influence of external magnetic fields on the reaction yield of recombining radical ion pairs of polymethylene-linked acceptor/donor systems (pyrenelNfl-dimethylaniline) is investigated in solvents of varying dielectric constant ( E = 7-37). Different bulk DKs are also adjusted with binary solvent mixtures. Similar to nonlinked radical ion pairs of the same type, the highest magnetic field effects (MFEs) on the yields of products measured (exciplexes and pyrenyl triplets) are found in solvents of medium DK ( E 20). In such linked systems, only geminate recombination is necessarily possible, while homogeneous recombination does not occur. We conclude, therefore, that earlier theoretical models for the explanation of the so-called “medium-DK MFE maximum” in free-radical ion pair systems must be considered obsolete. These earlier models are mainly based on the competition between geminate and homogeneous recombination pathways. Based upon support from all present experimental results, an alternative model is proposed which correlates the radical ion-pair lifetime with the achievable magnitude of the MFE.
I. Introduction External magnetic fields are known to influence photochemical reaction yields, whereby the total spin multiplicity of an intermediate radical ion pair has a magnetic-field-dependent probability to change from the singlet to the triplet state, or vice versa, respectively. The hyperfine-interaction-induced magnetic field effect (MFE) which is seen in the recombination of photochemically formed radical ion pairs (RIPS) has been described in its various forms and in review articles since about 1975.1-4 A number of investigators have explored the effect of the solvent polarity on the magnitude of the MFE. In some cases, the most pronounced MFE has been found in solvents of medium polarity rather than in solvents of highest polarity. In the following discussion, the maximum MFE will be referred to as the mDK maximum, where mDK means medium dielectric constant (medium bulk permittivity). The solvent polarity has an important influence on the MFE based on a number of reasons: 1. The energy levels of exciplex and RIP are affected differently by the solvent polarity, E. The interaction with the solvent can be calculated approximately in accordance with the Kirkwood-Onsager model under the simplified assumption that the system comprising an acceptor and a donor is a “spherical” dipoles5 The exciplex free energy, AGE,,, and the free energy of the radical ion pair, A G s s ~have , been given as semiempirical equations by Weller.6-8 Overall, it is found that the difference /(AGExc- AGssp)( between exciplex and RIP can become zero, e.g., for the system anthracenelN,N-dimethylaniline,if E 7.6 RIPS are favored in polar solvents, whereas exciplexes are favored in weakly polar solvents. 2. The diffusive mobility of ions is influenced by viscosity and polarity of the solvent. Diffusion of charged particles separated by d i n a potential U = eo2/Edis given by the DebyeSmoluchowsky e q ~ a t i o n . ~Conceptually, the attraction is Present address: The Institute of Physical and Chemical Research (RIKEN), Molecular Photochemistry Laboratory, Hxosawa 2-1, Wako, Saitama 351-01, Japan. @Abstractpublished in Advance ACS Absrrucrs, December 1, 1994.
0022-365419512099-0248~09.00l0
stronger between the two ions of the pair in a nonpolar solvent because screening of the Coulomb force is weaker. Therefore, in a nonpolar solvent, the average distance between the ions of the pair will be smaller; thus, the probability will be higher that the two ions of the pair will reencounter each other within a certain time. The influence of solvent polarity on the distance distribution has also been evidenced in recent Monte-Carlo calculations,1°namely, that conformations of chain-linked radical ion pairs with short distances become more probable the less polar the solvent is. Taking both effects together (the relative position between the exciplex and the RIP energy levels as a function of E and the solvent-related ion-screening effect), the mDK maximum can be explained, as has been shown quantitatively by Nath and Chowdhury” and Petrov et a1.,12by solving the DebyeSmoluchowski diffusion equation. Petrov et al.I2 have determined Aq(B)/q(O),which is the ratio of the magnetic-field-induced (B) portion relative to the total exciplex fluorescence yield, q, at B = 0, in pyrene and N,Ndimethylaniline (DMA) and N,N-diethylaniline, respectively, in alcohols and alcohol mixtures of varying polarity. For the first time, these investigators saw a maximum of the MFE for Aq(B m,E)Iq(O) in solvents of medium polarity ( E 20). These workers assume a distinct potential barrier between exciplex and RIP which increases with increasing solvent polarity, as would be expected from the E dependence of AGExc and A G ~ S ~The . ~decrease , ~ of the MFE toward lower DK values has been explained by way of these influences: (a) A larger fraction of molecules undergoes charge transfer at small donorlacceptor distances; the exciplex is therefore formed directly and without magnetic field effect. (b) The fraction, initially present as the RIP state, reaches a large distance d = Q less frequently in view of the Coulomb attraction, whereas beyond Q the exchange interaction between the radical ions is sufficiently weak to allow a hyperfine-coupling-induced (hfc) intersystem crossing. At d > rB one has 2J < AEhfc. 2J is the energy splitting of the singlet and triplet radical ion pair states (with J being the exchange interaction between the unpaired electrons); AEhfCis the hyperfine coupling energy. The distance
