Quantitative Analysis of Intramolecular Exciplex and Electron Transfer

Sep 7, 2012 - Marius Koch , Giuseppe Licari , and Eric Vauthey. The Journal of Physical Chemistry B 2015 119 (35), 11846-11857. Abstract | Full Text H...
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Quantitative Analysis of Intramolecular Exciplex and Electron Transfer in a Double-Linked Zinc Porphyrin−Fullerene Dyad Ali Hanoon Al-Subi,*,† Marja Niemi,† Nikolai V. Tkachenko,† and Helge Lemmetyinen† †

Department of Chemistry and Bioengineering, Tampere University of Technology, P.O. Box 541, 33101, Tampere, Finland S Supporting Information *

ABSTRACT: Photoinduced charge transfer in a doublelinked zinc porphyrin−fullerene dyad is studied. When the dyad is excited at the absorption band of the charge-transfer complex (780 nm), an intramolecular exciplex is formed, followed by the complete charge separated (CCS) state. By analyzing the results obtained from time-resolved transient absorption and emission decay measurements in a range of solvents with different polarities, we derived a dependence between the observable lifetimes and internal parameters controlling the reaction rate constants based on the semiquantum Marcus electron-transfer theory. The critical value of the solvent polarity was found to be εr ≈ 6.5: in solvents with higher dielectric constants, the energy of the CCS state is lower than that of the exciplex and the relaxation takes place via the CCS state predominantly, whereas in solvents with lower polarities the energy of the CCS state is higher and the exciplex relaxes directly to the ground state. In solvents with moderate polarities the exciplex and the CCS state are in equilibrium and cannot be separated spectroscopically. The degree of the charge shift in the exciplex relative to that in the CCS state was estimated to be 0.55 ± 0.02. The electronic coupling matrix elements for the charge recombination process and for the direct relaxation of the exciplex to the ground state were found to be 0.012 ± 0.001 and 0.245 ± 0.022 eV, respectively. characterization of the exciplex.9−11,13 Thus, the important energetic parameters associated with the exciplex, such as the free, vibrational, and reorganization energies, the electronvibrational coupling, and the electronic coupling matrix element can be obtained from the analysis of this band9−11,13,16,17 in the frame of the semiquantum Marcus theory of the electron transfer.6,18−20 For the CCS state, the electronic coupling between the donor and the acceptor can be evaluated from the analysis of the ET rate dependence on the free energy of the reaction,19−22 but this requires synthesis of a series of compounds with varying redox properties of the donor and acceptor moieties.14,23−25 The analysis of the steady state absorption and emission spectra associated with the exciplex was previously carried out for a doubly linked zinc porphyrin−C60 dyad, ZnTBD6be (Figure 1), in a range of solvents with varying polarities.16 The energetic parameters of the exciplex were evaluated, and the charge separation degree in the exciplex was estimated from the linear dependences of both the free and the reorganization energies on the solvent polarity and found to be ∼40%. The dynamics of the photoinduced reactions of ZnTBD6be were also studied in a range of solvents. Two different relaxation pathways were demonstrated for two extreme cases of polar

1. INTRODUCTION In simple photoinduced electron-transfer (ET) reactions of porphyrin−fullerene donor−acceptor (DA) compounds, the reactant state is the locally excited state of either the porphyrin donor or the fullerene acceptor and the product state is the CCS state. However, when interaction between the donor and the acceptor is strong, an encounter complex can rapidly form an intermediate which may have sufficiently long lifetime to undergo light emission.1−3 Such common excited state is termed as an exciplex, and it exhibits partial charge character on each chromophore, and a large dipole moment, which reflect the degree of charge transfer.4−8 For covalently linked porphyrin−fullerene dyads, with face-to-face orientation between the porphyrin and fullerene species the characteristic exciplex emission has been observed in the red and the near IR spectral regions.9−14 In addition to the orientation and the distance between the porphyrin and fullerene moieties, the environment plays a substantial role in tuning of the energetic and spectral features of the exciplex and the CCS state. Both the energies and the lifetimes of the exciplex and the CCS state depend on the solvent polarity.9,12,13,15 The exciplex intermediate has features of both the reactant and product states, and it is not easily distinguishable in the transient absorption measurements. However, the covalently linked porphyrin−fullerene dyads with short center-to-center distances show a relatively strong red-shifted charge-transfer (CT) band, associated with the ground state interaction of the chromophores. This phenomenon can be used for quantitative © 2012 American Chemical Society

Received: July 13, 2012 Revised: September 5, 2012 Published: September 7, 2012 9653

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where ε1 and ε2 are the dielectric constants of the less polar and more polar solvents, respectively,28 εmix is the dielectric constant of the solvent mixture, and φ1 is the volume fraction of the less polar solvent. The dielectric constants of the solvent mixtures toluene/anisole and anisole/PhCN were calculated as 3.37 and 14.88, respectively (Table 3). The refractive indices of the solvent mixtures were calculated from the Lorentz−Lorenz mixing rule as29

and nonpolar environments with the CCS state formed only in highly polar media.13 Any complete quantitative analysis of the ET reactions of porphyrin−fullerene DA compounds with face-to-face orientation was so far not performed because of the interference between the spectral and energetic properties of the four existing intermediates, i.e., the locally excited states of the porphyrin and fullerene, the exciplex, and the CCS state. The problem can be simplified if the number of intermediate states is reduced. This can be done by direct excitation of the exciplex from the ground state, and thus avoiding formation of the locally excited states of porphyrin or fullerene chromophores. This strategy is used in the present study to acquire timeresolved absorption spectra of ZnTBD6be in different environments. Furthermore, the dependences of the experimental lifetimes on solvent polarity can be analyzed within the semiquantum Marcus ET theory. This allowed us to determine quantitatively the conditions for the equilibrium between the exciplex and the CCS state and estimate the key parameters of ET, such as the electronic coupling matrix elements and the internal reorganization energies.

