Bianthryl in Solution Studied by Photoacoustic Calorimetry and

The photophysics of singlet excited 9,9′-bianthryl has been studied in solution by stationary and time-resolved experiments using photoacoustic (PAC...
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2012

J. Phys. Chem. 1996, 100, 2012-2018

Deactivation of 9,9′-Bianthryl in Solution Studied by Photoacoustic Calorimetry and Fluorescence Matthias Schu1 tz and Reinhard Schmidt* Institut fu¨ r Physikalische und Theoretische Chemie, J. W. Goethe-UniVersita¨ t, Marie-Curie-Str. 11, D60439 Frankfurt am Main, Germany ReceiVed: April 26, 1995; In Final Form: September 4, 1995X

The photophysics of singlet excited 9,9′-bianthryl has been studied in solution by stationary and time-resolved experiments using photoacoustic (PAC) and fluorescence methods. The results are interpreted under the assumption of a very fast solvent-dependent equilibrium between a pure local excited (LE) and a charge transfer (CT) state. The deactivation of the CT state is treated as nonadiabatic back electron transfer using the formalism developed by Gould et al. for radiative and radiationless deactivation of radical ion pairs. Fluorescence spectra have been separated into LE and CT emission spectra. Calculated CT spectra yield reasonable values for the free enthalpy change of back electron transfer and for the LE a CT equilibrium constant. The energy of the nonpolar triplet state as well as the quantum yields Qisc of intersystem crossing have been determined by the PAC method. The sum of Qisc and the fluorescence quantum yield Qf is near unity, independent of solvent polarity. A procedure for the quantitative correction of electrostriction effects in PAC is presented, which allows the determination of the enthalpy and entropy changes of the LE f CT reaction and of the solvent reorganization reaction in the ground state. Intersystem crossing CT f T1 competes efficiently with CT fluorescence in strongly polar solvents due to spin-orbit coupling, the much smaller energy gap, and the large solvent reorganization energy.

Introduction Since the discovery of the dual fluorescence of 9,9′-bianthryl (BA), its photophysics has found strong interest.1-13 The extraordinary solvatochromism of the fluorescence of BA has mostly been interpreted by the assumption of an equilibrium between molecules in a nonpolar local excited state (LE) and in a strongly polar charge transfer state (CT), with positively and negatively charged anthracene moieties.3-9 It was demonstrated in time-resolved experiments that the intramolecular electron transfer equilibrium LE a CT is already reached in much less than 1 ns.6-9 The fastness of the only weakly exergonic electron transfer equilibrium was explained by a small barrier adiabatic reaction where the raction coordinate corresponds to a solvent coordinate.9 However, the two-state fluorescence scheme is not generally accepted. Recently, Wortmann et al. showed that at least in nonpolar (alkane) and moderately polar solvents (benzene) the spectral changes of the BA fluorescence could be the consequence of a solvent dependent torsional potential in a single excited state without charge transfer.10-12 On the other hand, on the basis of the rather large dipole moment of the emitting species in alkanes, benzene, and dioxane, Visser et al. interpreted the solventinduced spectral changes as a result of BA-solvent exciplex formation.13 Deactivation of the singlet excited species occurs on the nanosecond time scale. In contrast to the fluorescence, only little or nothing is known about the radiationless deactivation of BA, about the importance of intersystem crossing (isc) compared with internal conversion (ic), and about the triplet state T1. Since time-resolved photoacoustic caloriometry (PAC) is particularly suited for the investigation of dark processes and dark states,14 we used our fast PAC setup with a minimum time resolution of 5 ns to determine the triplet state energy ET, the quantum yields Qisc and Qic, and in addition the singlet state X

Abstract published in AdVance ACS Abstracts, January 1, 1996.

0022-3654/96/20100-2012$12.00/0

energy ES of the fluorescing species in a series of solvents of different polarity. To perform the necessary correction of PAC data for the volume changes caused by the electrostriction of the solvent due to CT formation, one has to calculate the fraction fCT of S1 excited BA molecules in the CT state. This can be done assuming the fast equilibrium LE a CT as basis of the evaluation, neglecting possible mixing between these states.6,9 A different procedure compared with previous work is used for the separation of the stationary BA fluorescence spectra into the LE and CT components.4-6 Hereby, a spectrum LE(ν)est being representative for the LE fluorescence is required. We derived LE(ν)est from the BA fluorescence spectrum recorded in perfluorodecalin, considering the solvent-dependent broadening of the vibrational structure as well as the red shift. It is assumed that the deactivation of CT can be treated as nonadiabatic back electron transfer. On the basis of the semiclassical description of optical charge transfer transitions by Marcus,15 Gould et al. developed a refined formalism for the radiative and radiationless deactivation of radical ion pairs which is used to calculate the CT emission spectra and CT deactivation rate constants.16,17 By this way, from the combination of stationary and time-resolved results thermodynamic and dynamic data are obtained, describing the photophysics of BA on the nanosecond time scale. Experimental Section BA18 and 9,10-dinaphthylanthracene (DNA)19 were prepared as described in the literature. BA was purified by repeated crystallizations from CCl4. Purity was verified by thin-layer chromatography. Phenalenone (PHE, Aldrich, 97%) was purified by column chromatography (silica gel/dichloromethane). 2-Hydroxybenzophenone (HBP, Aldrich, 99%) was crystallized twice from ethanol. Perfluorodecalin (PFD, Aldrich, 95%) was purified by column chromatography (neutral aluminum oxide). The further chemicals were 9-phenylanthracene (PHA, Lancaster, 99%), n-hexane (HEX, Riedel-de Haen, 99%), benzene © 1996 American Chemical Society

Deactivation of 9,9′-Bianthryl in Solution

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TABLE 1: Solvent Dependence of the BA Fluorescence

a

solvent

Qfa

τf,b ns

kf, 108 s-1

ν00(LE),c cm-1

Qf(LE)

Qf(CT)

PFD HEX BNZ DEE THF ACT ACN

0.59 0.60 (0.55,3 0.67d) 0.81 (0.536) 0.59 (0.593) 0.77 0.58 (0.393) 0.40 (0.233)

5.1 7.0 (5.7,13 83) 11.1 (11.8,3 12,13 146) 12.3 (153) 21.3 38.5 (323) 43.0 (34,6 35,3 4513)

1.16 0.86 0.73 0.48 0.36 0.15 0.093

25 380 25 000 24 570 24 940 24 750 24 810 24 810

0.57 0.57 0.39 0.35 0.15 0.06

0.03 0.24 0.20 0.42 0.43 0.34

Uncertainty (10%. b (5%. c (50 cm-1. d Reference 12, solvent 2-methylbutane.