-
1995 American Chemical Society
Recombination Reaction of Radical Ion Pairs ~g is rarely reached for another reason, namely, recombination under exciplex formation promoted by the smaller barrier. Therefore, Ap decreases with increasing p so that the ratio Ap/p is decreasing strongly. For E > 26, Ap/p decreases firstly because of a lower dissociation barrier (function eo2/Ed) and secondly because the banier for exciplex formation becomes higher. For this reason, the magnetic-field-dependent portion of exciplex fluorescence (Ap) becomes smaller, and p decreases more gently, since a certain fraction of electron transfer proceeds within such a short distance so that the exciplex is formed directly. Nath and Chowdhury" have measured the MFE of the exciplex fluorescence in pyrene in DMA in both a series of alcohols and mixtures of aprotic solvents. Their results exhibit maxima at medium solvent polarity in the range from E = 15 to 28, although with distinct differences. The various aprotic mixtures show €-independent maxima of differing intensity, the most pronounced maximum having been observed in a mixture of DMF and THF. For the explanation of this observation, a numerical solution of the Debye-Smoluchowsky equation seemed sufficient, in which a barrier between SSIPs and contact ion pairs (CIPs) was considered independent of solvent polarity. The approach of these investigators envisions formation of RIPs exclusively at a distance rg, whose magnitude is chosen to provide the best fit to the experimental data. d = rg = 8 8, is a spacing beyond the barrier. In addition to the variation of Ap/rp, the exciplex yield as a function of DK was simulated with a diffusion model. In a further p~blication,'~ the appearance of an mDK maximum was reported in THF/DMF mixtures with E = 16, where pyrene and DMA were incorporated in a polystyrene string with an average distance of 40 8, between pyrene and DMA. The explanation for this result seems to be similar to the above arguments, but this interpretation appeared somewhat ambiguous to those authors. The use of linked A D pairs (as in the present work) provides one fundamental difference in experimental conditions: Because the molecules diffuse painvise through the solvent, the concentration can be chosen orders of magnitude lower, while the mean intrapair distance corresponds to an effective quencher concentration of typically 0.1- 1 M, compared with free systems. B ~ s m a n n measured ~ ~ J ~ the MFE of the polymethylene-linked systems p yrene-(CH2)16-DMA and pyrene-(CH2)9-DMA in isoviscous mixtures of ethyl acetate and acetonitrile mainly via triplet absorption and to some extent via exciplex emission. In all cases, Busmann found a monotonic increase of the MFE with solvent polarity. While the increase in emission was monotonic, it was clearly not linear but rather saturated at some intermediate DK value. By using the linked compound phenanthrene-(CH&o-DMA, Tanimoto et a1.I6 also observed a monotonic increase with solvent polarity, rather than an mDK maximum. These findings are consistent with and supportive of the explanations discussed above: Without the possibility for homogeneous recombination, a decrease of the MFE going from medium to high DKs should not be observed. The model for explaining the mDK maximum, based on diffusion-dominated competition between geminate and homogeneous recombination at high solvent polarities and associated increased magnetic-field-independentexciplex formation at low solvent polarities, has been established as a plausible mechanism on the basis of the previously cited works. This can be inferred from review articles of Steiner and Wolfp and Bhattacharya and Chowdhury.17 Petrov et a1.,l8 however, have recently provided a deviating explanation of an mDK maximum for pyreneDMA in mixtures of dimethyl sulfoxide (DMSO) and benzene, as well as DMSO/ dioxane. Their interesting qualitative interpretation, which also
J. Phys. Chem., Vol. 99, No. 1, 1995 249 includes the system DMF/THF, suggests that these solvent mixtures are not homogeneous but rather that microdomains of the more polar solvent are formed around the RIPs. This then is suggested to lead to a preference of the RIP relative to the exciplex, although free mobility exists for the ions enclosed within the domains surrounding the ion pairs. An additional report of an mDK maximum is provided by Levin et al.,19 in which the MFE of triplet exciplexes (measured in absorption) of durochinone and triphenylamine exhibit a maximum in alcohols at E = 13. In the course of exploring geminate radical ion recombination reactions in general, we reinvestigated the relationships in the mDK MFE of polymethylene-linked radical ion pairs, arriving at new and surprising findings which call for a substantially different interpretation, leaving a competition between geminate and homogeneous recombination out of consideration.