nmix

2

(2)

where nmix is the refractive index of the mixture, n1 and n2 are the refractive indices of the pristine solvents,30 and φ1 and φ2 are the volume fractions of the respective components in the mixture. The pump−probe method was used to measure the transient absorption spectra in the picosecond and subpicosecond time domains with a time resolution of ≈200 fs. The excitation wavelength was 780 nm and the transient absorption was monitored in the visible region of the spectrum (445−750 nm). About 70−90 spectra were measured at variable delay times up to 1 ns. The collected data were fitted globally to obtain decay time constants and spectra associated with the decays, using the data analysis procedure described earlier.11,31 Time-resolved fluorescence spectra in the nanosecond and subnanosecond time scales were measured with the timecorrelated single-photon counting (TCSPC) technique described earlier.32 The samples were excited with a pulsed diode laser at 405 nm, which promotes the molecule to second singlet excited state of the porphyrin chromophore. The emission decays were measured in the wavelength range 580−840 nm and fitted globally. The resulting spectra of the pre-exponential factors (the emission decay associated spectra, DAS) were corrected by taking into account the photomultiplier tube quantum yield spectrum provided by the manufacturer.11,15 The time resolution of the TCSPC measurements was 60−80 ps.

2. MATERIALS AND METHODS A free-base double-linked dyad 61,62-di-tert-butyl 61,62-[10,20bis(3,5-di-tert-butylphenyl)porphyrin-5,15-diylbis(1-phenyl-3oxy)diethylene]-1,9:49,59-bismethano[60]fullerene61,61,62,62-tetracarboxylate (TBD6be) was synthesized as previously described,26 and metalated to ZnTBD6be in a reaction with Zn(OAc)2 (Figure 1).13

3. RESULTS 3.1. Transient Absorption Pump−Probe Measurements. The charge-transfer (CT) absorption band that corresponds to the direct transition from the ground state to the exciplex state is observed in the steady state spectrum in all the studied solvents (see the Supporting Information for the details). The excitation wavelength in the pump−probe measurements was set as 780 nm because the individual porphyrin and C60 moieties absorb negligibly (5% relative to the CT band) at this wavelength (Figure S1). The transient absorption decay component spectrum of ZnTBD6be in toluene is presented in Figure 2. The monoexponential fit model was sufficient in this case and the decay time constant is 1.12 ± 0.2 ns. The biexponential fitting was done but it gave very minor improvement in sigma value (∼3%) and the absorption change corresponding to the second component was very weak. Considering that toluene is a nonpolar solvent, the obtained long-lived component can be attributed solely to the exciplex.13 In other solvents apart from toluene, biexponential models were needed to fit the data. The shapes of the component spectra were similar in all polar solvents (see spectra in DMF as an example in Figure 3). The short-lived component indicates increase of absorption in the 600−750 nm region (Figure 3),

Figure 1. Chemical structure of the studied compound.

The solvents, toluene (99.9%, Aldrich), anhydrous anisole (99%, Aldrich), o-dichlorobenzene (DCB, 99%, Aldrich), anhydrous benzonitrile (PhCN, 99%, Aldrich), and dimethylformamide (DMF, 99.8%, LAB-SCAN) were used as received. The solvent mixtures toluene/anisole and anisole/PhCN were used with 1:1 ratio. The dielectric constants of the solvent mixtures were determined using the Bruggeman equation:27 ⎡ εmix − ε1 ⎤⎛ ε2 ⎞1/3 ⎥⎜ ⎢ ⎟ = 1 − φ1 ⎣ ε2 − ε1 ⎦⎝ εmix ⎠

⎡ n 2 − 1⎤ ⎡ n 2 − 1⎤ ⎥ + φ2⎢ 22 ⎥ = φ1⎢ 12 +2 ⎣ n2 + 2 ⎦ ⎣ n1 + 2 ⎦

nmix 2 − 1

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Figure 2. Transient absorption decay component spectrum for ZnTBD6be in toluene.

Figure 4. Transient absorption decay component spectra (solid lines with symbols) and time-resolved transient absorption spectrum right after excitation (at 0 ps, dashed line) for ZnTBD6be in anisole.

component, and a slight difference in the shape of the longlived component (Figures 3 and 4). 3.2. Time-resolved Fluorescence Decay Measurements. Relaxation of the exciplex can be monitored by measuring its emission decay in the near IR region of the spectrum.11−13,15 The TCSPC method was used for this purpose. The instrument time resolution is ∼60−80 ps, which is sufficient for determining the emission lifetimes in toluene, toluene/anisole, and anisole, but too long for emissions in solvents with higher polarities than that of anisole. Another reason for not observing the exciplex emission in polar solvents is its minor population as will be discussed later. The emission intensity of the exciplex is relatively low even in nonpolar media,9−15 and the decay measurements can be affected by the presence of even very minor traces of synthesis side products. However, the exciplex can be distinguished from the side products spectrally. Therefore, the decays were measured in the wavelength range 580−840 nm, fitted globally, and the decay associated spectra (DAS) were used to assign the correct lifetime to the exciplex decay11,15 (Figure 5 and Table