(BNZ, Aldrich, 99+%), diethyl ether (DEE, Merck, 99%), tetrahydrofuran (THF, Aldrich, 99.5%), acetone (ACT, Aldrich, 99.5%), and acetonitrile (ACN, Aldrich, 99.5%). The PAC setup has been described previously.20,21 The following transducers from Panametrics (Hofheim) were used: A106S, 1 MHz, and A113R 15 MHz. A MSG 1600 TM N2 laser from LTB (Berlin) with 0.5 ns pulse width and 0.7 mJ pulse energy was the excitation source. Fluorescence lifetimes have been determined with a home-built setup already described.22 Stationary emission spectra were recorded with a 650-40 fluorescence spectrometer (Perkin-Elmer) and are corrected for the wavelengthdependent spectral sensitivity of the instrument.23 Fluorescence quantum yields have been determined using quinine bisulfate as standard (Qf ) 0.546 in 1 n H2SO4).24 Each sample was excited at the third absorption maximum of BA around 350 nm. The absorbances of samples and reference were optically matched at the excitation wavelength and always below 0.07 per cm optical path length. All photoacoustic and fluorescence experiments have been performed at room temperature in the absence of O2. Results and Discussion Spectral Analysis of the Fluorescence. The fluorescence quantum yields Qf and lifetimes τf of BA in a series of solvents are given in Table 1. Larger values of Qf than reported in the literature have been found. Therefore, the purity of solvents and of BA has been checked again, and the experiments have been repeated, however, without change of the results.23 Furthermore, to get certainty about the values of Qf, we determined the fluorescence quantum yield of 9,10-diphenylanthracene in degassed cyclohexane and obtained Qf ) 0.86 ( 0.09, in agreement with the recommended value of 0.90 ( 0.02, proving the reliability of our Qf data.24 The reason for the larger deviation of some literature data remains unknown. No systematic deviation from literature lifetimes is noticed, but the scatter of the published data is remarkable. The emission spectra of BA are analyzed on the basis of a solvent dependent LE a CT equilibrium. The broad and structureless red-shifted CT spectrum dominates the BA fluorescence in polar solvents, whereas it consists mainly from the weakly structured LE emission in nonpolar solvents.4-6 There is experimental evidence that CT emission contributes to the BA fluorescence already in HEX. (1) Visser et al. determined by measurements of the transient dielectric loss the dipole moment of the singlet excited BA species to 4.4 D in HEX.13 On the basis of the excited states equilibrium, this result indicates that the CT state is already populated in HEX. (2) We determined for BA in PFD Qf ) 0.59 and τf ) 5.1 ns; see Table 1. These data yield the rate constant of fluorescence as kf ) 1.16 × 108 s-1, which fits very well to the radiative rate constants of LE state model compounds 9-phenylanthracene (PHA) of 1.0 × 108 s-1 (cyclohexane) and 9,10-dinaphthylanthracene (DNA) of 1.2 × 108 s-1 (BNZ).25 kf depends for LE states quadratically on the refractive index n of the surrounding medium.26 Therefore, kf should be slightly larger in HEX (n ) 1.3749) than in PFD (n ) 1.3146),27 if in both solvents BA

Figure 1. Fluorescence spectra of BA in PFD (left) and in HEX (right). For better comparison they are scaled to the same maximum height. The inset gives the entire spectrum FL(ν) (1) and the separated spectra LE(ν) (2) and CT(ν) (3) in HEX.

emission originates only from LE. However, we determine in HEX kf ) 0.86 × 108 s-1; see Table 1. Since the rate constant kf(CT) of CT f S0 fluorescence of BA is distinctly smaller than kf(LE),6 this result demonstrates that CT f S0 fluorescence participates to an appreciable extent already in HEX. Solute-solvent interactions are even weaker in perfluorinated alkanes than in normal alkanes.27 The dielectric constant expressed as  ) n2 amounts to only 1.73 for PFD compared with 1.89 for HEX. We therefore assume the BA fluorescence spectrum in PFD to be a better basis for the estimation of LE(ν)est than the corresponding spectrum in HEX; see Figure 1. However, generally a broadening of the vibrational pattern of fluorescence spectra is observed in changing the solvent from PFD to alkanes. Therefore, not all of the diminution of the already PFD poor vibrational resolution of the BA spectrum can be attributed to an admixture of a broad and structureless CT emission in HEX. We investigated the shape of the fluorescence spectrum of the LE model compound PHA in PFD and HEX in the region between the first and the third vibrational band, i.e., in that region where the BA fluorescence spectrum exhibits most of its vibrational structure. The PHA spectrum in PFD can be represented in this region by a sum of three Gaussian curves: ∑Bi exp(-b(ν - νi)2), where νi is the wavenumber, Bi is the amplitude of the ith vibrational transition, and the parameter b ) 2.27 × 10-6 cm2 determines the Gaussian width. The PHA spectrum has less vibrational structure in HEX and can be reproduced by reducing b by 9%, keeping B2 and B3 constant and increasing B1 by 4%, and shifting νi by a constant red shift of ∆ν ) 400 cm-1. The shape of the BA fluorescence spectrum in PFD can also be represented very well by this procedure requiring b ) 2.07 × 10-6 cm2 because of the closer vibrational progression. If the diminution of the vibrational resolution of the BA fluorescence in going from PFD to HEX is only caused by increased solute-solvent interactions without CT formation, then the reduction of b by 9% and the shift of νi by ∆ν ) 400 cm-1 should be sufficient to account