11. Experimental Section Apparatus. The MFE of the exciplex emission was measured at about 595 nm. The apparatus, using UV excitation and lock-in detection, has been described elsewhere.20 The MFE in the triplet absorption was measured with a laser-pumpprobe at 415 nm. The chosen delay time between the excitation pulse (337 nm, 7 ns) and the measuring sampling pulse (415 nm, 5 ns) was 200 ns. Fluorescence spectra, corrected by comparison with a chinin bisulfate standard, were obtained with a Perkin-Elmer LS50 spectrometer. The timecorrelated single-photon-counting method was applied to measure fluorescence decay curves with time resolution of about 1 ns. Decay curves of the RIP absorption were determined at 495 nm with a time resolution of 5 ns using a transient recorder, after excitation with an N2 laser (337 nm, 3 ns). All experiments were carried out at room temperature. Preparation of Samples. All compounds were of HPLC quality. 1-Pyrene-(CH2),-N,N-dimethylaniline (abbreviated Py(n)DMA) with n = 8,9, 10, and 16, was dissolved in different solvents (as purchased): acetonitrile (ACN), ethyl acetate (EthAc), tetrahydrofuran (THF), acetone, and diethyl ether (DEE), all Merck Uvasol for fluorescence spectroscopy; N,Ndimethylformamide (DMF) purissimum from Fluka (plus molecular sieve) or Uvasol from Merck, respectively. The refractive index, density, and DK of the solvents and their binary mixtures were measured; linear plots were obtained without exceptions, and anomalies were not evident. For the extensive series of solvent mixtures in each case, mother solutions were prepared in both solvents and of identical optical density (0.7 at 337 nm). For the unlinked system, concentrations were M pyrene and 7.6 x M DMA. The individual probes were then obtained by mixing the mother solutions in the desired ratio. The freshly prepared probes were then bubbled with dry nitrogen for 20 min and sealed. The measurements were carried out within 1 h after probe preparation. Comparison with probes prepared by the freeze-pumpthaw technique did not show significant differences. All series of measurements were carried out repeatedly with new samples in changing succession. 111. Results Magnitude of the Magnetic Field Effect. The MFE of the exciplex fluorescence of the compounds Py-(CH&-DMA and Py-(CH2)16-DMA was measured in various solvents and solvent mixtures. The resulting data for Py(9)DMA are shown in Table 1. The values Aplp = P(B)/Z'(O) - 1 describe the change of the exciplex fluorescence intensity at field strength ( B ) relative to B = 0. Ap/pIsat is the magnitude of the saturation MFE at B = 3000 G (see Figure 1). The intensities of the
Werner and Staerk
250 J. Phys. Chem., Vol. 99, No. 1, 1995
TABLE 2: Py(16)DMA: Values of the MFE (Aq/qlsat)in Mixtures of Aprotic Solvents
TABLE 1: Py(9)DMA: Values of the MFE ( A q I q l 3 in Mixtures of Aprotic Solvent@ vol%
E
100 85/15 75/25 65/35 50150 35/65 25/75 15/85 100
36.7 32 29.4 26.5 22.0 17.7 14.7 11.8 7.4
8.7 11.9 12.2 15.9 18.1 16.9 11.8 6.1
100 86/14 75/25 65/35 50/50 35/65 25/75 16/84 100
37.5 33.3 30.0 27.0 22.5 17.9 14.9 12.2 7.4
5.5 7.3 9.3 11 12.3 12.5 9.9 4.3
ACN ACNIEthAc ACNIEthAc ACNIEthAc ACNIEthAc ACNEthAc EthAc
100 75/25 63/37 37/63 25/75 100
37.5 29.6 25.7 21.8 17.9 14.0 6.4
5.5 7.4 9.2 9.4 7.7 4.3 0
DMF AcetoneDMF Acetone
100 50150 100
36.7 28.7 20.7
8.7 11 11
ACNDEE
50150
18.7
7.4
DMSOhenzole
25/75
THF ACN ACNRHF ACNRHF ACNRHF ACNRHF A C N M ACNRHF ACNRHF
THF
50150
solvent
vol %
E
A d d s a t .%
DMF D M F R DMFRHF D M F R D M F R D M F R
100 75/25 65/35 50150 35/65 25/75 100
36.7 29.4 26.5 22.0 17.7 14.7 7.4
59 69 70 72 56 38 0
4 4.5 6.2 10 17 30 134
110
580 5 80 575 570 565 565 561 552 518
6
THF
37.5 22.5 7.4
44
6.9 8.8 11.3 18.5 31.5 49 64 110
577 575 573 570 559 556 548 537 518
100 50150 100
ACN ACNIEthAc EthAc
100 50150 100
37.5 21.8 6.4
44 34 0
acetone acetone/DMF acetone/ACN
100 50150 50150
20.7 28.7 29.2
46 69 48
A . Q ) / . Q% ) ~ ~ ~4~c, , au
solvent DMF D M F R D M F R D M F R DMFRHF D M F M D M F R DMF/THF
3 4.5 6.1 11.7 19 28
0
0
12gXc,nm
THF ACN A C N R
9
Intensities of the exciplex emission band ( P E ~at~ LExc ) in arbitrary units (au). 0.20
r
1
...._ _._. 25 % DMF 0.15
-
0.10
-
0.05
-
t
8
0
______
35 % DMF
,,.-__ ”..”..........-
65 % DMF
-100%DMF
200
400
653
800
1M)o
1200
1400
magn. field strength [GI Figure 1. Magnetic field effect of exciplex fluorescence of compound Py(9)DMA in four different binary mixtures (vol %) of the solvents ~~,, DMF and THF. The arrows indicate Aq/qlfin and A ~ p l q ( respectively, for the 100% DMF curve.
exciplex fluorescence are designated as Z‘ (primed). is the intensity of the exciplex emission determined at the maximum of the exciplex band, 2 ~ ~The ~ )last. column in Table 1 shows the measured wavelength shift of the exciplex emission bands with solvent polarity as is also predicted from the AGxc(e) dependence.6s8 An mDK maximum is observed in almost all series of measurements. Even in the single solvent of medium polarity, acetone, a more pronounced MFE, is observed compared to the most polar solvent. Within the series of DMF/THF mixtures, a well-formed maximum is obtained, just like the maximum
au
.