Figure 3. Transient absorption decay component spectra (solid lines with symbols) and time-resolved transient absorption spectrum right after excitation (at 0 ps, dashed line) for ZnTBD6be in DMF.

which can be attributed to the formation of the porphyrin cation.33 The short- and the long-lived components in polar solvents correspond to the formation and decay of the CCS state, respectively, and the lifetimes are in agreement with the previously published results13 (Table 1). Table 1. Experimental Lifetimes Obtained from the Pump− Probe (τfast and τslow) and TCSPC (τ) Measurements in Different Solvents, and Lifetimes (τ1 and τ2) Calculated to Reaction Scheme 1 and Using Intrinsic Reaction Rate Constants Obtained as the Result of Global Data Analysisa solvent toluene toluene/ anisole anisole DCB anisole/ PhCN PhCN DMF a

τ (ps)

τfast (ps)

τ1 (ps)

τslow (ps)

τ2 (ps)

1260 ± 228 325 ± 43

12.6 ± 2.1

12.6

1120 ± 200 331 ± 54

1220 303

9.8 ± 1.6 8.7 ± 1.4 4.2 ± 0.7

9.7 7.9 3.8

177 ± 33 154 ± 25 62 ± 10

170 145 56

2.5 ± 0.4 1.0 ± 0.1

2.3 0.9

46 ± 7.8 16 ± 3.2

42 15

142 ± 28

Figure 5. Fluorescence decay associated spectra of ZnTBD6be in toluene/anisole.

1). The characteristic exciplex emission rising above 750 nm is seen for the 325 ± 43 ps component, whereas the other two components are weak in the measured spectral range and show spectral features different from those expected for the exciplex. These minor components arise most likely from some small traces of porphyrin as an impurity in the solutions.

See Discussion for the details.

In toluene/anisole, anisole, and DCB a biexponential fits were required (see spectra in anisole as an example in Figure 4), but the relative amplitude of the fast component is weaker than that observed in more polar solvents, i.e., anisole/PhCN, PhCN, and DMF (Figure 3). The long-lived component has contributions of both the exciplex and the CCS state; i.e., it can be attributed to a mixture between the two states.34 The trend is that the decrease in the solvent polarity results in an increase of both lifetimes, a decrease in intensity of the short-lived

4. DISCUSSION The photoexcitation of the dyad at the near IR spectral region in the pump−probe measurements produces only two intermediate states: the exciplex, formed directly after the excitation, and the CCS state. Therefore, only three states are involved in the excitation−relaxation scheme: the ground state, 9655

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where [ex] and [cs] are the populations and ΔGex and ΔGcs are the free energies of the exciplex and the CCS state, respectively. kB is Boltzmann’s constant, and T is the temperature. Right after the excitation only the exciplex is populated and the thermodynamic equilibrium between the exciplex and CCS state is established with the rate constants kET and kcx according to Scheme 1. This is observed as the fast process in pump− probe measurements. Because the rate constants of the fast processes are 16−26 times greater than those of the final relaxation in all studied solvents (Table 1), we will first consider the relaxation under condition of established thermodynamic equilibrium (eq 3), which formally means that kET + kcx > kex and kCR, and the exciplex and CCS state are relaxing synchronously, though the relative populations of the states may be very different in different solvents. According to this assumption, the common relaxation rate constant depends on the relative ratio between their populations as follows:

the exciplex, and the CCS state. It has been reported previously13,15 that depending on the solvent polarity the energy of the CCS state can be either lower (in polar media) or higher (in nonpolar media) than that of the exciplex. As a result, one can expect an equilibrium between the exciplex and the CCS state (Scheme 1). Relaxation of the exciplex and the Scheme 1. Reaction Scheme of the Excitation−Relaxation Process of ZnTBD6bea

a kET and kCR are the rate constants for the charge separation and charge recombination processes, respectively, kcx is the rate constant for the back-conversion of the CCS state to the exciplex, and kex is the relaxation rate constant of the exciplex to the ground state.

k fit = kexβex + k CR βcs = kexβex + k CR (1 − βex )

where kfit is the common decay rate constant (Table 3), and βex and βcs are the relative fractions of the exciplex and the CCS state, i.e., βex = [ex]/([ex] + [cs]) = ([ex]/[cs])/([ex]/[cs] + 1) and βcs = [cs]/([ex] + [cs]). The value for βex can be calculated from eq 3. The direct relaxation rates of the exciplex and the CCS state to the ground state can be obtained from the semiquantum Marcus ET theory:19,20,35,36

CCS state to the ground state can be described by four rate constants depicted in Scheme 1: the direct relaxation of the exciplex to the ground state, kex, the transition from the exciplex to the CCS state, kET, the back-reaction from the CCS state to the exciplex, kcx, and the decay of the CCS state to the ground state, or the charge recombination (CR) process, kCR. There are only two observable transient states associated with Scheme 1, and the apparent lifetimes of the states depend on four intrinsic rate constants, in a general case. Therefore, not much can be said about the intrinsic reaction rate constants by using solely the experimentally obtained lifetimes. More information can be obtained from the transient absorption component and emission decay associated spectra, which were previously used to assign the long-lived component in polar solvents to the CCS state and in nonpolar solvents to the exciplex.13,15 In polar solvents the energy of the CCS state is considerably lower than that of the exciplex and the equilibrium between these two states is shifted more to the side of the CCS state, i.e., kET ≫ kcx, and the reaction ZnP+−C60− → (ZnP− C60)* could be neglected. On the contrary, in nonpolar media the energy of the CCS state is higher than that of the exciplex, kET ≪ kcx, and the reaction (ZnP−C60)* → ZnP+−C60− can be neglected. Apparently, in an intermediate case neither of these reactions can be neglected, and a more advanced analysis method has to be developed to gain information on the reaction parameters. The aim of the following discussion is to look at the internal relations between the intrinsic rate constants, build a model which accounts for all four reactions depicted in Scheme 1, and connect them with the two observable lifetimes. The kinetics of relaxation process of the dyad (Scheme 1) can be considered in frame of the thermodynamic point of view. For an established equilibrium, the population ratio between the exciplex and the CCS state does not change in time and is given by the Boltzmann distribution: ⎡ (ΔGex − ΔGcs) ⎤ [ex] = exp⎢ − ⎥ [cs] kBT ⎦ ⎣