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completely for the solvent effect. This, however, is not the case. Although maximum and neighbored shoulders are in the right positions, the vibrational resolution of the calculated part of the spectrum of BA in HEX is still slightly stronger than the corresponding part of the experimental spectrum and lies approximately halfway between the resolutions of the experimental BA fluorescence spectra in PFD and in HEX. Since the vibrational structure of the PHA fluorescence changes only little in the rest of solvents used in this investigation, we assume that the average of the complete experimental BA fluorescence spectra recorded in PFD and in HEX, the latter blue-shifted by 400 cm-1, can be used as a realistic approximation for the spectrum of the LE state. We have found for the LE state model compounds PHA and DNA identical solvent-dependent fluorescence red shifts. These are added to the wavenumber of the 0-0 transition of the LE emission of BA in PFD of 25 380 cm-1 to calculate the 0-0 transitions of the LE emission, given in Table 1, and the red-shifted spectra LE(ν)est in the rest of solvents. The radiative and radiationless deactivation CT f S0 can be treated as nonadiabatic electron transfer. Thus, the CT emission spectrum is calculated according to Gould et al. from eqs 1a1g.16,17

CT(ν) ) Aν3FC(g)

(1a)

(

(1b)

A) ∞

FC(g) ) ∑Fj(4πλskBT) j)0

)

64π4 n2 + 2 2 2 n M 3 3hc3 -1/2

(

exp -

)

(jhνv + g + λs)2 4πλskBT

g ) ∆G-et + hν -S j

(1c)

is a result of the separated spectra, and from the LE state formation enthalpy ∆H(LE). This improved estimate of ∆G-et is set constant in addition to νv and λv in a second optimization. Figure 1 demonstrates the results of this procedure by means of the calculated CT(ν) and LE(ν) in HEX. Application of eqs 1a-1g leads to broad and structureless CT spectra. The relative importance of the CT emission increases with solvent polarity. The shape of the calculated LE spectrum changes moderately, however, a weak vibrational structure is retained in all solvents. From the integrated spectra the quantum yields Qf(CT) and Qf(LE) are calculated, which are listed in Table 1. Excited State Equilibrium. The fraction fCT of S1 excited BA molecules in the CT state can be calculated from our data under the assumption of a pure LE a CT equilibrium without LE-CT mixing. Since the equilibrium is much faster than the single decays of LE or CT, the excimer kinetics developed by Birks can be applied to the singlet excited states decay.29 Equation 2 holds for the equilibrium constant K*.

K* ) fCT/(1 - fCT)

The decay kinetics can be treated as if there were only one excited species present.29 For example, the overall rate constant ki ) Qi/τf of deactivation process i is given by the weighted mean of the corresponding rate constants of deactivation process i occurring from CT and LE (eq 3).6,29

ki ) fCTki(CT) + (1 - fCT)ki(LE)

(1e)

S ) λv/hνv

(1f)

M ) V(µCT - µS0)/hνmax

(1g)

Here CT(ν) is the intensity of CT emission at frequency ν, and FC(g) is the Franck-Condon weighted density of states which depends on the free enthalpy change g occurring in the radiative CT f S0 transition. h is Planck’s constant, c the velocity of light, n the solvent refractive index, and M the electronic transition moment. kB is Boltzmann’s constant, λs and λv are the reorganization energies associated with the solvent and with a single averaged high-frequency skeletal mode of frequency νv, ∆G-et and V are the free enthalpy change and the electronic coupling matrix element associated with the back electron transfer, µCT and µS0 are the dipole moments of CT and S0, and νmax is the frequency of the maximum of CT emission. The separation of the experimental fluorescence spectrum FL(ν) into the CT(ν) and LE(ν) components occurred by subtracting the calculated CT(ν) from FL(ν) and comparison of the difference with LE(ν)est, which is multiplied by a scaling factor s. The fit parameters of the CT spectrum were varied by a nonlinear least-squares fitting program based on the Marquardt algorithm28 minimizing the difference between sLE(ν)est and FL(ν) - CT(ν). By this way we obtain optimized calculated spectra CT(ν) and LE(ν) ) FL(ν) - CT(ν). νv ) 1500 cm-1 and λv ) 950 cm-1 have been set constant in the fitting procedure. λs, A, s, and ∆G-et are fit parameters in a first optimization. As will be shown below ∆G-et can then be calculated from the LE a CT equilibrium constant K*, which

(3)

The solvent dependence of the rate constant of fluorescence of a LE state is only caused by changes of n. We assume that kf ) 1.16 × 108 s-1 determined in PFD holds true for the pure LE f S0 emission. Then we calculate kf(LE) ) (n/nPFD)2 × 1.16 × 108 s-1 for a solvent of refractive index n. Equation 4 relates the equilibrium constant with the fluorescence quantum yields.

(1d)

Fj ) e S /j!

(2)

K* )

Qf(CT) kf(LE) Qf(LE) kf(CT)

(4)

From eqs 2-4 follows eq 5, which serves for the evaluation of K* and of the free enthalpy ∆G* of the LE f CT reaction.

K* )

(

Qf(CT) Qf(LE)

+1

)

kf(LE)τf -1 Qf

(5)

The LE state has the same zero dipole moment as S0.30 Therefore, the S0 f LE transition occurs without volume change and the LE state energy obtained as the average of the frequencies of 0-0 transitions of LE emission and BA absorption is equal to the enthalpy ∆H(LE) and to the free enthalpy ∆G(LE) of LE state formation. Thus, the free enthalpy of CT formation is given by eq 6.