54
0
134
seen in a nonlinked system. In DMF (e = 36.7), the MFE increases from 8.7% until it reaches a magnitude of 18.1% with a 50% mixture ( E = 22). We also note that the mDK maximum in the isoviscous mixtures of ethyl acetate (EthAc)/ACN increases from 5.5% to 9.4%. For the DMF/THF and ACN/ THF series, Table 1 also provides the exciplex fluorescence intensities (PE,,), which generally decrease in the range of medium-to-high polarities. Table 2 shows the corresponding data for Py( 16)DMA, with the most pronounced MFE increase also seen for the DMF/ THF mixtures. The mDK maxima are less clearly evolved in all solvent series. In the case of ACN/EthAc, we note a monotonic decrease, in as much as it can be inferred from the three data points. The MFE values are relatively large, with the 72% increase in the 50% DMFtTI-LF mixture representing somewhat of a new “record” value. This is all the more remarkable, since the intensity of the exciplex bands is already quite strong, and the increase of fluorescence intensity induced by the magnetic field can be seen with the unaided eye. The exciplex yields increase as in Py(9)DMA with decreasing DKs. Up to a 50% mixture, the fluorescence intensity increases more slowly, and beyond 50%, the increase is steeper. Figure 1 depicts a series of MFE traces of Py(9)DMA in DMFRHF, shown as A q l q vs B. A positive value indicates a magnetic-field-induced increase of the exciplex fluorescence, while a negative value is equivalent to a fluorescence decrease. In addition to the variation of the magnitude of the MFE, we note a small shift of the characteristic features B I B and B-, where B1/2 is the magnetic field strength where MFE reaches half its saturation level and B- is the field strength corresponding to the position of the minima. This shift is most probably related to viscosity differencesz5 (1;1~m = 0.80 “a-s; 1;1m = 0.47*a%). In the more nearly isoviscous series of ACNEthAc in ACNA-IF, this shift is no longer evident. The characteristic field strengths are invariant with polarity variations in these mixtures. In the following measurements and representations,we extract the parameters A&lSat = P(3000 G)/Z‘(O G) - 1 and Aq/qlmin = Z’(O)/Z‘(B-) - 1, which are the magnitudes of the MFEs at saturation and at the minimum, respectively. For the trace, 100% DMF hq/qIsat and Aq/qlmin are indicated in Figure 1 by the arrows. In Figure 2 is shown the DK dependence of the MFE for various molecules in the solvent mixture DMF/THF. All four molecules exhibit a maximum at medium polarities. A characteristic variation is apparent as a function of chain length: Arp/qIsat decreases with decreasing chain length, the mDK
J. Phys. Chem., Vol. 99, No. 1, 1995 251
Recombination Reaction of Radical Ion Pairs Py8DMA
J 0
10
20
30
o
10
PylODMA
i
I
20
30
20
10
I
I
1
I
60
80
100
120
140
160
Pyi6DMA
time [ns]
I
0
I
I
40 00
I
30
dielectric mnstanl
0
10
20
30
dielectricconstant
-
Figure 2. Comparison of ''minimum'' (extremum) MFEs (+) and "saturation" ( B -) MFEs (0)of the four compounds investigated in the binary mixtures DMFRHF. In each case, the mDK maximum is lower and shifted to higher values of the bulk DK. In of nmrI@& the series of molecules Py(l6)DMAto Py(S)DMA, the mDK maxima
become increasingly accentuated. The ordinates are differently scaled.
Figure 3. Normalized decay curves of the exciplex fluorescence of
Py(9)DMA in different DMFlTHF mixtures (cf. Table 3). When plotting the ~ A A Tvalues ~ vs solvent polarity, the traces for all four molecules substantially agree with the exciplex emission t r a ~ e s . 2 ~ Lifetimes of Radical Ions. The pyrene radical anion Py- is identified by its absorption band at 495 nm. In many measurements of the temporal decay of the RIP concentration and of the exciplex emission (the latter with the time-correlated singlephoton-counting method), it was found that both lifetimes are comparable among all compounds of the pyrene-linkageDMA type in medium-to-highly polar solvents (e > 15). It can therefore be concluded that the exciplexes (which are actually CIPs) are in equilibrium with the SSIPs and thus have the same lifetime as the SSIPS?~indicating that the diffusion rate of the ions is higher than the recombination rates for singlet SSIps and singlet CIPs (exciplexes). Since the method of timecorrelated single-photon counting is simpler and more precise than the measurement of transient radical ion absorption, the decay kinetics of RIPs in solvents with e > 15 were determined via the temporal decay of the CIP emission. Figures 3 and 4 show the decay curves of the CIP emission for Py(9)DMA in DMFRHF mixtures. All traces are shown as normalized best fit curves following triple-exponential fitting by
maximum becomes more defined, and its position shifts toward lower solvent polarity. The MFE vanishes at DK < 10. The relative scaling for the maxima, particularly for Py(9)DMA, is noteworthy. In Py(8)DMA, the exciplex intensity at saturation (3000 G) increases by about 1% in pure DMF, whereas a 6% increase is observed in the solvent mixture 35% DMFRHF. With respect to the saturation MFE Ap7/qlsat and the minima Aqlpl-, two phenomena are apparent in Figure 2: the mDK maxima (IAq/p71) are weaker in Aq/ql,, than in Ap7/qlsat,and they are displaced toward higher DK values. This displacement is evident from the processes depicted in Figure 1: In a solvent of polarity somewhat lower than the solvent providing the mDK maximum, the saturation effect is more pronounced. If the solvent polarity somewhat exceeds that of the mDK maximum, then the resonance at B- (FWHM) is more pronounced in comparison to the shifts at saturation. Magnetic Field Effect of the Triplet Concentration. In order to demonstrate that the mDK maximum evolves exclusively in the sequence of the intersystem crossing step related ~ ' ( t=) cle-"rl + C2e-''"2 + c3e-'/r3 to spin conversion in the RIP states and not in the exciplex (1) formation step, all series were also characterized by absorption. The measurement procedures were described p r e v i ~ u s l y . ~ * - ~ ~where tl is the emission rise time and ranges from about 1 ns Here, the MFE is determined by the magnetic-field-dependent for DMF to about 3 ns for THF. This rise time reflects the triplet absorption after excitation. formation of RIPs from the locally excited state ('A*-D) and It is observed that the highest triplet concentration occurs in is identical with the lifetime of the excited state. From the decay the least polar solvents. The largest triplet fraction cannot be times z2 and t3 and their variations among various compounds generated by way of the hyperfine-induced step in the S S P , and solvents, there is no direct evidence for the reaction since virtually no long-lived RIPs are formed in THF in view mechanism and its kinetics. Rather, we assume that the of energy level considerations (cf. refs 6 and 8). Rather, the observed kinetics result from a complicated interplay among mechanism of triplet formation is based on the exciplex-related the distance-related rates and the diffusional motion of the enhanced matrix element governing singlet-to-triplet transition charged end groups of the molecules. Therefore, a singleby spin-orbit coupling.26 The isc mechanism effective in the exponential process cannot be expected. The six free-fitting exciplex does not provide an MFE. Therefore, conclusions parameters in accordance with eq 1 are sufficient to represent cannot be drawn on the dependence of the hfc mechanism on the measured data points within the relevant time frame. In solvent polarity based on triplet absorbance, AT@), alone. Only order to obtain a value for the decay, we introduce an average in highly polar solvents like ACN can the MFE be described lifetime (z), directly by the AT(B) curves, since the exciplex fraction from which triplets can yield due to spin-orbit coupling is small. To separate out the magnetic-field-independent contribution, we where (z) is that time at which the area under the actual decay evaluated the term ~AAT(B)I= /AT@) - AT(O)I. From this, a curve is identical to the area under a single-exponential curve direct measure is attained of the additional (or reduced) with lifetime (t)and with C2 C3 as the prefactor. Table 3 absorbance attributable to an external magnetic field.