(4)

k=

4π 2V 2e−S h(4πErkBT )1/2

∞

∑ i=0

⎡ (ΔG + E + iE )2 ⎤ Sn r v ⎥ exp⎢ − i! 4ErkBT ⎦ ⎣ (5)

where k is the reaction rate constant, i.e., either kex or kCR in Scheme 1, V is the electronic coupling matrix element, S is the electron-vibrational coupling, h is Planck’s constant, Er is the total reorganization energy of the intermediate state, i is the vibrational level, and Ev is the vibrational energy. One can assume that the vibrational energy and the electronicvibrational coupling have similar values for the exciplex and the CCS state relaxation. However, the electronic coupling, the free energy, and the reorganization energy are clearly different for these two reactions. Furthermore, ΔG and Er depend on the solvent polarity.19,35,37 The free energy of the exciplex (ΔGex) has been found to depend linearly on the inverse of the dielectric constant of the solvent as follows:16 ⎡a⎤ ΔG = E0 + ⎢ ⎥ ⎣ εr ⎦

(6)

where E0 is a constant that presents the free energy of the intermediate when the Coulombic attraction between the donor and acceptor is neglected (which can be applied in extremely polar solvents), a is a coefficient showing how strong is the dependence, and εr is the dielectric constant of the solvent. Assuming simple point-to-point interaction and that the only solvent-sensitive part of the free energy of the exciplex and the CCS state is the Coulombic interaction between the donor and the acceptor, the coefficient a in eq 6 can be expressed as16,19,35,37

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Table 2. Energetic Parameters Obtained from the Fita state

E0 (eV)

Eri (eV)

γ

V (eV)

exciplex CCS

1.199 ± 0.01 1.072 ± 0.001

0.082 ± 0.002b 0.105 ± 0.02

0.55 ± 0.02 1c

0.254 ± 0.022 0.012 ± 0.001

a E0 is the solvent independent part of the free energy, γ is the charge separation degree, Eri is the internal reorganization energy, and V is the electronic coupling matrix element. The standard deviations were estimated using sensitivity analysis and without taking into account the crosscorrelations between the different fit parameters. bFrom ref 16. cFixed value.

⎡ γ 2q2 ⎤ ⎥ a=⎢ ⎣ 4πε0RDA ⎦

⎡b ⎤ bcs = ⎢ ex2 ⎥ ⎣γ ⎦

(7)

where bex and bcs are the reorganization energy coefficients of the exciplex and the CCS state, respectively. Therefore, the solvent dependences of the free and reorganization energies of both the exciplex and the CCS state can be modeled by guessing γ, E0, and Eri values for the two states and using the aex and bex coefficients estimated previously.16 Substituting eqs 3, 5, 6, 8, 9, and 11 into eq 4, one can construct a mathematical model to calculate the common lifetimes (1/kfit) and to fit the dependence of the lifetimes on the solvent polarity. The fixed parameters were taken from the previous report on the exciplex;16 these are the coefficients aex = 0.35 eV and bex = 0.22 eV, the exciplex internal reorganization energy, Eri = 0.082 eV, the electron-vibrational coupling, S = 0.54, and the vibrational energy, Ev = 0.158 eV. The fit criterion was the minimum value of the average of the relative deviation squares of the calculated lifetimes from the measured ones, σr2. The average of the relative deviation was 0.0102 for the best fit found. The fit parameters obtained from the model are given in Table 2 and the dependence of the calculated common lifetimes (1/kfit) obtained from the fit model on the solvent polarity factor is shown in Figure 6.

where q is the elementary charge, γ is the charge separation degree, which is unity in the case of the CCS state and 0 < γ < 1 for the exciplex, ε0 is the permittivity of vacuum, and RDA is the center-to-center distance between the donor and acceptor.13,16 We have previously estimated the coefficient a for the exciplex of ZnTBD6be as 0.35 ± 0.01 eV from the dependence of ΔGex on the solvent polarity, on the basis of the analysis of the steady state absorption and emission data.16 Although eq 7 is derived for the point-to-point electrostatic interaction, and an exact expression is not available for γ, one can still expect similar square dependence of a on γ in case of the CCS state even if point-to-point approximation is not strictly valid. Thus, the coefficient a of the CCS state can be calculated from that of the exciplex and the γ value, regardless of the RDA value, which may differ from the geometrical distance between the porphyrin donor and the fullerene acceptor:

⎡a ⎤ acs = ⎢ ex2 ⎥ ⎣γ ⎦

(11)

(8)

where aex and acs are the free energy coefficients of the exciplex and the CCS state, respectively, and γ is the charge separation degree in the exciplex. The dependence of the total reorganization energy (Er) of the exciplex on the solvent polarity factor (f) was found to be linear as follows:16 ⎡1 1⎤ Er = Eri + bf = Eri + b⎢ 2 − ⎥ εr ⎦ ⎣n

