Bimolecular Photoinduced Electron Transfer in Static Quenching

Article pubs.acs.org/JPCB

Bimolecular Photoinduced Electron Transfer in Static Quenching Regime: Illustration of Marcus Inversion in Micelle Puspal Mukherjee, Aritra Das, Arunava Sengupta, and Pratik Sen* Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur 208 016, UP, India S Supporting Information *

ABSTRACT: Ultrafast bimolecular photoinduced electron transfer (PET) between six coumarin dyes and four viologen molecules in the stern layer of sodium dodecyl sulfate micelle have been studied using femtosecond broadband transient absorption spectroscopy and femtosecond fluorescence up-conversion spectroscopy over a broad reaction exergonicity (ΔG0). Emanating the formation of radical cation intermediates of viologen molecules using the transient absorption and the fast decay component of coumarins using the fluorescence up-conversion studies the forward bimolecular electron transfer rate (ket) have been measured with high accuracy. The relationship of ket with ΔG0 found to follow a Marcus type bell-shaped dependence with an inversion at −1.10 eV. In this report, we have studied PET reaction using ultrafast spectroscopy at the quencher concentration where static quenching regime prevails. Moreover, the incompetency of Stern−Volmer experiments in studying ultrafast PET has been revealed. In contrary to previous claims, here we found that the ket is lower for lower lifetime coumarins, indicating that static, nonstationary and stationary regime of quenching have the minimal role to play to in the bimolecular electron transfer process. By far, this report is believed to be the most efficient and immaculate way of approaching Marcus inverted region problem in the case of bimolecular PET and settles the long-lasting debate of whether the same can be observed in micellar systems.

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INTRODUCTION

ΔG‡ =

Marcus theory for outer sphere electron transfer reactions is one of the most remarkable and paramount achievements in chemistry in the 20th century. The theory of electron transfer, for which Rudolph Marcus was awarded the Nobel Prize in Chemistry in 1992, spoke of two parabolic potential energy surfaces for the initial and final states of the system.1−3 Here the initial state of the system undergoing electron transfer is a preequilibrium ensemble between the donor and acceptor molecule known as the encounter complex.4 After the electron transfer, a successor complex of an ion pair is formed, which then undergoes solvation to form a solvent separated ion pair (SSIP) or remain as a contact ion pair (CIP).4−6 The rate constant for this process is expressed as4,7 ⎛ ΔG ket = νNkel exp⎜ − ⎟ ⎝ RT ⎠

(2)

Here λ is the reaction reorganization energy, which consists of two types of reorganization namely inner or internal nuclear reorganization [λi] and outer or solvent reorganization energy [λs]. λ = λ i + λs

(3)

The nuclear reorganization was derived by Marcus using a harmonic oscillator model and the classical expression for this is4,7,8 ⎛ f D ··· A f D.+ ··· A.− ⎞ i ⎟Δq 2 λ i = ∑ ⎜⎜ i i D ··· A D. + ··· A. − ⎟ + fi ⎝ fi ⎠

‡⎞

(1)

(4)

Here Δqi is the change in interatomic distance and f i is the force constant of vibration. The solvent reorganization is expressed as4,7,8

In the above equation, νN is the average nuclear frequency factor, kel is the electronic transmission coefficient or the electronic barrier for the reaction, ΔG‡ is the free energy of activation, R is the universal gas constant, and T is the temperature. The free energy of activation [ΔG‡] is related to the standard free energy change of the reaction or reaction exergonicity [ΔG0] as4,7 © 2017 American Chemical Society

(ΔG° + λ)2 4λ

Received: November 8, 2016 Revised: January 31, 2017 Published: January 31, 2017 1610

DOI: 10.1021/acs.jpcb.6b11206 J. Phys. Chem. B 2017, 121, 1610−1622

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The Journal of Physical Chemistry B ⎛ 1 1 1 ⎞⎛⎜ 1 1⎞ + − − ⎟⎟ λs = e 2 ⎜ ⎟⎜ εs ⎠ 2rA rDA ⎠⎝ εop ⎝ 2rD

perturb the electronic states of the donor and acceptor molecules and consequently the nondiffusive scenario MIR was achieved. But Rehm−Weller could not reach MIR as the electron transfer in the encounter complex is faster than diffusion and the overall rate constant is diffusion controlled.18 Till then, the encounter diffusion in the intermolecular PET was the primary concern, and many reports were published in successive years to establish the existence of MIR until date.20−23 Different techniques other than fluorescence quenching, such as scanning tunneling microscopy, dynamic nuclear polarization, etc., were also employed to establish the MIR but still, the quenching technique remained the most applicable one.24,25 Two very recent publications can be highlighted in this context. Petersson et al. studied PET between Zn- and Mgtetrasulphonatophenylporphyrin complexed with different viologens by exciting the porphyrins at the Soret band.26 They followed the formation of radical cation of the viologens and the deactivation of the radical ion-pair, during the electron transfer through femtosecond transient absorption spectroscopy and thus obtained a bell-shaped dependence of rate constants with the ΔG0 of the reaction. Waskasi et al. have performed another transient absorption study that revealed the MIR in an Arrhenius type plot.27 Instead of varying the ΔG0, they changed the other parameter, i.e., temperature, in a PET reaction in a porphyrin-fullerene dyad and observed the charge recombination process. The basis of their observation was that both λs and ΔG0 were varied with temperature, but as ΔG0 is negative while the other parameter is positive; they can achieve the parabolic dependence. Another approach, which became popular over the years to obtain MIR is the use of constrained media such as micelle and reverse micelle.28,29 The primary reason behind this is the slow solvent relaxation time in such confined media. Zusman et al. first raised this issue in a report, where they derived a modified pre-exponential factor for Marcus theory, which incorporated the strong solvent interaction in polar solvent by introducing a

(5)

