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Article pubs.acs.org/JPCB

Photoinduced Bimolecular Electron Transfer from Cyano Anions in Ionic Liquids Boning Wu,† Min Liang,† Mark Maroncelli,*,‡ and Edward W. Castner, Jr.*,† †

Department of Chemistry and Chemical Biology, Rutgers, The State University of New Jersey, 610 Taylor Road, Piscataway, New Jersey 08854, United States ‡ Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States S Supporting Information *

ABSTRACT: Ionic liquids with electron-donating anions are used to investigate rates and mechanisms of photoinduced bimolecular electron transfer to the photoexcited acceptor 9,10-dicyanoanthracene (9,10-DCNA). The set of five cyano anion ILs studied comprises the 1-ethyl-3-methylimidazolium cation paired with each of these five anions: selenocyanate, thiocyanate, dicyanamide, tricyanomethanide, and tetracyanoborate. Measurements with these anions dilute in acetonitrile and 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide show that the selenocyanate and tricyanomethanide anions are strong quenchers of the 9,10-DCNA fluorescence, thiocyanate is a moderately strong quencher, dicyanamide is a weak quencher, and no quenching is observed for tetracyanoborate. Quenching rates are obtained from both time-resolved fluorescence transients and time-integrated spectra. Application of a Smoluchowski diffusion-and-reaction model showed that the complex kinetics observed can be fit using only two adjustable parameters, D and V0, where D is the relative diffusion coefficient between donor and acceptor and V0 is the value of the electronic coupling at donor−acceptor contact.

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INTRODUCTION

arises because the viscosities are typically 1−3 orders of magnitude larger than for typical neutral solvents.8 Bimolecular electron-transfer rates in ILs are not well described by simple rate theories.6,17−19 In particular, the rates are frequently observed to be much faster that those predicted based on measured temperatures and shear viscosities using the Smoluchowski equation. In part, this discrepancy results because diffusion in ILs is not well described by hydrodynamic theories.20−22 Even more important is the fact that slow diffusion in ILs requires a proper analysis of the nonstationary regime of bimolecular reactions that is typically ignored in simple analyses, because it is usually sufficient in conventional solvents.23,24 To investigate these interesting dynamics further, we expand upon the work begun by Vieira and Falvey18 and by Liang et al.23 Both groups studied the bimolecular photoinduced electron-transfer reaction between the neutral N,N-dimethylaniline (DMA) donor and 9,10-dicyanoanthracene (9,10DCNA) photoacceptor. An example of this photoreaction is shown in Figure 1. The electronic vacancy created by photoexcitation of 9,10-DCNA (A*) is filled by an electron from the donor D, which in this example is tricyanomethanide.

Interest in the use of ionic liquids (ILs) for energy-related applications continues to grow because these intrinsic electrolytes often have valuable properties, which include low vapor pressures, moderate thermal stabilities, and broad windows of electrochemical stability. Many classes of ILs are liquid at ambient temperatures, and an even larger set are liquid below 100 °C. Applications of these ILs include their use as electrolytes in batteries, fuel cells, and solar photoelectrochemical cells.1,2 The largest body of work on electron transfer in ILs derives from thermal electrochemical reactions, which have been widely reviewed.1,3−7 A significant number of reports on photoinduced electron transfer in ILs have appeared which are also reviewed, including both intramolecular charge shift reactions and bimolecular reactions.6 This body of work shows that ILs behave rather differently than typical neutral solvents, beginning with the broadly distributed relaxation kinetics that are observed in solvation dynamics.8 Fluorescence dynamics in ILs using red-edge excitation are known to sample different parts of photoreactant energy distributions, leading to significant rate heterogeneity.9−14 Time-resolved fluorescence measurements of rates on picosecond time scales demonstrate significant heterogeneities in rates of intramolecular charge shifts.15,16 Much of the heterogeneity in IL solvation dynamics © 2015 American Chemical Society

Received: September 21, 2015 Revised: October 26, 2015 Published: October 26, 2015 14790

DOI: 10.1021/acs.jpcb.5b09216 J. Phys. Chem. B 2015, 119, 14790−14799

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The Journal of Physical Chemistry B

NTf2− has a broad window of electrochemical stability over which neither the anions or cations of the IL are oxidized or reduced. Second, the short ethyl substituent on Im2,1+ is known to avoid the complexities of nanophase segregation that are widely observed for ILs with alkyl substituents of length n = 5 or longer.36−38 Liang et al. used a diffusion−reaction model to analyze the electron-transfer kinetics between DMA and 9,10-DCNA.23 Based on the approach of Dudko and Szabo, this diffusion− reaction model combines an approximate solution of a Smoluchowski type spherical diffusion equation with the semiclassical Marcus electron-transfer rate equation.39,40 In the present work, we use this method to model the reductive quenching of 9,10-DCNA by a series of cyano-containing anionic donors in both IL and CH3CN solvents. We also modify the approach used by Liang et al. in order to include both adiabatic and nonadiabatic regimes of electron transfer.41−43

Figure 1. Schematic for the mechanism of electron transfer between cyano anion donor tricyanomethanide and the 9,10-DCNA acceptor. The molecular orbitals (MOs) shown are the acceptor HOMO (lower left), the acceptor LUMO (upper left), and the donor HOMO (right).