+
Werner and Staerk
252 J. Phys. Chem., Vol. 99, No. 1, 1995 I
I
I
I
I
I
40
60
60
100
120
140
160
time Ins]
Figure 4. Normalized decay curves of the exciplex fluorescence of Py(16)DMA in different D M F m mixtures (cf. Table 3). TABLE 3: Average Decay Times (z) of the Exciplex Emission of Donor-Acceptor Systems in Binary Mixtures of DMF and THF at about Zero Magnetic Field Strength” (d.ns 8 DMF Py(l6)DMA Py(9)DMA Py(8)DMA pyrene -tDMA 3.1 16.1 12.4 100 16.0 3.6 22.6 17.5 75 16.3 5.5 36 30 50 19.0 15 48 47 25 35 0 71 78 64 80 The temporal behavior of the exciplex emission (CIP emission) at higher solvent polarities (6 > 15) is used as a monitor for the kinetics of the RIPS. contains these average lifetime values for four molecular systems in different solvent mixtures. The following is apparent from Table 3: In 100%THF, the exciplex decay among the three polymethylene-linked compounds is comparable, and the decay is longest. As solvent polarity increases, the lifetime of the exciplexes (and of the RTps) decreases. The variation of (r) over the entire E range ( E = 7.4-36.7) is much greater than the range among the various molecules (with different chain length) at fixed E . The nonlinked system pyrene DMA, dissolved with concentrations given in the Experimental Section, shows distinctly shorter lifetimes than the linked systems in polar solvents. Only in THF is a long lifetime observed which describes the decay of the exciplex (but not of RIPS). The influence of an external magnetic field on the temporal behavior of the exciplex emission is shown in Figure 5 for Py(16)DMA in 1:l D M F m , measured at 552 MI. Shortly after the excitation (by a 2 - m 337-MI excitation pulse), the signals are of comparable level with and without magnetic field. A difference evolves when those CIPs are emitting which were previously resident as intramolecular SSIPs in the “magneticfield-sensitive distance range”. The emission yield is increased by the applied magnetic field since fewer SSIPs are disappearing by the radiationless transition into the triplet state. The magnetic field affects the curve fitting in all parameters according to eq 1, which further indicates that the general shape of the decay curve is strongly influenced by diffusion processes in a complicated way (cf. ref 25).
+
N. Discussion As pointed out in the Introduction, the models by Petrov et aiel2and Chowdhury and Nath” are based on a competition between geminate and homogeneous recombination, where the
0
30
60
90
120
150
180
210
240
270
300 330
time (ns]
Figure 5. Temporal behavior of the exciplex emission of Py(l6)DMA in a 1:l mixture of DMF and THF, without and with an external magnetic field of lo00 G. Excitation intensities and measuring times were the same for both curves. distribution is governed by variable screening effects on the mutually attracting ions by the various solvents. In contrast, the linked molecules of the present investigation cannot have such a distribution, since ion pairs cannot diffuse apart farther than the linkage will allow. The probability of a “homogeneous recombination” of two unrelated ions (from different pairs) is quite low in view of the low concentration and short lifetime of such ion pairs. Thus, only geminate recombination is possible in linked systems. With this predisposition, a disappearance of the MFE at low polarities can be explained if the ions cannot diffuse to a distance greater than ~gdue to mutual attraction. At higher solvent polarities, the MFE is expected to reach and maintain its highest level. This behavior of linked compounds has been described by Busmann et al.14JJand Tanimoto et a1.16 However, the compounds and solvents under reinvestigation here have shown results quite similar to the free system. In light of the present results, it must be considered that the previous interpretation^^^*^^ may have been incomplete. Thus, for example, while the increase of the MFE with solvent polarity was observed in the triplet absorption of Py(9)DMA and Py( 16)DMA, its interpretation was incomplete because the contribution of tiplets generated by spin-orbit coupling in the exciplex was not considered at the time. The model by Nath and Chowdhuryll even suggests that not only the mDK maximum of the MFE but also the increase of the CIP-emission yield is caused by diffusion-related distribution between homogeneous and geminate recombination in nonpolar solvents. This would imply that the CIP emission (exciplex emission) in the linked system should be constant throughout the entire range of solvent polarities. Present observations do not support this view. With respect to the appearance of an mDK maximum of the IvlFE, we observe no fundamental difference in our linked systems compared to the free system. Thus, the above models apparently fail in their applicability in linked compounds, although the measured results are very similar to the results for the free A/D systems. The recent explanation, advanced by Petrov et al.,@ is based on the concept of an inhomogeneous mixture of solvents in the presence of donor and acceptor in solution (dielectric enrichmentlsb) so that polar microdomains are assumed to be formed around the RIPS. This postulation cannot explain the present results either, since under the view of those authors microdomains would exhibit a condition leading to saturation at higher solvent polarities, but not to a MFE decrease as observed here. From the foregoing discussion, it appears that neither model