Here, e is the electronic charge, rD and rA are the ionic radii of donor and acceptor, and rDA is the sum of them. The optical and static dielectric constants are given by εop and εs, respectively. Combining eq 2 with eq 1, Marcus has predicted a very unusual phenomenon. If, ΔG0 > − λ, then ket increases with reaction exergonicity, which is the normal behavior. When ΔG0 = −λ, ket reaches a maximum and with further increase in reaction exergonicity (ΔG0 < − λ) a reduction in the rate of electron transfer reaction should occur. This type of parabolic dependence of the electron transfer rate constant with reaction exergonicity was first of its kind and the region where ΔG0 < − λ is known as Marcus inverted region. As a whole Marcus theory gave the rate of electron transfer as4−9 ket =

4π 2 h

⎧ (ΔG° + λ)2 ⎫ ⎬ exp⎨− 4λkBT ⎭ 4πλskBT ⎩ Vel2

(6)

where, Vel is electronic coupling matrix element. Since then several attempts were made to prove this dependence experimentally.10−16 Photoinduced electron transfer (PET) reaction, which employed fluorescence quenching as a measurable parameter became the most used method.10−16 However, fluorescence quenching method has an intrinsic problem. The quenching rate constant (kq) is a harmonic mean of two rate constants, which are rate constant of electron transfer (ket) and rate constant of diffusion (kd).4 1 1 1 = + kq ket kd (7) So, in the case of a bimolecular quenching reaction in a solvent of low viscosity, where ket is much faster than kd, kq is mainly given by kd. This situation can be illustrated in a simple PET scheme as given in Scheme 1.17 In the scheme, kf is the

solvation term

Scheme 1. Kinetic Representation of Photoinduced Electron Transfer Reaction

( ) in the pre-exponential factor. 1 τL

28,30

In cases

of less viscous but highly polar solvents, such as water and short chain alcohols, extremely fast solvation time influences and modifies the rates of electron transfer. Bagchi and co-workers included classical low-frequency vibrational modes along with solvent relaxation to predict that the ultrafast component of solvation dynamics contribute significantly to the enhancement of the rate of electron transfer in MIR.31 Yet Yoshihara et al. suggested that in neat donor solvent the kinetics of electron transfer is faster than solvation.32 In organized assemblies, the solvation time does show a ultrafast component as demonstrated by Mandal et al. in their femtosecond solvation dynamics study of DCM dye in neutral TX-100 and cationic CTAB micelle, but the overall subnanosecond solvation time in micelle is much slower (∼100 times) compared to that in bulk solvents.33 Recently Choudhury et al. studied the subpicosecond solvation dynamics in SDS micelle using coumarin 500 as the probe molecule and got an ultrafast time component of 1.48 ps along with a slower time component 27 ps of solvation.34 However, in a micellar media, the donor and acceptor molecules stay very close to each other and thus the rate of electron transfer is expected to be free from the effect of diffusion and as fast as in neat solvents as studied by Yoshihara and co-workers.35 There is another advantage of studying the PET reactions in micelles. The width of the Marcus parabola

intrinsic fluorescence decay of the donor molecule, k−d is the reverse diffusion rate constant and kbet is the rate of deactivation to the ground state through back electron transfer pathway. In the said situation, the electron transfer is almost instantaneous compared to the equilibrium governed by diffusion, which essentially means that the reaction is diffusion controlled and the intermediates can be approximated by steady state condition. This situation was first explored by Rehm and Weller in their pioneering work.18 They elucidated that to achieve the inversion we need to have a reactant pair with a very high exergonicity, which is practically impossible to find. Miller et al. first established one of the ways to achieve the inversion behavior.19 They used a steroidal spacer to incarcerate the donor and acceptor molecules and thus completely nullified the effect of diffusion. In this intramolecular approach, the spacer backbone was chosen in such a way that it does not 1611


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The Journal of Physical Chemistry B Scheme 2. Chemical Structure of Coumarin Dyes and Viologen Molecules Used in the Present Study

depends on the solvent reorganization energy and with retardation of solvent motion near the Stern-layer of a micelle or the water pool of a reverse micelle the steepness of the parabola increases. This is to imply that solvent reorganization becomes less effective and an inversion, as predicted by Marcus, can be achieved at a much lower reaction exergonicity compared to the bulk solvents.36 Thus, this approach became very popular among scientists, and we got a large number reports in the early part of this millennium depicting MIR in micelles, reverse micelles, cyclodextrins, etc.37−41 Soon this idea is extended to other media, such as ionic liquids.42−45 All of these reports used fluorescence quenching method, both steady state and time-resolved, to obtain the desired result. However, speculation rose about the observation of MIR in the manner described above.46 It was pointed out that all these reports made a fundamental mistake, which is considering quenching rate constant to be a time independent quantity. Vauthey and co-workers employed diffusional encounter theory to the systems under study and claimed that all these observations are spurious.46 In brief, fluorescence quenching rate can be considered in three different time regimes in any solvent, namely static, nonstationary, and stationary.46 The contribution of each of the quenching rate constants in various time domains to the overall quenching rate constant can be very different depending upon the solvent viscosity and the lifetime of the fluorophore. It was shown that if we can extract the information on individual rate constants from a steady state and time-resolved quenching data; then we can observe that the static rate constant is free from the effect of diffusion whereas the stationary rate constant is not. This is because, at very early stage of quenching, some reactant pairs are situated in the optimum distance (quenching sphere of action) for electron transfer to occur and thus does not need to undergo diffusion to form the encounter complex as depicted in Scheme 1. However, at longer times, the quenching process becomes diffusion controlled. Thus, depending on the extent of the lifetime of fluorophore used, the contribution from these 3 quenching rate constants vary considerably and in cases of short lifetime fluorophores, we see a significant contribution from static part making the quenching rate fast whereas in cases of fluorophores with longer lifetimes the stationary part prevails making the quenching rate slow. This way the examples of MIR observations mentioned earlier were discarded by commenting that they were merely the effect of viscosity and the intrinsic fluorescence lifetime.46