∆G(CT) ) ∆H(LE) + ∆G* ) -∆G-et

(6)

Table 2 lists the results of the analysis of the BA fluorescence spectra. Values of -∆G-et obtained from the spectral fitting procedure agree quite well with ∆G(CT) resulting from eq 6. An estimate of the free enthalpy change of the back electron transfer reaction CT f S0 can be obtained via ∆G-et ) -(Eox - Ered) from the oxidation potential Eox) 1.09 V (vs SCE in ACN)31 and the reduction potential Ered ) -1.95 V (vs SCE in DMF)31 of anthracene. With ∆G-et ) -24 500 cm-1 a value results which agrees quite well with the ∆G-et data determined for the strongly polar solvents, confirming the spectral analysis. The values ∆G-et as well as λs are moderately solvent dependent. The sum -(∆G-et + λs + λv) should be equal to the average energy hνav of CT emission as was shown by Gould et al.17 In the limits -0.4% to -0.8% this is actually the case, further supporting the present spectral analysis. The equilibrium

Deactivation of 9,9′-Bianthryl in Solution

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TABLE 2: Results of the Analysis of the BA Fluorescence Spectra sol- ∆H(LE), λs, A, νav(CT), vent cm-1 cm-1 1030 J-2 cm-1 HEX BNZ DEE THF ACT ACN a

25 440 25 090 25 380 25 220 25 280 25 280

1400 2360 2260 2490 2890 3130

0.087 0.34 0.21 0.24 0.14 0.10

K*

23 320 0.54 21 700 2.0 22 020 2.9 21 430 7.0 20 800 31 20 310 86

fCT 0.35 0.66 0.74 0.88 0.97 0.99

-∆G-et,a ∆G(CT), cm-1 cm-1 25 580 24 900 25 120 24 760 24 510 24 230

25 570 24 960 25 160 24 820 24 570 24 360

Constant parameter in the spectral fit.

constant K* increases with increasing solvent polarity, as was recently found by others.4,6 However, our results demonstrate for the first time that CT formation of BA takes place already in HEX, in contrast to previous work, where it was assumed that the BA fluorescence in HEX represents the pure LE emission.4,6 Excited State Dipole Moments. Schneider and Lippert determined the dipole moment of the CT state by an analysis of the solvatochromism of the BA fluorescence in 13 polar solvents to µCT ) 18.2 D.2 The overall dipole moment of the excited molecules in the fast LE a CT equilibrium can be estimated as µ ) µCTfCT0.5.32 From the data of Table 2 we obtain values of 11 (HEX), 15 (BNZ), and 16 D (DEE), which are even distinctly larger than the values of 4.4 (HEX), 10 (BNZ), and 15 D (DOX) determined by Visser et al.13 Independent of whether the values of µ obtained by us are possibly too large, the HEX and BNZ data demonstrate that the emitting molecules have a rather large overall dipole moment already in nonpolar alkanes and in the moderately polar BNZ. These findings cast some doubt on the analysis of the BA fluorescence performed by Wortmann et al., who assume that in alkane and benzene solutions the spectral changes of the BA fluorescence could be the consequence of a solvent-dependent torsional potential in a single excited state without charge transfer.10-12 Visser et al. supposed that the large values of µ in nonpolar solvents must be caused by BA-solvent exciplexes. A principal argument for this hypothesis was the strong increase of µ on going from HEX to DOX, which in their mind could not be the result of classical electrostatic solute-solvent interactions, if the very similar dielectric constants of  ) 1.9 (HEX), 2.3 (BNZ), and 2.2 (DOX) are considered. However, due to a permanent quadrupole moment (BNZ) and to intramolecular dipole moments, which compensate macroscopically for each other (DOX), these solvents behave in intermolecular electrostatic interactions like medium polar solvents with effective values of  of about 5 (BNZ) and 7 (DOX).11,33-35 Thus, electrostatic interactions could well be the reason for the shift of the LE a CT equilibrium and the increase of the overall dipole moment in the series HEX, BNZ, DOX. PAC Measurement of ET and Qisc. The determination of the triplet state energy of BA was performed by PAC in sensitization experiments. HBP, which releases the entire absorbed photon energy in less than 0.1 ns,36 was taken as reference. The details of such experiments have been described previously.20,21 PHE (Qisc ) 1.0, ET ) 15 200 cm-1)20,37 was the sensitizer. The concentration of BA was 1.0 × 10-3 M to ensure complete energy transfer. The optical densities of sensitizer and acceptor at the excitation wavelength of 337 nm were 1.8 and 0.1 on the optical path length of 0.26 mm. The necessary correction for the inner filter effect was considered. The diffusion-controlled population of T1(BA) occurred with a time constant of about 50 ns, being shorter than the heat integration time of our PAC setup with the 1 MHz transducer. Thus, the fraction of heat dissipated until T1(BA) is populated is determined integrally as R1. The subsequent relaxation of T1(BA) takes then place on the time scale τ g 30 µs, which

Figure 2. Photoacoustic waves of reference HBP (1) and sample BA (2) in HEX. Absorbances at 337.1 nm were 0.390 on 0.52 mm optical path length. Fitted wave is drawn as curve through wave 2 and was calculated with fit parameters R1 ) 0.121, R2 ) 0.208, τ2 ) 8.0 ns, and fixed τ1 ) 0.1 ns.

is too slow to be detected by the transducer employed. Therefore, the triplet state energy is obtained as ET ) (1 R1)EL,14 with EL being the N2 laser photon energy of 29 665 cm-1. With R1 ) 0.571 ( 0.03 measured in HEX and R1 ) 0.546 ( 0.03 measured in ACN, we obtain values of ET of 12 700 ( 900 cm-1 in HEX and 13 500 ( 900 cm-1 in ACN. In the limits of experimental uncertainty there is no shift of ET with solvent polarity excluding a CT character of T1, in agreement with the much larger -∆G-et required for an electron transfer. A mean value of ET ) 13 100 ( 900 cm-1 results for BA, which is by 1800 cm-1 lower than the triplet state energy of anthracene.31 This energy difference is similar to the difference of energies of the local excited S1 states of BA and anthracene, which amounts to 1300 cm-1 in HEX. Using the 15 MHz transducer, we determined time resolved the fraction R2 of heat evolved in the radiationless decay of the LE a CT equlibrium of BA, which is characterized by time constant τ2. The fraction R1 of heat evolved in the fast relaxation into the equilibrium is dissipated with time constant τ1 in less than 1 ns, which is too fast to be detected time resolved by our PAC setup. The triplet state again acts as heat storage. Figure 2 presents typical PAC waves recorded directly after laser pulse excitation of optically matched solutions of BA (1) and HBP (2) in HEX. The fit of a convolution of the heat evolution function q(t) with the reference wave (2) to the sample wave (1) yields then the fractions of fast (R1) and the slow (R2) heat by eqs 7a-7c.38 -t/τ1 -t/τ2 q(t) ) (R* + (R* 1/τ1)e 2/τ2)e

R2 )

R* 2(τ2 - τ1) τ2

R1 ) R* 1+

R2τ1 τ2 - τ1

(7a) (7b)

(7c)

The triplet quantum yield Qisc is obtained from the stored heat by eq 8, where Ef is the average photon energy emitted in spectrum FL(ν).