J. Phys. Chem., Vol. 99, No. 1, 1995 253
Recombination Reaction of Radical Ion Pairs seems to be able to fully explain the mDK maximum of free as well as linked systems. Development of a New Conceptual Model. The most important experimental results are summarized here: (i) An mDK maximum can be observed in linked systems. The extent and location of the maximum varies with chain length. The mDK maximum is not a consequence of effects directly related to CIP emission. The maximum is also found in the direct MFE observation via the magnetic-field-dependent triplet concentration. (ii) Fundamental differences between free and linked systems are not apparent. (iii) The CIP (exciplex) lifetime increases with decreasing solvent polarity. (iv) The total yield of the CT emission increases strongly from medium solvent polarities ( E = 20) toward low polarities. The last point is not surprising, since this functional dependence of the exciplex is favored at low polarities, as has been found in many A/D systems before.28 In the low-polarity range, the quenching of a locally excited state proceeds predominantly by the mechanism
-.'A*D
~A*-D
U
h v D~
-. ~(A-D+)*
U
U
(3)
That process leads to light emission with high efficiency in the spectral range of typical exciplex bands. The decay curves measured in the single solvent THF therefore describe the kinetics of the exciplex since RIPs are no longer involved, or at best appear as short-lived transient intermediates. At high polarities, mainly RIPs are formed whose successor products are distributed along three reaction paths:
U
U
Reaction 4a comprises the magnetic-field-dependent spin conversion with overall rate k,@) followed by recombination to the locally excited triplet state with kn,29 (4b) describes the recombination to the ground state with krg, and (4c) describes the formation of the emissive CIP with fast dynamic equilibrium between SSIP and CIP.23325 As a consequence of the competition indicated in (4a) and (4b), the emission in (4c) is magnetic field dependent in contrast to the emission as indicated in (3). The transition between (3) and (4a)-(4c) occurs in the range E = 7-20, thus explaining the strong decrease of CT emission and the increase of the MFE from zero to its maximum value in this range. Relationship between MFE and RIP Lifetime. We have seen that the appearance of mDK maxima cannot be related to the competition between geminate and homogeneous recombination, neither in free systems nor in linked systems. The qualitative explanation of the mDK maximum proposed here is based on the observation of an increasing RIP lifetime with decreasing solvent polarity. A connection between RIP lifetime and the magnitude of the MFE is pointed out in Table 4 and also corresponds to observations of A-D molecules with partially rigid chain structures: The strongest MFEs were found whenever the RIP lifetime was particularly high.27,31 This apparent correlation can be understood by envisioning the steps required for the appearance of an MFE: Subsequent to excitation of the acceptor, ET, and formation of A - and D+,a diffusion step must take place, in which the two radical ions are brought
TABLE 4: RIP Lifetimes (ns)and MF'E (Arp(B)/qIsst)for Linked and Free Compounds in Solvent Mixtures of THF and DMF of High and Medium Bulk Dielectric Constant (DW Py(16)DMA rRIp
Py(9)DMA
MFE rRp
MFE
Py(8)DMA rRp
MFE
pyrene rRIp
+ DMA MFE
highDK 16.0 0.60 16 , 0.087 12.4 0.013 3.1 0.032 0.091 mediumDK 19.0 0.72 36 0.181 46.4 0.061 15 increase,% 18 20 220 210 380 470 480 280
"Medium DK refers to the mixture yielding the maximal MFE. More details are given in ref 27. to a separation distance of at least rg, beyond which the exchange interaction among the unpaired electrons is sufficiently small so that a hfc-induced transition from a total singlet radical pair state to a triplet radical pair state can take place; i.e., 25 < AEhfCfor d > rg.32 The hfc-induced kinetics of the spin system has been calculated e ~ 1 i e r . l . It ~ ~depends upon the applied magnetic field; 5 ns is a typical time to reach a final triplet probability. A related computation and diagram can be found in the literat~rel2~J~ in which it is explicitly shown that the MFE reaches its final value within a few nanoseconds. For the spin conversion which can take place, only time intervals are relevant in which the radical ion pair resides in the magnetic-fielddependent distance range (d > rg). The development time in a real molecular system, however, may be extended by about a factor 10 due to diffusional walks (stochastic time-dependent variation of the intrapair distance), if the magnetic-field-sensitive distance range is restricted to a small fraction (from I-B to d-) of the total accessible distance range (2r 5 d 5 d"). After the ion pair has resided for such an MFE-relevant time interval at distances d > rg, the distance between the ions must decrease again so that return electron transfer (RET) in the RIP can lead either to the ground state (A-D) or to the triplet state (e.g., 3A*-D) or, alternatively, recombination can occur via CIP formation whereby an MFE appears in the exciplex emission yield (cf. eqs 4 a - 4 ~ ) ~The ~ ~diffusional motion across the distance scale is assumed to take place on a shorter time scale than both the evolution of the spin system and the overall rate of RET (i.e., A$. During its lifetime, a RIP can attain numerous distances, residing at each distance only for a short time. This range of distances corresponds to a spectrum of exchange interaction^.