We found that both the ends of the debate have very strong arguments and it is important to resolve it experimentally. Earlier, we have indeed quantified the rate of bimolecular photoinduced electron transfer reaction in a low viscosity solvent like methanol by observing the rate of formation of a reaction intermediate, i.e., the ion pair.47 We demonstrated the application of femtosecond transient absorption spectroscopy in PET reaction by monitoring the formation of radical cation intermediate of methyl viologen produced upon electron transfer with pyrene and calculated the diffusion rate constant to an agreeable limit. In this report, we want to extend the idea further to solve the problem described above. In this article, we studied the electron transfer reaction between six different coumarin dyes and four viologen molecules (Scheme 2). Femtosecond transient absorption spectroscopic study was employed to observe the formation of radical cation intermediates of viologens and to calculate the actual rate of electron transfer as established in our previous study. The coumarin dyes have similarity in structure and have an average lifetime distribution from ∼0.5 ns to ∼6 ns. However, the major difference between our study and most of the previous studies is the fact that in our case coumarins act as electron donor whereas most of the previously mentioned studies employed coumarins as electron acceptors. This change gave us the opportunity to observe the short lifetime coumarins in the lower exergonic region and longer lifetime coumarins in the higher exergonic regions, unlike previous studies. Indeed, we observed a lowering of the rate in case of short lifetime coumarins and enhancement of the rate of longer lifetime coumarins, contrary to the claim of Vauthey and co-workers.46 Sodium dodecyl sulfate (Scheme 2) micelle was our choice of constrained media because of two reasons. First, dicationic viologen molecules at higher concentrations will be mostly present in the stern layer of the SDS micelle due to the Columbic attraction between the negatively charged head groups of the surfactants and the positively charged viologen molecules. Second, in the case of ionic micelles coumarin molecules are known to be present at the stern layer close to the headgroup of the surfactants.33,36 Thus, though we did not link the donor and acceptor, but somehow incarcerated them in a very specific region of a system. This situation allowed us to study the bimolecular PET reaction without the effect of diffusion. Indeed we observed a unique bell-shaped dependence of the rate of formation of radical cation intermediates with the reaction exergonicity, which is first of its kind. We also 1612


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The Journal of Physical Chemistry B

Figure 1. (a) UV−visible, (b) fluorescence spectra, (c) time-resolved data at 542 nm, and (d) Stern- Volmer plot of fluorescence quenching of C153 by MV2+.

resolved fluorescence intensity decays were collected using a commercial TCSPC setup (Life Spec II, Edinburgh Instruments, U.K.). All samples were excited at 375 nm, and the full width at half-maxima of the instrument response function is 120 ps. The fluorescence transients were analyzed by deconvoluting with the IRF and fitted with a sum of two exponentials for the present study. NMR spectra in deuterated DMSO solvent were recorded on a 400 MHz NMR spectrometer (JEOL, Japan). The details of our femtosecond transient absorption spectroscopy setup (Femto-Frame-II, IB Photonics, Bulgaria) have been discussed in details before48 and only a brief overview is presented here. The fundamental 800 nm light was obtained from a Ti-Sapphire regenerative amplifier (SpitfirePro XP, Spectra-Physics, USA) pumped by a 20-W Q-switched Nd:YLF laser (Empower, Spectra-Physics, USA) and seeded by a Ti-Sapphire femtosecond oscillator (MaiTai SP, SpectraPhysics, USA). The fundamental light thus obtained was divided into two parts. One part was passed through a β-barium borate crystal to generate 400 nm second harmonic light, which was used as pump light. Another part of the beam was passed through a delay stage, having a maximum delay time of 2 ns, and was focused on a sapphire crystal to generate the white light continuum which was used as the probe light having a wavelength spread of 460−750 nm. After passing through the sample, the probe light was dispersed in polychromator and detected using CCD. For all experiments, the power of the

correlated this data with the ultrafast decay component of fluorescence decay of coumarins and showed that the same dependence could be observed but with a slight change in rate constants in some cases. Moreover, we have elucidated the inefficiency of time-resolved Stern−Volmer type experiments in observing the MIR. Therefore, our study is a unique one to take care of all the possible scenarios and yet to prove that MIR does exist and can be observed experimentally.

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EXPERIMENTAL SECTION Materials. Laser grade coumarin dyes were purchased from Exciton and used as received. Methyl viologen dichloride dehydrate (MV2+), benzyl viologen dichloride (BzV2+), and sodium dodecyl sulfate were obtained from Sigma-Aldrich and used as received. 1,1′-Bis(cyanomethyl)-4,4′-bipyridine-1,1′diium bromide (CNMV2+) and 1,1′-dimethyl-2,2′-bipyridine1,1′-diium iodide (DM2+) were synthesized following literature procedure and characterized using NMR spectroscopy.26 The detailed procedure of synthesis and characterization are given in the Supporting Information. Spectroscopic grade acetonitrile was purchased from Fisher Scientific and used for the cyclic voltammetric measurement. Double distilled water was used throughout the study. Methods. All the UV−visible spectra were recorded in a commercial spectrophotometer (UV-2450, Shimadzu, Japan) and all the fluorescence spectra were recorded in a commercial spectrofluorimeter (Fluoromax-4, Jobin-Yvon, USA). Time1613