QiscET ) (1 - R1 - R2)EL - QfEf

(8)39

Since T1 and S0 of BA are nonpolar, no corrections for volume changes caused by CT reactions have to be made. Table 3 lists the experimental results of the PAC experiments and the quantum yield Qisc derived therefrom. The differences 1 - Qisc - Qf indicate that internal conversion plays no important role for BA deactivation in the solvents investigated. The time

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TABLE 3: Results of the PAC Experiments solvent

R1a

R2b

HEX BNZ DEE THF ACT ACN

0.121 0.142 0.134 0.142 0.179 0.174

0.208 0.170 0.220 0.175 0.234 0.266

a

τ2,c ns Ef, cm-1 8.0 11.4 11.4 20.0 34.3 37.2

23 570 22 800 23 050 22 370 21 570 20 890

Qiscd

1 - Qf - Qisce

0.43 (0.1740) 0.15 0.43 0.23 0.38 0.63 (0.4940)

-0.04 0.04 -0.02 0.00 0.05 -0.03

∆H(CT) )

Uncertainty (5%. b ( 5%. c (5%. d (15%. e (0.07.

constants τ2 measured by PAC agree quite well with the more accurate fluorescence lifetimes τf, confirming the reliability of the separation of the dissipated heat into R1 and R2. Values of Qisc are nonnegligible in nonpolar as well as in polar solvents and run through a minimum in medium polar solvents. This is an interesting and at first sight unexpected effect which will be investigated later. Correction of Electrostriction in PAC Measurements. In principle, it is possible to calculate from the fast heat R1 the overall excitation energy ES of the excited molecules in the LE a CT equilibrium. However, we have to consider that during excitation and subsequent fast relaxation dipole molecules are created from nonpolar ground state molecules, causing a volume contraction ∆V′el which adds to the thermal volume expansion ∆Vth to yield the entire fast volume change ∆Vsa of the sample. The experimental value R1 is the ratio of ∆Vsa over the fast volume change ∆Vrf of the reference. Thus, we obtain eq 9.

R1 )

∆Vth + ∆V′el ∆V′el ) Rth + ∆Vrf ∆Vrf

(9)

-∆V′el/∆Vrf is the electrostriction correction, which has to be added to the overall value R1 to obtain Rth, which is required to calculate ES ) (1 - Rth)EL. Mauzerall et al. considered for the first time electrostriction effects in PAC measurements of ion formation reactions by the Drude-Nernst equation.41 We will use a different approach for the electrostriction correction, which is more appropriate for the quantitative treatment of dipole formation reactions. Its basis is Kirkwood’s theory for the electrostatic interaction of sphere like dipole molecules with a continuum solvent.42 Hartmann et al. applied this theory to the transition state theory and developed an equation for the solvent polarity-dependent electrostriction part of the activation volume.43 If this procedure is applied to equilibria eq 10 results, which allows the evaluation of the molar volume contraction due to electrostriction.

d∆Gel ∆µ2 ∆Vel ) ) -NA 3 qp dp r

weighted mean of the LE and CT formation enthalpies. We obtain a PAC measure for ∆H(CT) by eq 11. Table 4 lists the values of qp, -∆V′el, ∆Vrf, Rth, ES, and ∆H(CT).

(10)

The parameter qp is related to the pressure derivative of : qp ) 3(2 + 1)-2(d/dp)T, NA is Avogadro’s number, r is the radius of the spherical assumed cavity containing the BA molecule, and ∆µ is the dipole moment change. NA(∆µ2/r3) ) 7700 cm-1 was determined by Schneider and Lippert.2 Since only the fraction fCT of CT molecules causes volume contraction, we obtain ∆V′el ) fCT∆Vel for BA. The values of qp or (d/dp)T are from the literature.44,45 With the thermal expansion coefficient β, the specific heat cp, and the density F of the solvent, we calculate ∆Vrf ) (EL β)/(cpF) required for the determination of Rth and ES. Very recently, Morais and Zimmt applied independently of us the same volume correction to PAC results on the deactivation of a CT compound. It was shown that the calculated values of ∆Vel of -18 (pentane) and -12 mL mol-1 (heptane) agreed with the experimental estimate of -14 mL mol-1 obtained in PAC measurements using a series of alkanes of different thermoelastic properties but similar .46 LE f CT Reaction Enthalpy and Entropy. ES is the

ES - (1 - fCT)∆H(LE) fCT

(11)

The CT formation enthalpies ∆H(CT) are key parameters which lead to the construction of a complete thermodynamic picture of the BA photophysics. Values of ∆H(CT) are slightly smaller than the values of ∆H(LE). The differences are the LE f CT reaction enthalpies ∆H*, given in Table 4, which show under a considerable scatter a trend to more negative values with increasing solvent polarity. The corresponding reaction entropies are calculated from ∆S* ) (∆H* - ∆G*)/T. Negative values of ∆S* are obtained in all solvents scattering around the mean value of -23 J K-1 mol-1. Negative entropies of reaction correlate with an increase of the degree of order in the system. Actually, this is the case in the formation of the CT state of BA from its nonpolar LE state, because of the increase of orientation of solvent molecules around the solute dipole. The accuracy of the data is not good enough to observe with certainty the expected decrease of the absolute values of ∆S* with solvent polarity. This is probably the consequence of the uncertainty of ∆H(CT), which is only rather indirectly accessible from the PAC results and the fact that we are looking for small differences of large numbers. Moreover, the correction of R1 for the electrostriction effect is only crude. In any case the correction is necessary. Without we would have found positive CT reaction entropies in all solvents but in ACN, which would make no sense. The values of ∆S* can qualitatively be compared with ∆S* ) -24 J K-1 mol-1 obtained by Leinhos et al. for the LE f CT reaction of p-(dimethylamino)benzonitrile in toluene from temperature-dependent measurements of ∆G*.35 Likewise, negative reaction entropies, which range from -18 (HEX) to -6 J K-1 mol-1 (ACN), can be estimated from the abovementioned continuum model of solvent electrostriction by eq 12 with qT ) 3(2 + 1)-2(d/dT)p.46 The decrease of the absolute values of ∆Sel results from the larger degree of order, which more polar solvents already have in the absence of a solute dipole.