(9)

where Eri is the inner sphere or internal reorganization energy, which does not depend on the solvent and arises from the structural differences of the molecule in the reactant and product states,19 n is the refractive index of the solvent, and b is the coefficient, which was earlier estimated as 0.22 ± 0.02 eV for the exciplex of ZnTBD6be.16 The second term in eq 9 represents the outer sphere or the solvent reorganization energy of the intermediate state, and according to the classic dielectric continuum approximation the coefficient b can be calculated as follows:16,19,35 b=

γ 2q2 ⎡ 1 1 1 ⎤ + − ⎥ ⎢ 4πε0 ⎣ 2RD 2RA RDA ⎦

Figure 6. Dependence of the measured decay time constants (longlived component) of ZnTBD6be on the solvent polarity factor (circles with error bars), fitted dependence of the common calculated lifetimes (solid line), and separate time constants for the direct relaxation of the exciplex and the CCS state to the ground state (dotted and dashed lines, respectively).

Because most parameters determining the direct exciplex relaxation to the ground state were adopted from the absorption and emission spectra analysis of the exciplex,16 the first critical part of the fit process was to find the best fit for the low polarity side of the dependence ( f < 0.2). At first only the electronic coupling of the exciplex, Vex, was varied, but it was not possible to get the right magnitude and slope by tuning a single value. Therefore, the solvent independent part of the exciplex free energy, E0, was also tuned to obtain a satisfactory fit at f < 0.2. The dotted curve in Figure 6 presents the polarity dependence of the direct relaxation of the exciplex to the ground state, which is the main relaxation process in media

(10)

where RD and RA are the radii of the donor and acceptor, respectively.13,16 Similarly to the free energy case, the solvent dependent part of the reorganization energy of the CCS state can also be calculated from the corresponding value of the exciplex and the charge separation degree, γ as follows: 9657

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fit values of V were 0.254 ± 0.022 and 0.012 ± 0.001 eV for the exciplex and the CCS state, respectively (Table 2). The electronic coupling for the CCS state to the ground state transition, ∼100 cm−1, is very reasonable for DA dyads of this type,14,23,25 but the value obtained for the transition from the exciplex to the ground state is larger than the previously reported values. Earlier studies on porphyrin−fullerene dyads revealed the electronic coupling for the exciplex relaxation to the ground state as 0.033−0.074 eV in different environments.9,10,13,17 In part, the discrepancy may be due to slightly inaccurate estimation of the oscillator strength for the chargetransfer absorption bands, although the difference is too big to be explained exclusively by this factor. In general, it is wellknown that the V value for the exciplex is much larger than that for the CCS state, because the wave function of the exciplex is described as a linear combination of the locally excited state and the CCS state, and thus it is expected to have greater coupling with the ground state wave function than the CCS state wave function alone.5,6,20,21 It was reported earlier that the electronic coupling of the exciplex can be 100 times larger than that of the CCS state in DA compounds of aromatic hydrocarbons,21 which is in agreement with the result obtained in this study. The electronic coupling for the exciplex state formed between a methylbenzene donor and a tetracyanoanthracenene acceptor was demonstrated to be ∼0.17 eV.38 The strong coupling of the exciplex state may suggest that the reaction is adiabatic rather than nonadiabatic.39 However, Gould et al. have explained the strong electronic couplings for exciplexes by studying the quantitative relationship between radiative and nonradiative electron transfer.20,38,40 They have shown that the nonadiabatic and adiabatic theories are in quantitative agreement when the sum of the reorganization and vibrational energies is considerably smaller than the driving force of the ET reaction, i.e., ΔGex ≫ Ev + Er for the direct relaxation of the exciplex to the ground state,20,40 which is the case for the studied dyad. Instead, if ΔGex would approach Ev + Er, the adiabatic theory should be applied to this case.40 Therefore, the reaction can be considered nonadiabatic for ZnTBD6be despite the large value of the electronic coupling for the exciplex state. From the side of the functional dependence derived here, a smaller value of the electronic coupling would require a much lower value for E0 of the exciplex, which is an unreasonable outcome. Therefore, assuming that the applied model is valid, we believe that the value obtained here is more reliable. It is noteworthy to mention here that the direct relaxation rate constants of the exciplex and the CCS state, kex and kCR, (Scheme 1 and Figure 6) are very sensitive to any change in the electronic couplings, Vex and Vcs, respectively (eq 5), which means that the accuracy of these parameters is high assuming that the free energies are determined correctly. Knowing the populations of the exciplex and the CCS state (eq 3) and their free energies (eq 6), one can calculate the rate constants of the equilibrium reaction between them, kET and kcx, in all of the studied solvents (Table 3). In equilibrium kET/ kcx = [cs]/[ex] and τfast = (kET + kcx)−1 which leads to