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The Journal of Physical Chemistry B pump light was kept ∼10 μW. The pulse width of the fundamental light was 80 fs, and the instrument response function was 110 fs. The fluorescent transients in the subpicosecond to the nanosecond time regime were measured using a commercial femtosecond fluorescence up-conversion setup (FOG-100, CDP Corp., Russia). The excitation light of 400 nm was generated in a 0.2 mm β-barium borate (BBO) crystal using the fundamental light 800 of nm a mode-locked Ti-Sapphire laser (Mai Tai HP, Spectra Physics, USA). The fluorescence emitted from the sample was obtained under the magic angle configuration and was up-converted in another 0.2 mm BBO nonlinear crystal by using the fundamental beam as a gate pulse. The up-converted light is dispersed in a monochromator and detected by a photomultiplier tube. The femtosecond fluorescence decays were deconvoluted using a Gaussian shape for the instrument response function having an fwhm of 250 fs using commercial software (IGOR Pro, WaveMetrics, USA). The pump power used in the measurement was ∼4 mW. Cyclic voltammetry experiments were performed using BAS Epsilon electrochemical workstation. A standard threeelectrode cell was selected with a BAS MF 2012 glassy carbon electrode as working electrode, a platinum wire as an auxiliary electrode and Ag/AgCl electrode as a reference electrode. The details of the cell configuration are previously reported.49 No correction was made for liquid junction potential. Potentials were measured at 298 K. To reduce the uncompensated solution resistance in the cell configuration the reference electrode tip was placed close to the working electrode. All the potentials are here reported vs SCE by converting the values obtained vs Ag/AgCl using a factor of −0.045 V. To calculate the radius of the coumarin and viologen molecules, their structure was optimized using Gaussian 09 software.50 Becke 3-parameter Lee−Yang−Parr functional (B3LYP) and 6-311G++(d,p) basis set was used for optimization. The radius is estimated by calculating the volume of the molecule. For all the measurements the concentration of SDS was kept at 40 mM unless pointed otherwise. The CV of coumarin molecules was measured in an acetonitrile solution containing 1.0 mM compound and 0.1 M in tetra-n-butylammonium hexafluorophosphate (TBAPF6) as supporting electrolyte. The CV of viologens was measured using 1.0 mM compound in a 70 mM SDS solution containing 50 mM NaCl as supporting electrolyte to compare with the reported value.51 The concentrations of the coumarins were adjusted in such a way that the absorption at the excitation wavelength was ∼0.1 to ∼0.2 thus keeping the coumarin concentrations close to ∼50− 80 μM.

Volmer equation (eq 8 and 9) we expect a linear relationship I between 0 and [Q]. Ii

I0 = 1 + KSV[Q ] Ii

(8)

τ0 = 1 + kqτ0[Q ] τi

(9)

However, as can be seen from Figure 1d, the plot of

I0 Ii

vs [Q]

completely deviates from linearity even at the lower concentration of quencher. This corresponds to the fact that in our case the quenching is of mixed type, i.e., both dynamic and static quenching is happening at the same time even at a very low quencher concentration. This situation may arise when the two reactants are situated in a close proximity of one another with a less contribution of diffusion. In our case, the coumarins and viologens are not connected by any chemical bond, but MV2+ is present in the Stern layer of the micelle due to the Coulombic attraction with SDS headgroups, and C153 is distributed in the micelle. Thus, we see the involvement of static quenching in the overall quenching process at a quencher concentration of ∼1 mM and higher. Nonetheless, in this scenario, we can extract the dynamic information by using timeresolved fluorescence studies at a low to moderate quencher concentration, and, the same has been done for C153 and MV2+ (Figure 1c,d). All the fluorescence transients were fitted with a sum of two exponential functions and the average lifetime was used to get the Stern Volmer plot. In case of C153/MV2+ in SDS micelle the value of the quenching rate constant (kq) was found to be 6.00 × 1010 M−1 s−1. The striking feature of Stern−Volmer quenching constant is being more than the diffusion rate constant may contributed from some long-range interaction and excitation transfer mechanism.55 We have performed the same Stern−Volmer experiment with all the 6 coumarin and 4 viologen molecules. In each case, we I observed that the 0 vs [Q] plot deviates from linearity over 1 Ii

mM quencher concentration. Thus, we confirmed that both static and dynamic quenching is operational in all cases. The full set of measured kq values are listed in Table 1. As argued in the Introduction Section and as it is clear from the Stern−Volmer plot that at lower quencher concentration dynamic quenching has a major role to play, thus the kq obtained is very close to diffusional rate constant. Therefore, it is very important to quantify ket. We have argued in our Table 1. Quenching Rate Constants Obtained from the Stern−Volmer Analysis

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RESULTS To obtain the rate of photoinduced electron transfer reaction between each of the pair we have chiefly employed transient absorption spectroscopy. In the purview of the studies mentioned in the Introduction Section, we also correlated the same with fluorescence up-conversion and Stern−Volmer type quenching experiments. To give a basic idea of our study, the detailed experimental results of PET reaction between C153 and MV2+ are discussed below. In Figure 1a,b we have represented the steady-state fluorescence quenching experiments of C153 by MV2+ in 40 mM SDS solution. The same has been performed with timecorrelated single photon counting method. Following Stern− 1614

reactant pair

kq (M−1s−1)/ 1010

reactant pair

kq (M−1s−1)/ 1010

C480 + MV2+ C466 + MV2+ C460 + MV2+ C153 + MV2+ C152 + MV2+ C152A + MV2+ C480 + CNMV2+ C466 + CNMV2+ C460 + CNMV2+ C153 + CNMV2+ C152 + CNMV2+

6.00 11.29 8.60 6.00 10.10 15.17 4.77 10.00 8.73 9.15 13.26

C152A + CNMV2+ C480 + DM2+ C466 + DM2+ C460 + DM2+ C153 + DM2+ C152 + DM2+ C480 + BzV2+ C466 + BzV2+ C460 + BzV2+ C152 + BzV2+ C152A + BzV2+

16.06 4.83 10.25 8.25 4.49 6.90 3.50 9.30 11.21 10.60 13.58


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Figure 2. Plot of (a) transient absorption spectra at different times, (b) kinetic traces at different wavelengths, and (c) comparison of kinetic traces for quenching of C153 by MV2+ in 40 mM SDS.