∆Sel ) -

d∆Gel ∆µ2 ) NA 3 qT dT r

(12)

Ground State Reorganization Enthalpy and Entropy. Figure 3 illustrates the thermodynamic aspects of the BA photophysics in ACN by means of a free enthalpy digram. The free enthalpy of the radiative CT f S0 back electron transfer reaction consists of contributions due to CT fluorescence and ground state reorganization: ∆G-et ) ∆Gf,ct + ∆Gr. CT fluorescence leads without solvent reorientation from the relaxed CT to a nonrelaxed Franck-Condon position on S0. Therefore, we obtain ∆Gf,ct ) ∆Hf,ct ) -hνav. Reorganization subsequently occurs on the ground state surface with ∆Gr ) -λs λv and ∆Hr ) -∆H(CT) + hνav. Thus, we obtain the reorganization entropy as ∆Sr ) (-∆H(CT) + hνav + λs + λv)/T. As entropy changes are assumed only to occur in the LE f CT and in the ground state reorganization reaction, of course ∆S* ) -∆Sr results. Values of ∆Hr are listed in Table 4. The reorganization reaction becomes distinctly more exothermic in the series from HEX to ACN, since the energy of an ensemble of solvent molecules oriented around a solute molecule, which no longer is a dipole, increases with increasing solvent polarity. The LE f CT reaction enthalpy ∆H*, in contrast, exhibits only a weak solvent polarity dependence. Apparently, the solvent depen-

Deactivation of 9,9′-Bianthryl in Solution

J. Phys. Chem., Vol. 100, No. 6, 1996 2017

TABLE 4: Correction of PAC Measurements for Electrostriction Effects Due to CT Formation solvent

1011qp, cm3 erg-1

-∆Vel′, cm3 mol-1

∆Vrf, cm3 mol-1

Rth

Es, cm-1

∆H(CT), cm-1

-∆S*, J mol-1 K-1

-∆H*, cm-1

-∆Hr, cm-1

HEX BNZ DEE THF ACT ACN

2.47 1.70a 1.70b 1.00 0.54 0.22

22.8 15.7 15.7 9.2 4.9 2.0

321.2 288.1 348.1 284.0 291.9 291.2

0.146 0.178 0.167 0.170 0.195 0.181

25320 24360 24680 24590 23850 24280

25080 23990 24440 24500 23800 24270

19.9 38.7 29.1 12.6 31.0 3.9

370 1100 940 720 1480 1020

1760 2290 2420 3070 3000 3950

a Estimated q value.47 b No literature data available. A rough correlation exists between q and q. Therefore, the q value of CHCl having the P P P 3 same  as DEE was taken.

among others on the number of σ bonds through which interaction may occur,49 we assume the size of the values of Table 5 to be reasonable. Internal Conversion. As already mentioned above, internal conversion (ic) plays no important role in the deactivation of singlet excited BA. For common nine-substituted anthracene derivatives Qf + Qisc > 0.9 was found.50 This relation allows the estimation of an upper limit of 107 s-1 for the rate constant kic(LE) of ic LE f S0. kic(LE) ≈ 107 s-1 is also estimated from Siebrand’s energy gap relation.21,51 The ic CT f S0 is the thermal back electron transfer reaction, for which the rate constant can be calculated by eqs 14a and 14b.17

Figure 3. Free enthalpy diagram of the photophysics of the deactivation of BA in ACN.

TABLE 5: CT Deactivation by Fluorescence and Isc solvent

kf(CT), 107 s-1

HEX BNZ DEE THF ACT ACN

1.1 3.3 2.1 2.2 1.2 0.8

a

-1

V, cm

1370 2210 2060 2020 1550 1330

kisc,a 107 s-1

kisc(CT), 106 s-1

kisc,b 107 s-1

6.2 1.3 3.5 1.1 1.0 1.5

0.07 3.6 1.9 4.8 8.3 13.2

5.2 2.9 2.2 1.4 1.1 1.5

Experimental data. b Calculated values.

dence of the solvation enthalpy is almost compensated by a reverse solvent dependence of the energy difference of LE and CT potentials. CT f S0 Fluorescence. The rate constants kf(CT) of CT fluorescence are calculated from values of kf, fCT, and kf(LE) with kf ) ki by eq 3. The values of kf(CT) listed in Table 5 are distinctly smaller than kf(LE), in agreement with findings of Kang et al.6 They vary between about 1 × 107 and 3 × 107 s-1 and show no significant trend with solvent polarity. By eq 13, where ∆µ )18.2 D and νav is in cm-1, we estimate the electronic coupling elements V associated with the back electron transfer, which are given in Table 5.17

V)

56.47 ∆µ

( ( )) ( ) 1/2

kf(CT)

1 νav

1/2

(13) n +2 n 3 The values of V lie between 1300 and 2200 cm-1. They are about 2-3 times larger than found for radical ion pairs without a σ bond connecting the oppositely charged moieties17 and up to 2-fold larger than values of V of CT compounds where three σ bonds separate positive and negative charges.48 In BA the separation occurs by only one σ bond. Keeping in mind that the size of the electronic coupling matrix elements depends 2

2

k-et ) (4π2/h)V2FC(g)

(14a)

g ) ∆G-et

(14b)