with low polarity. The other parameters involved in the fit determine the dependence of the CR process on the solvent polarity (shown by the dashed line in Figure 6) and the polarity factors at which the direct relaxation of the exciplex to the ground state switches to the process via the CCS state. As shown in Figure 6, the fit curve of the calculated common lifetimes matches well with the experimental results, which proves the successful construction of the mathematical model. The equilibrium process between the exciplex and the CCS state is more significant in solvents with polarities between those of anisole and DCB. However, it is clear that in anisole ( f ≈ 0.2) the direct relaxation of the exciplex to the ground state dominates over that of the formation of the CCS state, whereas the relaxation via the CCS state dominates in the case of DCB (f ≈ 0.3). The solvent independent part of the exciplex free energy (E0 in eq 6) was earlier estimated to be 1.395 ± 0.004 eV on the basis of analysis of the steady state charge-transfer absorption and emission bands associated with the exciplex.16 The best fit value obtained here is 1.199 ± 0.01 eV (Table 2), which is smaller by 0.194 ± 0.014 eV than the previously reported one. The difference is not big, but essential for a reasonable fit, because the direct relaxation rate constant of the exciplex to the ground state, kex, depends exponentially on the free energy (eq 5). Similarly, the solvent independent part of the CCS state free energy is smaller than the expected one. This energy is usually obtained from the electrochemical measurements as the difference between the oxidation and the reduction potentials of the donor and acceptor and it was previously reported to be 1.38 eV for ZnTBD6be.16 The best fit value in this model is 1.072 ± 0.001 eV (Table 2), i.e., smaller by 0.31 ± 0.001 eV. It has to be noted that within the model the polarity dependences of the exciplex energies were assumed to be known and the corresponding dependences for the CCS state were adjusted with the charge separation degree value, γ. Therefore, the best fit E0 value for the CCS state depends on the value for the exciplex, i.e., higher E0 value for the exciplex would result in higher E0 value for the CCS state. Nevertheless, the method reported here is an alternative for determining E0 of the CCS state, and it gives a lower energy estimation compared to the conventionally used electrochemical methods. The charge separation degree in the exciplex (γ) of ZnTBD6be was previously reported to be ∼0.4,16 and the best fit value in the new model is 0.55 ± 0.02 (Table 2). The γ value reported earlier was calculated on the basis of a rough estimation for the center-to-center distance (RDA in eqs 7 and 10) between the porphyrin and C60 moieties of the dyad, treating the solvent as a dielectric continuum, and approximating the electron donor and acceptor as spheres.16 In fact, C60 is a spheroid but the porphyrin moiety is not, and the model given by eqs 7 and 10 may not work well. The model considered here relies only on square dependence of the energies on γ value, or more precisely on eq 11. For this reason the value obtained here can be considered to be more accurate. The internal reorganization energy, Eri, is indicated by the intersection (f = 0) in eq 9. The best fit value of Eri for the CCS state is 0.105 ± 0.02 eV (Table 2), which is slightly larger than the value reported for the exciplex, 0.082 ± 0.002 eV,16 as can be expected. The electronic coupling matrix element V, is of great importance to our calculations because it determines the magnitude of the direct relaxation rates of both the exciplex and the CCS state to the ground state6,19−21,35,36 (eq 5). The best

⎡ 1 − βex ⎤ kET = ⎢ ⎥ ⎣ τfast ⎦

(12)

where τfast is the experimental lifetime of the fast component obtained from the pump−probe measurements (Table 1). 9658

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Table 3. Calculated Relative Populations (βex) of the Exciplex, Calculated Free Energies for the Exciplex and the CCS State (ΔGex and ΔGcs, Respectively), Calculated Rate Constants Obtained from the Fit Model, kET, kcx, and kfit, and the Experimental Direct Relaxation Rate Constants of the Exciplex and the CCS State, kexp, for ZnTBD6be in Variable Solvents solvent

εra

βexc

ΔGex (eV)d

ΔGcs (eV)d

kET (s−1)e

kcx (s−1)f

kfit (s−1)g

kexp (s−1)h

toluene toluene/anisole

2.38 3.37b

0.999 0.987

−1.346 −1.303

−1.558 −1.415

1.0 × 109

9.3 × 1010

0.8 × 109 3.4 × 109

anisole

4.33

0.908

−1.279

−1.339

9.4 × 109

7.8 × 1010

5.9 × 109

10.12 14.88b 25.90 38.25

0.139 0.057 0.024 0.017

−1.234 −1.223 −1.213 −1.208

−1.186 −1.149 −1.117 −1.102

9.9 2.2 3.9 9.8

× × × ×

1.6 × 1010 1.4 × 1010 9.8 × 109

7.4 1.4 2.5 6.6

0.8 3.0 3.0 5.6 7.0 6.5 1.6 2.2 6.3

DCB anisole/PhCN PhCN DMF

1010 1011 1011 1011

× × × ×

109 1010 1010 1010

× × × × × × × × ×

109i 109 109i 109 109i 109 1010 1010 1010

a From ref 28. bCalculated from eq 1. cCalculated from eq 3. dCalculated from eq 6. eCalculated from eq 12. fDerived from eq 12. gCalculated from eq 4. hFrom pump−probe (the slow component) with uncertainties ±13−18% (Table 1). iFrom TCSPC.