previous publication that following the formation radical ion intermediate we can measure ket and in this study also we have used the same technique.47 Moreover, in two recent publication depicting MIR, transient absorption spectroscopy has been employed in the same manner to track the formation and charge recombination of the radical ion intermediates.26,27 MV2+ is a well-known quencher and forms a radical cation MV+• accepting an electron from a donor and the species MV+. is known for its characteristic absorption band in the visible region. Kaifer and Bard already studied the reduction of MV2+ in SDS micelle and they showed that the absorption spectra of MV+• (first reduction of MV2+) has a peak around 620 nm.51 Thus, it is expected that in the wavelength span of the probe light of our transient absorption spectroscopy setup we should be able to see the signature of MV+• formed upon electron transfer from coumarin dyes. As a matter of fact, the radical cation formed from all these viologens have a peak around 600 to 620 nm and can be tracked using a visible probe light.26,51 Using coumarins as electron donor also have some additional advantages. All the coumarins have a broad absorption band near 400 nm (see Figure S1a of the Supporting Information), which is gave us the opportunity to use 400 nm as the pump. Moreover, at this wavelength, the viologens do not have any significant absorption (see Figure S1b of the Supporting Information) even at a very high concentration, which ensured that the transient absorption data would be free from the excited state dynamics of the viologens. SDS too does not have

any absorption at 400 nm and thus the possibility of the surfactant being the excited state electron donor can be ruled out. Porel et al. have studied the electron transfer between C153 and MV2+ in 30% acetonitrile water mixture using femtosecond transient absorption and could not obtain any absorbance due to MV+•.52 According to them, in such cases, the reaction is completely diffusion controlled and MV+• fails to accumulate in sufficient amount to be observed in transient absorption setup. Thus, in our case, if some coumarin is distributed outside the micelles in the bulk water phase, we should not observe any contribution from the PET in the bulk phase as in that phase the accumulation of MV+• will be very less. In Figure 2a we have represented the transient absorption spectra at different times obtained by exciting a mixture of C153 and 10 mM MV2+ in 40 mM SDS solution. From 500 to 550 nm region we can observe the stimulated emission (SE) band of C153 but in 580 to 700 nm region we can observe the peak of MV+•, which gradually grows with time then diminishes at longer times. This absorption band of MV+• does not have any special feature around 580 nm, and thus we exclude the possibility of dimerization of MV+•, which is expected given the time window of our observation at which PET cannot yield any intermediate with high enough concentration to form the dimer at a the subpicosecond time-scale.53 We have taken the kinetic data at a wavelength interval where the formation and decomposition of MV+• can be clearly observed and free 1615


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The Journal of Physical Chemistry B from the SE band of the coumarin, i.e., 580 to 680 nm and fitted the kinetics at all the wavelengths using a global fitting with a sum of four exponential functions. This analysis ensures that all the changes happening at a stretch of wavelengths are taken care at the same time. Few representative kinetic data are plotted in Figure 2b to show the excellence of our fitting procedure. The global fitting time constants thus obtained for PET between C153 and MV2+ are 0.46, 4.3, 95.75, and 139 ps of which the first one is the rise component and thus assigned to forward electron transfer. The second time component of 4.3 ps signifies the charge recombination rate between the ion pair formed by the forward electron transfer. Along with this process, the reactants come back to the ground state, and we have previously demonstrated that it is independent of quencher concentration.47 Therefore, we have assigned this decay component to the time constant of the back electron transfer process. The rest of the time components belong to the excited state dynamics of C153. The inverse of the forward and backward time components are 2.326 × 1012 s−1 and 2.33 × 1011 s−1 and designated as ket and kbet, respectively. It is clear that the forward rate constant is much faster than diffusional rate constant. In Figure 2c a comparison between the observed dynamics at 620 nm of the three systems, i.e., C153 with no added electron acceptor, MV2+ with no added electron donor, and C153 with MV2+, has been represented, where a clear evidence of rise and decay of MV+• can be observed. To ensure that there is no initial quencher concentration dependence of the rise time of MV+•, we have also performed a MV2+ concentration dependent (10, 15, and 20 mM) transient absorption spectroscopic study and the time trace at 620 nm is depicted in Figure 2d. The rise time components obtained from the global fitting are 0.46, 0.44, and 0.43 ps for 10, 15, and 20 mM MV2+, respectively. This experiment preserves the fact that we are indeed watching the first order electrons transfer step as depicted in Scheme 1 and this time constants are not concentration dependent. Perhaps another interesting observation is the fact that the rising part starts immediately after the pulse or the instrument response function. This signifies that the formation of MV+• started almost immediately after the excitation and there was no lag period before it. In our previous paper, we reported a time lag before the start of the MV+• signal due to the approach of the two reactants before electron transfer.47 In the present case, the immediate formation of the MV+• signifies that both the donor (C153) and the acceptor (MV2+) are present nearby the Stern layer of the micelle. A similar feature has been observed in the transient absorption kinetics of all other donor−acceptor pairs and all the four time constants obtained from global analysis of the data, in the same manner, is reported in Table 2. At least a wavelength range of 80−100 nm around the absorption maxima of the radical cation has been used to fit the data in each case. The concentration of MV2+ and CNMV2+ is kept at 10 mM in each case while the concentration of DM2+ was 20 mM as at any lower concentration of DM2+ we were unable to achieve any clear signal. Experiments with BzV2+ had to be performed at a maximum of 8 mM as we found that it is close to the saturation of BzV2+ in SDS solution. The time constant of forward electron transfer obtained from the global fitting of the transient absorption data for all the 22 reaction pairs varies from 0.3 to 1.16 ps. Here one clarification needs to be given about the longest lifetime component of the fitting. As one can observe in some donor−acceptor pairs we got a shorter value of τ4 but in some cases we got a much longer value, which

Table 2. Time Constants Obtained from Global Fitting of Transient Absorption Data reactant pair

τ1 (ps) (rise)

τ2 (ps) (decay)

τ3 (ps) (decay)

τ4 (ps) (decay)

C480 + MV2+ C466 + MV2+ C460 + MV2+ C153 + MV2+ C152 + MV2+ C152A + MV2+ C480 + CNMV2+ C466 + CNMV2+ C460 + CNMV2+ C153 + CNMV2+ C152 + CNMV2+ C152A + CNMV2+ C480 + DM2+ C466 + DM2+ C460 + DM2+ C153 + DM2+ C152 + DM2+ C480 + BzV2+ C466 + BzV2+ C460 + BzV2+ C152 + BzV2+ C152A + BzV2+

0.34 0.30 0.42 0.46 0.50 0.68 1.04 0.58 0.40 0.32 0.34 0.30 0.32 0.38 0.50 0.68 1.16 0.38 0.32 0.30 0.56 0.58

1.16 2.96 3.00 4.30 3.10 4.50 4.54 0.80 1.26 1.58 2.24 1.26 3.00 3.14 2.76 1.34 1.22 1.80 3.34 2.96 0.88 16.02