^^^^^^^^ In short chains (e.g., with Py(8)DMA or Py(9)DMA), distances d > rg (where a hyperfine-induced spin conversion becomes possible) will be reached less frequently than in longer chains (e.g., with Py(l6)DMA). In molecules with a linkage shorter than (CH2)8, this distance range is not reached at all. From the presence of the necessary diffusion steps in the evolution of the MFE, the connection between RIP lifetime and achievable magnitude of the MFE becomes evident: An increase of the RIP lifetime leads to a longer residence time in the magnetic-field-sensitive distance range and therefore, averaged over the ensemble, to a larger MFE. We attribute the lifetime variation of the RIPS predominantly to the AG(E)variation in the "Marcus inverted region"; AG for the singlet RET for our system varies between about 2.7 eV in DMF and 3 eV in THF. A systematic investigation of k(RET) vs AG in flexibly linked systems is in progress in this laboratory. For our chain-linked A-D systems, theoretical models of increasing complexity, which are presently under investigation, are considered, in which the following hierarchy of different aspects is taken into account: (1) The case of single A--D+ distances without diffusion leads to single time-invariant rates for RET. A treatment which is probably appropriate for describing RET in the inverted region has been applied by Gould et al.30336 They obtained rates of
254 J. Phys. Chem., Vol. 99, No. 1, 1995
return electron transfer within SSIPs and CIPs in the framework of the well-known golden rule in which the rate is given as a function of an electronic coupling matrix element, reorganization energies for the rearranged high-frequency (skeletal vibration) and low-frequency (mainly solvent and libration) motions, and an averaged frequency for the skeletal modes. It should be pointed out that, whereas the last step in reaction 4b is in the inverted region, the triplet recombination reaction in (4a), right side, is in the normal regime and may therefore be treated with a similar formalism as the primary step of excited-state electron trnasfer in the normal region. That kfl for the triplet RET, 3(A--D+) 3A*-D, is much larger than kgfor the singlet RET, '(A--D+) A-D, has indeed been verified by absorption measurements of the kinetics of the products mentioned in (4a). (2) The case of flexible A--D+ pairs, where a distribution of A--D+ distances exists,1° possibly results in complex decay kinetics for recombining A--D+ pairs. ( 3 ) If fluctuations occur between various conformations during the lifetime of the A--D+ pairs, the kinetic behavior becomes more complex. This situation requires knowledge of end-to-end diffusion coefficients of flexibly linked ion pairs in the presence of a superimposed attractive Coulomb force. (4) The influence of diffusion is not limited to the intramolecular RET reaction as such; rather, diffusional motion in a complicated way also determines the spin dynamics in the radical ion pairs through the modulation of the spin-exchange i n t e r a c t i ~ nand, ~ ~ ~hence, ~ ~ , ~indirectly ~ affects the partitioning of the RET channels, their kinetics, and the magnetic-fielddependent product yields. Consideration of all four of the above aspects together would require that the quantum mechanical stochastic Liouville equat i ~ be n ~combined ~ with the formalism for singlet and triplet RET and with the proper diffusion equation that describes the relative end-to-end motion of a flexible molecular chain. This combination, however, is a challenge too complex at the current level of understanding and computational practicability. In our recent work, we have attempted to view and characterize the different aspects separately; for points 2 and 4, cf. refs 10, 25, and 35. A conceivable additional influence of preferential solvation in binary liquids (so-called dielectric enrichment)18 cannot be estimated quantitatively at present and is therefore not considered here; however, a systematic investigation of this point is in progress in this laboratory applying spectro-streak te~hniques.3~ The above results and thoughts are of great relevance to fluorescence probe systems of the type pyrene-linker-oligonucleotides (for hybridization studies with single-strand nucleic acids) in studies presently under intense investigation in this laboratory.
- -
Acknowledgment. We thank Dr. W. KiiMe and his collaborators for supplying the polymethylene-linked model compounds used in this work. We also thank A. Wiessner, H.Ch. Rohland, and T. Fiebig for helpful discussions. We appreciate assistance provided by B. Frederichs and H. Meyer. References and Notes (1) Schulten, K.; Staerk, H.; Weller, A.; Wemer, H.-J.; Nickel, B. Z. Phys. Chem. 1976, 101, 371. (2) Michel-Beyerle, M. E.; Haberkom, R.; Bube, W.; Steffens, E.; Schroder, H.; Neusser, H. J.; Schlag, E. W.; Seidlitz, H. Chem. Phys. 1976, 17, 139. (3) (a) Steiner, U. E.; Ulrich, T. Chem.Rev.1989,89,51. (b) Salikhov, K. M.; Molin, Yu. N.; Sagdeev, R. Z.; Buchachenko, A. L. In Spin Polarization and Magnetic Field Effects in Radical Reactions; Molin, Yu. N., Ed.; Elsevier: Amsterdam, 1984.