The calculated rate constants, kfit, kcx, kET, the measured rate constant of the slower component, kexp, and the relative populations of the exciplex, βex, are given in Table 3. A careful inspection of Table 3 gives one a lot of information about the relations between the experimental and the calculated intrinsic rate constants in the excitation relaxation process of the dayd. In all solvents, the sum of the rate constants in the equilibrium is greater than the rate constant of the relaxation to the ground state measured experimentally (kET + kcx > kexp). As stated above, this indicates the existence of the equilibrium between the exciplex and the CCS state. The population of the CCS state is very low in nonpolar media, e.g., toluene, and the direct relaxation of the exciplex becomes dominating process. The opposite trend is observed in strongly polar environments, i.e., in DMF. The dominating relaxation pathway is governed by the balance between the free energies of the exciplex and the CCS state, ΔGex and ΔGcs, respectively, and indicated in Table 3 as the relative population of the exciplex, βex. The free energy of the exciplex in toluene is less negative than that of the CCS state, and the relative population of the CCS state is 0.1%. Thus, the CCS state was not observed experimentally, and no information on kET and kcx can be obtained in this case. In contrast, the energy of the exciplex in DMF is higher than that of the CCS state, and the relative population of the exciplex is very minor (1.7%), which leads to the fastest ET rate among the studied solvents (kET ≈ 1012 s−1) and a negligible backward transition to the exciplex. It can be concluded that at a polarity factor of about 0.27 (εr ≈ 6.4), both the energies and the populations of the CCS state and the exciplex are equal (Figure 6), and kET and kcx shall have the same value in this case. As presented in Table 3, the relative population of the exciplex decreases sharply switching to solvents with polarity higher than that of anisole. The minor population of the exciplex in such solvents results in a significant decrease in its emission intensity. This factor represents the second reason for not observing the exciplex emission in solvents more polar than anisole (Table 1). The first factor is the decrease in the exciplex lifetime as stated above (Figure 6). Earlier kinetic studies on intermolecular contact radical-ion pairs (CRIP) and solvent separated radical-ion pairs (SSRIP) of a tetracyanobenzene acceptor with various methylbenzene donors revealed similar photodynamic reactions. 7,8 An equilibrium between CRIP and SSRIP was observed after formation of the intermolecular CRIP upon the excitation of the ground state CT complex. The absolute energies of CRIP

and SSRIP, and the ET rate constants were measured in solvents of different polarities.7,8 It was found that the critical point of the solvent polarity, in which the energies of the two states and the equilibrium rate constants become equal, is 7.8 Even though the system studied here is rather different, the quantitative treatment used in this study has been earlier proved to be valid and successful for analyzing such kinetic reactions. Once we have obtained all four intrinsic rate constants, kex, kET, kcx, and kCR (Table 3 and Figure 6), associated with the excitation relaxation process of the dyad, the validity of the derived model can be further evaluated. The thermodynamic analysis performed to construct the fit model and the accuracy of the calculated rate constants can be tested. This is done as follows: The exact solution of the kinetic differential equations corresponding to the reactions shown in Scheme 1 gives two time constants, which correspond to two lifetimes obtained from the fits of the experimental data. The time constants are41,42 τ1,2 = 2[X + Y ±

(Y − X )2 + 4kETkcx ]−1

(13)

where X = kex + kET, Y = kCR + kcx, and τ1 and τ2 correspond to the fast and slow lifetimes (τfast and τslow in Table 1) obtained from pump−probe and from emission decay measurements (τ in Table 1). The results of the calculations (Table 1) revealed very good agreement, and the calculated values deviate from the experimental ones by only 4−10%. This confirms that the difference between the relaxation rate constants, kex and kCR, and the rate constants involved in the equilibrium, kET and kcx, is large enough to consider the relaxation as a reaction, in which both the exciplex and CS state decay synchronously. Moreover, this outcome confirms applicability of the constructed model to the studied problem and indicates that the four calculated intrinsic rate constants are reasonably accurate, because the thermodynamic analysis used to derive the fit model gives reasonable solution for the kinetic treatment of the photoinduced ET reaction in all studied solvents.

5. CONCLUSIONS A complete quantitative analysis of the ET reaction in a doubly linked zinc porphyrin−fullerene dyad, ZnTBD6be, was done by studying the photodynamic behavior of the exciplex and the CCS state in different environments. The analysis became reasonably simple because the locally excited states of the 9659