19.40 80.75 39.00 95.75 10.20 18.05 38.20 10.20 25.40 23.00 15.50 5.85 33.65 31.15 23.60 17.85 21.00 45.8 33.76 19.80 7.18 78.40

1800 (fixed) 1000 (fixed) 1000 (fixed) 139 367 303 1800 (fixed) 842 1000 (fixed) 1800 (fixed) 800 333 716 1000 (fixed) 620 1800 (fixed) 220 1500 1000 (fixed) 1000 (fixed) 243 900

is even greater than the normal fluorescence lifetime of the dye (see table S1 of the Supporting Information) following which we have to fix a certain value to obtain the fitting. The origin of the unusually long lifetime component can be explained in the following way. At this high quencher concentration, a large number of dicationic viologens are bound to SDS through Columbic force with a certain binding constant. Upon accepting an electron, they are converted to a monocationic form having lower binding constant than the dicationic form due to less charge. Thus, there is a possibility of some displacement of these monocations at the micellar interface following the change in the binding constant. For such events the back electron transfer process is not favorable and contributes to the residual signal in our observation. As discussed until now, using transient absorption technique we can isolate and quantify ket and clearly with change in the reactant pair, we obtained a variation in ket. However, most of the previous studies employed time-resolved fluorescence technique to obtain the same data.36−41 As shown in Table 1, time-resolved Stern−Volmer experiments yield nothing but the diffusional rate and later it will be shown that kq basically is incorrect in this kind of studies, we had to turn our eyes toward femtosecond fluorescence up-conversion because of the following argument. When the fluorophore is excited in the presence of quencher, it always has some quencher molecules within its vicinity or within the quenching sphere of action.46 Thus, some of the fluorophore decays back to the ground state in a very short time within which the reaction does not become diffusion controlled. Later solvation and diffusion takes over and controls the excited state deactivation process and thus we observe a slow kq. However, there must exist a very short decay profile, which should be equal to ket, and can be extracted using fluorescence up-conversion technique.44 Since our systems showed an appreciable amount of static quenching at high quencher concentration, it was expected that the said analogy 1616


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The Journal of Physical Chemistry B shall also apply in our system. Therefore, we have studied the same systems using fluorescence up-conversion technique and measured the decay profiles at the wavelength maxima of the coumarin dyes. Figure 3 shows the same for the C153 MV2+

Table 3. Time Constants Obtained from Fitting of Fluorescence Up-Conversion Data

Figure 3. Plot of fluorescence transients at 542 nm for C153 and C153 + MV2+ in 40 mM SDS.

system measured at 542.5 nm which is the emission maxima for C153 in SDS. The data was fitted with a sum of four exponential functions and the time constants obtained were 0.56, 8.50, 112.0, and 644 ps. The first time component is faster than the fastest solvation time in SDS micelle which is 1.48 ps and very much comparable to the same obtained by transient absorption studies.34 This signifies that we can assign this component to ket. In Figure 3 we have also showed the kinetics of C153 without the addition of quencher, which prominently shows a long growth part due to solvation. The same experiment has been performed with other reactant pairs at their accumulating to the decay at the emission maxima of each of the coumarin (see Table S1 of the Supporting Information) and the fastest time component obtained is reported in Table 3. Except for a few cases the time constants match well enough with the same obtained through transient absorption. To calculate the ΔG0 value for each pair of donor and acceptor, Rehm−Weller equation has been used which is given in eq 10 with a slight modification. ΔG° = E D/D+ − E A2+ /A+ − E0,0 +

e2 εsr0

reactant pair

τ1 (ps)

τ2 (ps)

τ3 (ps)

τ4 (ps)


0.38 0.32 0.36 0.56 0.92 1.20 0.61 0.48 0.38 0.34 0.37 0.40 0.40 0.48 0.54 1.40 1.40 0.36 0.32 0.36 0.80 1.32

11.90 12.15 6.50 8.50 7.60 5.60 7.50 10.70 5.05 8.75 4.30 6.90 4.20 4.20 6.45 12.70 34.70 13.70 8.92 2.60 12.95 8.70

100.4 145.0 38.4 112.0 205.5 70.4 58.0 49.5 55.0 100.0 66.1 87.2 36.3 34.3 84.4 77.5 184.0 113.3 69.5 37.2 50.4 91.0

425.0 495.0 250.0 644.0 722.4 441.1 578.0 205.2 577.7 986.0 760.9 820.0 217.7 246.9 443.4 334.4 503.5 807.3 495.0 451.4 442.2 515.3

tron transfer reactions. E1/2 values were measured by the differential pulse voltammetry. A shift factor of +0.16 V has been used for SDS from acetonitrile based on previous literature.56 The cyclic voltammetry of MV2+, CNMV2+, BzV2+, and DM2+ in 40 mM SDS solution (see Figure 4 and Figure S3 of

(10)

The Columbic term in our case has to be taken as a positive term and not as a negative term because in the ion-pair formed upon electron transfer both the molecules has a positive charge. Thus, instead of an attractive potential term, we used a repulsive potential term. The oxidation potentials of four coumarins used in this study, which are C480, C153, C460, and C152A, are already reported previously in acetonitrile solvent.54 Rest of the oxidation and reduction potentials were needed to be measured and to do that cyclic voltammetry experiments were carried out on C152, C466, and all the four viologens. The cyclic voltammetry of C152 and C466 in acetonitrile (see Figure S2 of the Supporting Information) show one electron oxidation process at E1/2 values 1.14 V (peak to peak separation, ΔEp = 240 mV) and 0.915 V (peak to peak separation, ΔEp = 170 mV) vs SCE, respectively. The oxidations for both coumarins are chemically irreversible (ratio of cathodic and anodic peak current ipc/ipa ≈ 0.6 and 0.2, respectively) and electrochemically quasi-reversible elec-

Figure 4. Cyclic voltammetry of MV2+ in 40 mM SDS with 50 mM NaCl as supporting electrolyte.