Wemer and Staerk (4) (a) Steiner, U. E.; Wolff, H.-J. Photochemistry and Photophysics; J. Rabek, J., Ed.; CRC: Boca Raton, FL, 1991; Vol. IV,Chapter 1, p 1. (b) Hayashi, H. lbid. 1990, Vol. I, Chapter 2, p 59. (5) Kavarnos, G. J. Fundamental Concepts of Photoinduced Electron Transfer. Topics in Current Chemistry: Photoinduced Electron Transfer; Springer-Verlag: Berlin, 1991; Vol. 156. (6) Weller, A. Z. Phys. Chem.(Wiesbaden) 1982, 133, 93. (7) Rehm, D.; Weller, A. Z . Phys. Chem. 1970, 69, 183. (8) Weller, A. In The Exciplex; Farster, T., Ed.; Academic: New York, 1975. (9) Clifford, P.; Green, J. B.; Pilling, M. J. J. Phys. Chem. 1984, 88, 4171. (10) Wemer, U.; Staerk, H. J . Phys. Chem. 1993, 97, 9274. (11) Nath, D. N.; Chowdhury, M. Pramana 1990,34, 51. (12) Petrov, N. Kh.; Shushin, A. I.; Frankevich, E. L. Chem. Phys. Lett. 1981, 82, 339. (13) Basu, S.; Nath, D. N.; Chowdhury, M.; Winnik, M. Chem. Phys. 1992, 162, 145. (14) Busmann, H.-G. Dissertation, University G$mgen, 1987. (15) Staerk, H.; Busmann, H. G.; Kiihnle, W.; Weller, A. Chem. Phys. Len. 1989, 155, 603. (16) Tanimoto, Y.; Hasegawa, K.; Okada, N.; Itoh, M.; Iwai, K.; Sugioka, K.; Takemura, F.; Nakagaki, R.; Nagakura, S. J. Phys. Chem. 1989, 93, 3586. (17) Bhattacharya, K.; Chowdhury, M. Chem. Rev. 1993, 93, 507. (18) (a) Petrov, N. Kh.; Borisenko, V. N.; Starostin, A. V.; Alfimov, M. V. J . Phys. Chem. 1992, 96, 2901. (b) Suppan, P. J. Chem. Soc., Far& Trans. 1987,83,1. (c) Petrov, N. Kh.; Boriseuko, V. N.; M i o v , M. V. J. Chem. Soc., Faraday Trans. 1994, 90,709. (19) Levin, P. P.; Raghavan, P. K. N.; Kuzmin, V. A. Chem. Phys. Lett. 1990, 167, 67. (20) Werner, U.; Kiihnle, W.; Staerk, H. J . Photochem. Photobiol., A: Chem., in press. (21) Staerk, H.; Kiihnle, W.; Weller, A,; Werner, U. Z. Phys. Chem., in press. (22) Treichel, R.; Staerk, H.; Weller, A. Appl. Phys. B 1983, 31, 15. (23) Staerk, H.; Kiihnle, W.; Treichel, R.; Weller, A. Chem. Phys. Lett. 1985, 118, 19. (24) L a d , N. L.; Wemer, U.; Molin, Yu. N.; Staerk, H. J . Chem. Phys. 1993, 99, 304. (25) Staerk, H.; Busmann, H.-G.; Kiihnle, W.; Treichel, R. J . Phys. Chem. 1991, 95, 1907. (26) McGlynn, S . P.; Azumi, T.; Kinoshita, M. The Triplet State; Prentice-Hall: Eaglewood, Cliffs, NJ, 1969. (27) Wemer, U. Dissertation, University of Gottingen, 1993. (28) Beens, H.; Knibbe, H.; Weller, A. J. Chem. Phys. 1%7,47, 1182. (29) Weller, A.; Staerk, H.; Treichel, R. Faraday Discuss. 1984, 78, 271. (30) Gould, I. R.; Young, R. H.; Moody, R. E.; Farid, S. J . Phys. Chem. 1991, 95, 2068. (31) Werner, U.; Kiihnle, W.; Staerk, H. J. Phys. Chem. 1993,97,9280. (32) For the sake of a simplified discussion, is used here as a crude distance mark. One has to keep in mind that motional effects determine the probability distribution w ( U ) of the exchange interaction so that the dynamic w ( U ) distribution and the most probable singlet-triplet splitting, 2Je#, generally deviate from the static ones, particularly being much more in evidence in linked system^.*^^^^ (33) Wemer, H. J.; Schulten, Z.; Schulten, K. J. Chem. Phys. 1977,67, 646.
(34) Schlenker, W.; Ulrich, T.; Steiner, U. E. Chem. Phys. Lett. 1983, 103, 118. (35) (a) Busmann, H. G.; Staerk, H.; Weller, A. J . Chem. Phys. 1989, 91, 4098. (b) Bittl, R.; Schulten, K. J. Chem. Phys. 1989, 90, 1989. (36) Gould, I. R.; Noukakis, D.; Gomez-Jahn, L.; Young, R. H.; Goodman, J. L.; Farid, S. Chem. Phys. 1993, 176, 439. (37) (a) Hopfield, J. J. Proc. Natl. Acad. Sei. U S A . 1974, 71, 3640. (b) Van Duyne, R. P.;Fischer, S.F. Chem. Phys. 1974,5, 183. (c) Ulstrup, J.; Jortner, J. J. Chem. Phys. 1975.63.4358 and references to earlier work therein. (d) Siders, P.; Marcus, R. A. J . Am. Chem. SOC.1981, 103, 741, 748. (e) Marcus, R. A. J. Chem. Phys. 1984,81,4494. (f)Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 81, 265. (38) (a) Staerk, H.; Wiessner, A.; Kiihnle, W. J. Fluoresc. 1994,4, 87. (b) Wiessner, A.; Staerk, H. Rev. Sci. lnstrum. 1993,64, 3430. (c) Petrov, N. Kh.; Wiessner, A.; Fiebig, T.; Staerk, H. Manuscript in preparation. JP9413758