The required parameters have all been determined. With the data of V evaluated above we obtain very small values of kic(CT) < 2 × 102 s-1. Independent of whether the simple parabolic approximation can be applied for such strongly exergonic reactions, those results demonstrate that the ic CT f S0 cannot be efficient. Thus, in agreement with the experimentally determined values of 1 - Qf - Qisc, only an insignificant contribution of ic from the LE and CT states of BA is expected. Intersystem Crossing. The main radiationless deactivation path of BA is isc. Table 5 contains the overall rate constants kisc obtained from Qisc and τf. The rate constants have in part large values and are nonnegligible in nonpolar and in polar solvents, indicating that deactivation by isc can proceed from both the LE and the CT states. For common nine-substituted anthracene derivatives T2 is of slightly larger energy than S1 whereas T1 is far below S1. Therefore, isc occurs thermally activated from S1 to T2. If the energy barrier is too large, isc is unimportant.50 In order to prove whether a dual-channel isc is capable of simulating the solvent dependence of kisc, in a first approximation it is assumed that kisc(LE) ) 8 × 107 s-1 obtained from (1 - Qf)/τf in PFD can be taken constant. With increasing fCT the importance of isc LE f T1 becomes smaller. The nonvanishing values of kisc in the polar solvents must therefore be a consequence of the isc CT f T1. The free enthalpy change for back electron transfer isc is by ET less exergonic than for back electron transfer ic. If we assume for the spin-forbidden isc the electronic coupling matrix elements V to be by the constant factor 264 smaller than for the spinallowed fluorescence LE f S0, we calculate values kisc(CT) ) k-et by eqs 14a and 14b, which increase from HEX to ACN by 2 orders of magnitude. With kisc ) ki we finally calculate by eq 3 values of kisc, which are also listed in Table 5. With the exception of the BNZ value, a rather good agreement is found between calculated and experimental isc rate constants, proving that isc of BA actually occurs from both the LE and the CT states. The relative importance of both deactivation channels varies with solvent polarity. The spin-prohibition factor of the back electron transfer isc compared with back electron transfer

2018 J. Phys. Chem., Vol. 100, No. 6, 1996 fluorescence is surprisingly small and amounts to only 7 × 104. It is more than a factor of 10 smaller than the corresponding factor of 106 determined recently by Morais et al. for the deactivation of a rigid donor-spacer-acceptor molecule.48 The comparatively large rate constants of CT f T1 isc are probably a consequence of the particular structure of BA. In a simple MO description the CT state is a ππ* state with singly occupied orbitals πA and πB* localized on two different anthracene moieties A and B. The T1 state, in contrast, can be considered as a πAπA* state, where both singly occupied orbitals are localized on the same anthracene moiety. Since the planes of both anthracene moieties are orthogonal, the CT(πAπB*) f T1(πAπA*) transition produces a change of the orbital angular momentum, which promotes the simultaneous change of spin. A similar promoting effect was already found by El-Sayed to cause the increase of the rate of the isc S1(nπ*) f T1(ππ*) compared with the isc S1(nπ*) f T1(nπ*).52 Conclusions Existing theories on electron transfer reactions have been used for the interpretation of the deactivation of the intramolecular CT state of BA. CT emission spectra and CT deactivation rate constants have been calculated by the formalism developed by Gould et al.16,17 The separation of the fluorescence into LE and CT emission spectra leads to reasonable values of -∆G-et and K*. PAC experiments yielded the energy of the nonpolar T1 state, values of Qisc, and after correction of electrostriction effects the enthalpies of the CT state. The latter results are particularly important, since they allow the calculation of reaction enthalpies and entropies of the LE f CT and the ground state reorganization reaction. Negative CT formation entropies have been found which are in accordance with the increase of the degree of order in the system. The exothermicity of the ground state reorganization reaction increases strongly with solvent polarity. Besides fluorescence only isc is important for the deactivation of the excited states equilibrium. The dynamics of CT deactivation depends on the solvent polarity. kf(CT) is distinctly smaller than kf(LE). Internal conversion CT f S0 is not efficient because of the large exergonicity of the back electron transfer. However, intersystem crossing CT f T1 competes efficiently with CT fluorescence in strongly polar solvents due to spin-orbit coupling, the much smaller energy gap, and the large solvent reorganization energy. Acknowledgment. Financial support by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie is gratefully acknowledged. We thank Professor W. Rettig for a sample of BA and M. Hild for support in the spectral fitting calculations. References and Notes (1) Schneider, F.; Lippert, E. Ber. Bunsen-Ges. Phys. Chem. 1968, 72, 1155-1160. (2) Schneider, F.; Lippert, E. Ber. Bunsen-Ges. Phys. Chem. 1970, 74, 624-630. (3) Nakashima, N.; Murakawa, M.; Mataga, N. Bull. Chem. Soc. Jpn. 1976, 49, 854-858. (4) Rettig, W.; Zander, M. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 1143-1149. (5) Mu¨ller, S.; Heinze, J. Chem. Phys. 1991, 157, 231-242. (6) Kang, T. J.; Kahlow, M. A.; Giser, D.; Swallen, S.; Nagarajan, V.; Jarzeba, W.; Barbara, P. F. J. Phys. Chem. 1988, 92, 6800-6807. (7) Kobayashi, T.; Nagakura, S.; Szwarc, M. Chem. Phys. 1979, 39, 105-110. (8) Mataga, N.; Yao, H.; Okada, T.; Rettig, W. J. Phys. Chem. 1989, 93, 3383-3386. (9) Kang, T. J.; Jarzeba, W.; Barbara, P. F. Chem. Phys. 1990, 149, 81-95. (10) Wortmann, R.; Elich, K.; Lebus, S.; Liptay, W. J. Phys. Chem. 1991, 95, 6371-6386.