the Supporting Information) shows two reductions, however except MV2+ only first reduction potentials are reported here as required. The E1/2 values for the first one electron reduction of MV2+, CNMV2+, BzV2+, and DM2+ are at −0.65 V (peak to peak separation, ΔEp = 65 mV), −0.26 V (peak to peak separation, ΔEp = 60 mV), −0.57 V (peak to peak separation, ΔEp = 30 mV), and −0.79 V (peak to peak separation, ΔEp = 80 mV) vs SCE, respectively, whereas for MV2+ E1/2 value for second one-electron reduction potential is at −1.12 V (peak to peak separation, ΔEp = 90 mV) vs SCE. The reduction potentials of MV2+ are comparable to the previously reported values.51 The first reductions for MV2+ and BzV2+ are both 1617


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The Journal of Physical Chemistry B Table 4. Electron Transfer Parameters for Different Coumarin and Viologen Pairs

a

reactant pair

ED/D+ (V vs SCE) in acetonitrile

ED/D+ (V vs SCE) in SDS micelle

EA2+/A+ (V vs SCE) in SDS micelle

E0,0 (eV)

e2/εsr0 (eV)

ΔG0 (eV)

a kTA rise (s−1)/1012

a kUC fast (s−1)/1012


0.72b 0.92 1.09b 0.89b 1.14 1.2b 0.72 0.92 1.09 0.89 1.14 1.2 0.72 0.92 1.09 0.89 1.14 0.72 0.92 1.09 1.14 1.2

0.88 1.08 1.25 1.05 1.3 1.36 0.88 1.08 1.25 1.05 1.3 1.36 0.88 1.08 1.25 1.05 1.3 0.88 1.08 1.25 1.3 1.36

−0.65 −0.65 −0.65 −0.65 −0.65 −0.65 −0.26 −0.26 −0.26 −0.26 −0.26 −0.26 −0.79 −0.79 −0.79 −0.79 −0.79 −0.57 −0.57 −0.57 −0.57 −0.57

2.8182 2.8972 2.9384 2.5051 2.6496 2.6552 2.8182 2.8972 2.9384 2.5051 2.6496 2.6552 2.8182 2.8972 2.9384 2.5051 2.6496 2.8182 2.8972 2.9384 2.6496 2.6552

0.04674 0.0479 0.0465 0.0461 0.0468 0.0466 0.0462 0.0473 0.0460 0.0456 0.0463 0.0461 0.0453 0.0464 0.0451 0.0447 0.0454 0.0409 0.04179 0.0407 0.0410 0.0408

−1.24 −1.12 −0.99 −0.76 −0.65 −0.60 −1.63 −1.51 −1.38 −1.15 −1.04 −0.99 −1.10 −0.98 −0.85 −0.62 −0.51 −1.33 −1.21 −1.08 −0.74 −0.68

2.941 3.333 2.381 2.174 2.000 1.470 0.962 1.724 2.500 3.125 2.933 3.333 3.125 2.632 2.000 1.471 0.862 2.632 3.125 3.333 1.786 1.724

2.632 3.125 2.778 1.786 1.087 0.833 1.627 2.083 2.632 2.941 2.673 2.500 2.500 2.083 1.852 0.714 0.714 2.857 3.226 2.778 1.250 0.758

TA and UC designate the transient absorption and upconversion studies, respectively. bData taken from ref 54.

chemically reversible (ratio of cathodic and anodic peak current ipc/ipa ≈ 0.9 for both) and the same for CNMV2+ and DM2+ are chemically irreversible whereas all the reductions are electrochemically reversible electron transfer reactions. The E0,0 term has been calculated from the overlap of normalized absorption and emission spectra of coumarin. The last term which is columbic term is calculated taking a value of static dielectric constant of the SDS medium as 32.38 The separation between donor and acceptor is taken as a sum of their radii estimated from the optimized structure. All of the parameters thus required to calculate ΔG0 and the same obtained for different pairs have been summarized in Table 4 along with the rate constant of formation of radical cation intermediate from transient absorption studies and the fast decay component from the fluorescence up-conversion studies. To give an idea of how the rate of electron transfer is changing with changes in ΔG0, we have plotted the kinetics at 620 nm obtained from transient absorption data for three representative pairs in Figure 5. For the same pair the upconversion transients are plotted in Figure 6 along with the I Stern−Volmer plots for them in Figure 7. The plots of 0 vs [Q]

Figure 5. Comparison of transient absorption kinetics for different donor−acceptor pairs at 620 nm.

predicted in Marcus theory. We fitted the same with a function similar to eq 6. The point of inversion obtained at −1.10 eV where ΔG0 is equal to reorganization energy. This observation is at par with previous studies done in micellar environment confirming the existence of MIR in present case.36−40 The inverted region is designated by at least 7 points unlike previous studies, where a maximum of 1−2 points were achieved in this region. This is of course not within the error bar in our case (∼10%). Considering that the change in nuclear reorganization energy is negligible for each pair as the structure of the coumarins used are very similar to each other as well as the viologens, we can claim that this is the definitive proof of existence of MIR in case of bimolecular PET in micelle. This is the first time such evidence has been obtained for donor− acceptor pairs which are not linked by any chemical bond. When we have plotted the fast decay components obtained

Ii

for the three pairs are also given in Figure S4 to show that the deviation from linearity arose early in all cases. Hence, static quenching mechanism is expected to be operational for all the coumarin-viologen pairs and at the concentration where femtosecond experiments were performed it was safe to assume that maximum contribution arose from the static quenching mechanism. The three pairs were chosen to represent three widely different values of ΔG0 and it is clear from the plots that at an intermediate value of ΔG0 the fastest rate of electron transfer is observed. Both increasing and decreasing in ΔG0 leads to decrease in ket. Thus, we have plotted the measured ket along with the kq values for all the pairs as a function of ΔG0 in Figure 8. The variation of ket with ΔG0 clearly shows a bell-shaped dependence, which was 1618


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Figure 9. Plot of kfast vs ΔG0 for different donor−acceptor pairs obtained from fluorescence up-conversion studies.

Figure 6. Comparison of fluorescence up-conversion kinetic traces for different donor−acceptor pairs at emission maxima of the donor.

the exact estimation of the rate constants can only be acquired from transient absorption studies.