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(7) Arnold, B. R.; Noukakis, D.; Farid, S.; Goodman, J. L.; Gould, I. R. J. Am. Chem. Soc. 1995, 117, 4399−4400. (8) Arnold, B. R.; Farid, S.; Goodman, J. L.; Gould, I. R. J. Am. Chem. Soc. 1996, 118, 5482−5483. (9) Armaroli, N.; Marconi, G.; Echegoyen, L.; Bourgeois, J.-P.; Diederich, F. Chem.Eur. J. 2000, 6, 1629−1645. (10) Imahori, H.; Tkachenko, N. V.; Vehmanen, V.; Tamaki, K.; Lemmetyinen, H.; Sakata, Y.; Fukuzumi, S. J. Phys. Chem. A 2001, 105, 1750−1756. (11) Vehmanen, V.; Tkachenko, N. V.; Imahori, H.; Fukuzumi, S.; Lemmetyinen, H. Spectrochim. Acta A 2001, 57, 2229−2244. (12) Tkachenko, N. V.; Lemmetyinen, H.; Sonoda, J.; Ohkubo, K.; Sato, T.; Imahori, H.; Fukuzumi, S. J. Phys. Chem. A 2003, 107, 8834− 8844. (13) Chukharev, V.; Tkachenko, N. V.; Efimov, A.; Guldi, D. M.; Hirsch, A.; Scheloske, M.; Lemmetyinen, H. J. Phys. Chem. B 2004, 108, 16377−16385. (14) D’Souza, F.; Maligaspe, E.; Karr, P. A.; Schumacher, A. L.; Ojaimi, M. E.; Gros, C. P.; Barbe, J.-M.; Ohkubo, K.; Fukuzumi, S. Chem.Eur. J. 2008, 14, 674−681. (15) Kesti, T. J.; Tkachenko, N. V.; Vehmanen, V.; Yamada, H.; Imahori, H.; Fukuzumi, S.; Lemmetyinen, H. J. Am. Chem. Soc. 2002, 124, 8067−8077. (16) Chukharev, V.; Tkachenko, N. V.; Efimov, A.; Lemmetyinen, H. Chem. Phys. Lett. 2005, 411, 501−505. (17) Al-Subi, A. H.; Niemi, M.; Ranta, J.; Tkachenko, N. V.; Lemmetyinen, H. Chem. Phys. Lett. 2012, 531, 164−168. (18) Marcus, R. A. J. Phys. Chem. 1989, 93, 3078−3086. (19) Bolton, J. R.; Archer, M. D. Adv. Chem. Ser. 1991, 228, 7−23. (20) Gould, I. R.; Young, R. H.; Moody, R. E.; Farid, S. J. Phys. Chem. 1991, 95, 2068−2080. (21) Gould, I. R.; Farid, S. Acc. Chem. Res. 1996, 29, 522−528. (22) Imahori, H.; Tamaki, K.; Guldi, D. M.; Luo, C.; Fujitsuka, M.; Ito, O.; Sakata, Y.; Fukuzumi, S. J. Am. Chem. Soc. 2001, 123, 2607− 2617. (23) Guldi, D. M.; Hirsch, A.; Scheloske, M.; Dietel, E.; Troisi, A.; Zerbetto, F.; Prato, M. Chem.Eur. J. 2003, 9, 4968−4979. (24) Schuster, D. I.; Cheng, P.; Jarowski, P. D.; Guldi, D. M.; Luo, C.; Echegoyen, L.; Pyo, S.; Holzwarth, A. R.; Braslavsky, S. E.; Williams, R. M.; Klihm, G. J. Am. Chem. Soc. 2004, 126, 7257−7270. (25) Yamada, H.; Ohkubo, K.; Kuzuhara, D.; Takahashi, T.; Sandanayaka, A. S. D.; Okujima, T.; Ohara, K.; Ito, O.; Uno, H.; Ono, N.; Fukuzumi, S. J. Phys. Chem. B 2010, 114, 14717−14728. (26) Efimov, A.; Vainiotalo, P.; Tkachenko, N. V.; Lemmetyinen, H. J. Porphyrins Phthalocyanines 2003, 7, 593−599. (27) Lou, J.; Hatton, T. A.; Laibinis, P. E. J. Phys. Chem. A 1997, 101, 5262−5268. (28) Marsh, K. N., Ed. Recommended Reference Materials for the Realization of Physicochemical Properties; Blackwell Scientific Publications: Oxford, U.K., 1987. (29) Aminabhavi, T. M. J. Chem. Eng. Data 1984, 29, 54−55. (30) Dean. Lange’s Handbook of Chemistry, 15th ed.; McGraw-Hill, Inc.: New York, 1999. (31) Tkachenko, N. V.; Rantala, L.; Tauber, A. Y.; Helaja, J.; Hynninen, P. H.; Lemmetyinen, H. J. Am. Chem. Soc. 1999, 121, 9378−9387. (32) Niemi, M.; Tkachenko, N. V.; Efimov, A.; Lehtivuori, H.; Ohkubo, K.; Fukuzumi, S.; Lemmetyinen, H. J. Phys. Chem. A 2008, 112, 6884−6892. (33) Gasyna, Z.; Browett, W. R.; Stillman, M. J. Inorg. Chem. 1985, 24, 2440−2447. (34) Al-Subi, A. H.; Niemi, M.; Tkachenko, N. V.; Lemmetyinen, H. J. Phys. Chem. A 2011, 115, 3263−3271. (35) Marcus, R. A. Rev. Mod. Phys. 1993, 65, 599−610. (36) Barbara, P. F.; Meyer, T. J.; Ratner, M. A. J. Phys. Chem. 1996, 100, 13148−13168. (37) Kavarnos, G. J.; Turro, N. J. Chem. Rev. 1986, 86, 401−449. (38) Gould, I. R.; Young, R. H.; Mueller, L. J.; Albrecht, A. C.; Farid, S. J. Am. Chem. Soc. 1994, 116, 3147−3148.

porphyrin and fullerene chromophores were excluded from the consideration by exciting the dyad in the near IR region which populates the exciplex directly from the ground state. A fit model was constructed on the basis of the Marcus theory of electron transfer and utilizing parameters previously reported for the exciplex of ZnTBD6be. When the fit model was applied, a clear quantitative distinction between the exciplex and the CCS state was obtained in all environments even though there is no sharp spectral difference between the two states. The energies of the exciplex and the CCS state become equal in solvents with dielectric constants of ∼6.4. In the range of the model applicability, the obtained fit parameters, e.g., the solvent independent part of the free energies and the electronic coupling matrix elements for the exciplex and the CCS state, can be considered to be more reliable than the previously reported ones. Another advantage of the model is that it covers a wide range of environments and succeeds to explain quantitatively the photodynamic behavior of the dyad in polar and nonpolar solvents.

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ASSOCIATED CONTENT

S Supporting Information *

Additional experimental data including absorption spectra of ZnTBD6be and the zinc porphyrin and fullerene reference compounds. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*To whom correspondence should be addressed. E-mail: ali.alsubi@tut.fi Fax: +358 3 3115 2108; Tel: +358 3 3115 3628. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Technology Agency of Finland and Finnish Academy. ABBREVIATIONS CCS, complete charge separated; CR, charge recombination; CRIP, contact radical-ion pairs; CT, charge transfer; DA, donor−acceptor; DAS, decay associated spectra; DCB, odichlorobenzene; DMF, dimethylformamide; ET, electron transfer; IR, infrared; PhCN, benzonitrile; SSRIP, solvent separated radical-ion pairs; TCSPC, time-correlated singlephoton counting

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REFERENCES

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