Schu¨tz and Schmidt (11) Wortmann, R.; Lebus, S.; Elich, K.; Assar, S.; Detzer, N.; Liptay, W. Chem. Phys. Lett. 1992, 198, 220-228. (12) Elich, K.; Lebus, S.; Wortmann, R.; Petzke, F.; Detzer, N.; Liptay, W. J. Phys. Chem. 1993, 97, 9947-9955. (13) Visser, R.-J.; Weisenborn, P. C. M.; van Kan, J. M.; Huizer, B. H.; Varma, C. A. G. O.; Warman, J. M.; de Haas, M. P. J. Chem. Soc., Faraday Trans. 2 1985, 81, 689-704. (14) Braslavsky, S. E.; Heibel, G. E. Chem. ReV. 1992, 92, 1381-1410. (15) Marcus, R. A. J. Phys. Chem. 1989, 93, 3078-3086. (16) Gould, I. R.; Young, R. H.; Moody, R. E.; Farid, S. J. Phys. Chem. 1991, 95, 2068-2080. (17) Gould, I. R.; Noukakis, D.; Gomez-Jahn, L.; Young, R. H.; Goodman J. L.; Farid, S. Chem. Phys. 1993, 176, 439-456. (18) Bell, F.; Waring, D. H. J. Chem. Soc. 1949, 267-269. (19) Willemart, A. Bull. Soc. Chim. Fr. 1937, 4, 357. (20) Schmidt, R.; Tanielian, C.; Dunsbach, R.; Wolff, C. J. Photochem. Photobiol. A: Chem. 1994, 79, 11-17. (21) Dunsbach, R.; Schmidt, R. J. Photochem. Photobiol. A: Chem. 1994, 83, 7-13. (22) Grewer, C.; Brauer, H.-D. J. Phys. Chem. 1993, 97, 5001-5006. (23) Parker, C. A. Photoluminescence of Solutions; Elsevier: Amsterdam, 1968. (24) Eaton, D. F. Pure Appl. Chem. 1988, 60, 1107-1114. (25) Berlman, I. Handbook of Fluorescence Spectra of Aromatic Molecules; Academic Press: New York, 1971. (26) Hirayama, S.: Phillips, D. J. Photochem. 1980, 12, 139-145. (27) Maciejeweski, A. J. Photochem. Photobiol. A: Chem. 1990, 176, 87-131. (28) Marquardt, D. W. J. Soc. Ind. Appl. Math. 1963, 11, 431-441. (29) Birks, J. B. Photophysics of Aromatic Molecules; Wiley-Interscience: New York, 1994; p 301 ff. (30) Liptay, W.; Walz, G.; Baumann, W.; Schlosser, H.-J.; Deckers, H.; Detzer, N. Z. Naturforsch. 1971, 26A, 2020-2038. (31) Murov S. L.; Carmichael, I.; Gordon, L. H. Handbook of Photochemistry; Dekker: New York, 1993; p 270. (32) Schuddeboom, W.; Jonker, A. S.; Warman, J. M.; Leinhos, U.; Ku¨hnle, W.; Zachariasse, K. A. J. Phys. Chem. 1992, 96, 10809-10819. (33) Liptay, W.; Schlosser, H.-J.; Dumbacher, B. Z. Naturforsch. 1968, 23A, 1613-1625. (34) Liptay, W.; Weisenberger, H.; Tiemann, F.; Eberlein, W.; Konopka, G. Z. Naturforsch. 1968, 23A, 377-393. (35) Leinhos, U.; Ku¨hnle, W.; Zachariasse, K. A. J. Phys. Chem. 1991, 95, 2013-2021. (36) Hou, S.-Y.; Hetherington, W. M.; Korenowski, G. M.; Eisenthal, K. B. Chem. Phys. Lett. 1979, 68, 282-284. (37) Oliveros, E.; Suardi-Murasecco, P.; Aminian-Saghafi, T.; Braun, A. M.; Hansen, H.-J. HelV. Chim. Acta 1991, 74, 79-90. (38) Rudzki-Small, J.; Libertini, L. J.; Small, E. W. Biophys. Chem. 1992, 42, 29-48. (39) Due to a typos error R1 ) R1* + R2τ2/(τ2 - τ1) was given in ref 21 instead of the correct eq 7c. (40) After submission of our work a paper appeared (Mac, M.; Najbar, J.; Wirz, J. J. Photochem. Photobiol. A: Chem. 1995, 88, 93-104.) reporting values of Qisc of BA determined by the method of Medinger and Wilkinson, which requires a single fluorescing species with a solvent-independent rate constant of fluorescence. Ethyl iodide (EI) was used as heavy atom quencher. The addition of larger amounts of EI to HEX leads to an increase of the solvent polarity and consequently to a shift of the LE a CT equilibrium, which in turn should reduce kf, see Table 1. We therefore believe that the value Qisc ) 0.43 determined in HEX by the much simpler PAC method is more realistic. (41) Mauzerall, D.; Feitelson, J.; Prince, R. J. Phys. Chem. 1995, 99, 1090-1093. (42) Kirkwood, J. G. J. Chem. Phys. 1934, 2, 351-361. (43) Hartmann, H.; Brauer, H. D.; Kelm, H.; Rinck, G. Z. Phys. Chem. (Munich) 1968, 61, 53-62. (44) Hartmann, H.; Neumann, A.; Schmidt, A. P.; Ber. Bunsen-Ges. Phys. Chem. 1968, 72, 877-880. The parameter qp is obtained with P ) 1 from the data of ref 41 as qp ) A/(B + P)/ln(10) instead of qp ) A/(B + P). Erroneously in ref 43 the log/ln conversion factor was omitted. (45) Hill, W. W.; Rosenzweig, S.; Franck, E. U. Ber. Bunsen-Ges. Phys. Chem. 1990, 94, 564-568. (46) Morais J.; Zimmt, M. B. J. Phys. Chem. 1995, 99, 8863-8871. (47) The electrostatic solute-solvent interaction in BNZ is not appropriately described by the parameter ( - 1)/(2 + 1). This holds true to a minor degree also for the parameter qp. BNZ has an effective  ≈ 5. Therefore, the qp value of CHCl3 ( ) 4.7) is also taken for BNZ. (48) Morais J.; Hung, R. R.; Grabowski, J. J.; Zimmt, M. B. J. Phys. Chem. 1993, 97, 13138-13144. (49) Closs, G. L.; Miller, J. R. Science 1988, 240, 440-446. (50) Schoof, S.; Gu¨sten, H.; von Sonntag, C. Ber. Bunsen-Ges. Phys. Chem. 1977, 81, 305-309. (51) Siebrand, W.; Williams, D. F. J. Chem. Phys. 1967, 46, 403-404. (52) El-Sayed, M. A. J. Chem. Phys. 1962, 36, 573-575.

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