■

DISCUSSION This study revealed the existence of MIR in a unique way. The rate of electron transfer estimated from measuring the rate constant of the formation of intermediate radical cation clearly gave evidence in support of it along with fluorescence upconversion studies. However, keeping in mind the arguments presented in the Introduction Section, favoring or disfavoring of the existence of MIR in constrained media, such as micelles, few more points need to be discussed here. First of all, we agree with Vauthey and co-workers regarding the impossibility of observing MIR through dynamic Stern− Volmer experiment.46 All the measured kq values plotted in Figure 8 have no specific trend, which Vauthey and co-workers worked out using differential encounter theory. We present a plot of inverse of natural lifetime of the coumarin dyes in SDS micelle with ΔG0 (Figure S5 of the Supporting Information) and compare the trend with the same kq vs ΔG0 plot. One can easily see that the dynamic part of the quenching (low quencher concentration region) follows the same trend as the lifetime of the coumarin dyes. The longer lifetime coumarins, i.e., C480 and C153, have the slowest kq values and shorter lifetime coumarins like C152A and C152 have the faster kq values. This happens because of the diffusion controlled nature of quenching. This probably is the cleanest evidence achieved until date of the nonobservation of MIR without applying any special treatment to the quenching data, which Vauthey and coworkers tried to establish so far using differential encounter theory.46 But when we inspect the transient absorption data and the fluorescence up-conversion data we see that this lifetime trend is completely destroyed. For example, though C152A and C152 have the shortest lifetimes, ket for PET between C152A and DM2+, C152 and DM2+, C152A and MV2+, C152 and MV2+, etc. are slow compared to others. The same is valid for pairs like C153 and CNMV2+, and C480 and MV2+, where the lifetime of the coumarin dyes are long but they show fast electron transfer as they are positioned close to the inversion point of the parabola. This shows the importance of our study and the techniques employed here. This also signifies that MIR does exist and can be observed in micellar environment contrary to the claim of Vauthey and co-workers. The effect from change in concentration of the quencher can also be neglected as all the quenchings have appreciable

Figure 7. Stern−Volmer plot for different donor−acceptor pairs at emission maxima of the donor.

Figure 8. Plot of ket vs ΔG0 for different donor−acceptor pairs obtained from transient absorption spectroscopy along with kq vs ΔG0 for the same.

from fluorescence up-conversion studies vs ΔG0 we also observed a similar bell shaped dependence as depicted in Figure 9. Upon fitting the dependence a similar point of inversion has been observed considering the error associated with the measurements. Hence we think that the ultrafast component of the fluorescence quenching can be used to obtain MIR but 1619



■

amount of static component. The only thing remains though is the effect of solvation in our study. The ultrafast solvation time estimated in SDS micelle is 1.48 ps as reported previously.34 While doing transient absorption studies we did not agonize about solvation because of the following reasons. First of all the spectra of radical cations are observed at the red side of the emission band of the coumarins and the time constants obtained are also much faster than solvation time. Moreover, the quencher concentration used in the study ensured a more or less complete quenching of the emission band thus making the rise part of kinetic traces free from SE. In up-conversion studies, we also have observed faster electron transfer than solvation in most of the cases. However, in some reactant pairs, where the electron transfer is considerably slower, solvation does affect the kinetic traces as they are taken in the emission maxima of the fluorophore. Therefore, we observed a mismatch between ket acquired from transient absorption and upconversion studies for such pairs with slower electron transfer rate. Though we have concluded mainly from the ion-pair formation process but it is a popular idea to follow the charge recombination process as well.27 However, when the electron transfer process occurs from the excited state there are two limitations. First is the estimation of ΔG0 in the excited state is difficult and can only be estimated roughly from the Rehm− Weller equation. Second is the entropy factor has to be taken care. The back electron transfer originates from the ion-pair formed in the excited state, where the donor and acceptor are present in some kind of a molecular ensemble. This differentiates the back electron transfer from the forward electron transfer. We are sure that if these factors are taken care of properly, from our charge recombination data one can obtain the MIR for back electron transfer process as well, which is beyond the scope of this report. Maybe in a further report we will elucidate on this analysis.

Article

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b11206. Synthesis procedure of two viologen molecules; lifetime of coumarin dyes in SDS in the absence of quencher; absorption spectra of coumarins and viologens; cyclic voltammetry of C152, C466, CNMV2+, DM2+, and BzV2+; Stern−Volmer plot for different donor−acceptor pairs at emission maxima of the donor and plot of intrinsic lifetime of different coumarins (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Pratik Sen: 0000-0002-8202-1854 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS P.M. and A.S. thank University Grants Commission, India, and A.D. thanks Ministry of Electronics and Information Technology, Government of India for awarding fellowships. We thank Prof. R. N. Mukherjee and Prof. J. K. Bera for the CV measurements. This work is financially supported by SERB, Government of India, and IIT Kanpur.

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REFERENCES

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CONCLUSION Marcus inverted region for bimolecular photoinduced electron transfer reaction between coumarin and viologens has been successfully demonstrated in SDS micelle following the formation of radical cation intermediate of viologens and the ultrafast decay of coumarin fluorescence. In our study, we studied the process in completely static quenching regime and therefore both the forward electron transfer rates obtained from femtosecond transient absorption measurements and fluorescence up-conversion measurements correlated to a bell-shaped dependence of ket with ΔG0. We have also demonstrated the inadequacy of dynamic Stern−Volmer measurements to predict Marcus inverted region in the same medium. Indeed we have assumed that because of similarities in structure of the coumarins and the same for viologens, electronic coupling and nuclear reorganization energy do not vary. We have not discussed the charge recombination process, the rate of which we obtained from our studies. But we are sure that a complete analysis taking into account the excited state oxidation reduction potential, the change in reaction entropy in the excited state, etc. will also correlate the charge recombination rates to MIR. This article successfully demonstrates the usability of broadband transient absorption measurements to study PET reactions and in the future can be used to study MIR in low viscous solvents and other medium. 1620


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