Liang et al. studied the bimolecular reaction between the DMA donor and photoexcited 9,10-DCNA acceptor in a variety of different ILs.23 Here we present work on electron transfer from a series of anionic electron donors to photoexcited 9,10-DCNA in a single ionic liquid solvent, 1-ethyl-3methylimidazolium bis(trifluoromethylsulfonyl)amide (Im2,1+/ NTf2−). The change of donor from the neutral DMA to the series of anionic donors permits us to both select for different values of the overall reaction free energy, and to compare how the slower transport of the anionic donors relative to the faster diffusivity of the neutral acceptor affects reaction rates and mechanisms. The series of cyanosubstituted anions is shown in Figure 2 selenocyanate (SeCN−), thiocyanate (SCN−), dicyanamide

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EXPERIMENTAL METHODS Ferrocene was purchased from Sigma-Aldrich and sublimed at 100 °C before use. Tetrabutylammonium perchlorate was used as the electrolyte for cyclic voltammetry in CH3CN and was purchased from Sigma-Aldrich and used without further purification. 9,10-Dicyanoanthracene was purchased from TCI-America and recrystallized from a mixture of pyridine and acetonitrile using the method described by Fujita et al.44 1Ethyl-3-methylimidazolium tetracyanoborate (Im 2,1 + /B(CN)4−) was received from EMD Millipore USA. The IL solvent Im2,1+/NTf2− was purchased from IoLiTec together with 1-ethyl-3-methylimidazolium dicyanamide (Im2,1+/N(CN)2−), 1-ethyl-3-methylimidazolium tricyanomethanide (Im2,1+/C(CN)3−), and 1-ethyl-3-methylimidazolium thiocyanate (Im2,1+/SCN−). 1-Ethyl-3-methylimidazolium selenocyanate (Im2,1+/SeCN−) was synthesized following the methods described by Solangi et al.45 Further details of this synthesis and purification are available in the Supporting Information. Steady-state fluorescence spectra were measured using a Jobin-Yvon Horiba FluoroMax-3 instrument with 1 nm bandpass and the temperature regulated to 293.2 ± 0.1 K for CH3CN solutions and 298.2 ± 0.1 K for Im2,1+/NTf2− solutions. The optical density of the samples was set to about 0.1 at 420 nm to reduce the possibility of reabsorption of the emitted light. The optical path length was 1 cm for all the samples. All fluorescence studies used an excitation wavelength of 420 nm, the peak absorption spectrum of 9,10-DCNA in solutions of both CH3CN and Im2,1+/NTf2−. Time-resolve fluorescence transients were measured using a laboratory built time-correlated single photon counting (TCSPC) apparatus, as previously described.16,46 Transients were recorded so that the number of counts in the peak channel was in the range from 10 000 to 65 000. The instrument time response was typically 90 ps full width at half-maximum (fwhm). Fluorescence decays were recorded over time windows of 7−160 ns, depending on the fluorophore lifetime in a particular solvent. For all of the TCSPC transients used for analysis in the diffusion−reaction model below, the excitation and emission wavelengths were 420 and 460 nm, respectively. To resolve time constants in the ∼20 ps range from the TCSPC transients, standard convolute-and-compare numerical analysis is used to effectively deconvolute the instrument temporal response from the observed fluorescence dynamics.

Figure 2. Chemical structures of electron transfer acceptor, donors, and the ionic liquid solvent.

(N(CN)2−), tricyanomethanide (C(CN)3−), and tetracyanoborate (B(CN)4−)along with the IL used as a solvent, Im2,1+/ NTf2−. One reason we have chosen to use this series of cyanosubstituted anions is because the ILs formed from them have been of significant interest to the ionic liquids research community, and because they are well-characterized for electrochemical applications,25−31 electron-transfer studies,32 and stability for radiolytic applications,33 as well as for possible use in capturing carbon dioxide.34 Another reason is that using these electron-donating anions with the Im2,1+ cation minimally perturbs the properties of the Im2,1+/NTf2− solvent. For example, at the highest concentrations of these anionic donors used here the solution viscosity should be different from that of neat Im2,1+/NTf2−, but by no more than a few percent. We note that Ren et al. investigated the molecular origins of the viscosity in this class of ILs (for Im4,1+/NTf2−) using the SCN− anion as a local probe for two-dimensional vibrational spectroscopy.35 Bimolecular photoinduced electron-transfer dynamics in Im2,1+/NTf2− are compared with rates in the strongly dipolar neutral solvent acetonitrile (CH3CN). Two key characteristics of Im2,1+/NTf2− are pertinent for our studies. First, Im2,1+/ 14791


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The Journal of Physical Chemistry B The appropriate instrument response function R(t) depends on the characteristics of both the detector and the timing electronics and is recorded from an aqueous scattering suspension of nondairy creamer. The measured fluorescence decay IM(t) is a convolution of the ideal decay IR(t) and the instrument response function using the following equation:47 IM(t) = ∫ t0 IR(t) R(t′) dt′. All decays were fit to sums of exponential functions, IR(t) = I0∑ni=1 ai exp(−t/τi) (where ∑ni=1 ai = 1) . From the fitting results, the average lifetime of the fluorophore is then defined as ⟨τ⟩ = ∑ni=1 aiτi. In addition to the sums-of-exponentials modeling, we also applied a distributed lifetime model based on a quadratic programming algorithm, as discussed previously.16,46 We have applied both methods of analysis to the full set of data for concentration-dependent fluorescence quenching of 9,10DCNA by the five cyano anion ILs. The distributed exponential analysis of 9,10-DCNA quenching by C(CN)3− in Im2,1+/ NTf2− is given in the Supporting Information. Equally good fit statistics are obtained for both the discrete exponential and distribution of exponential models, so for simplicity we have chosen to use the discrete exponential model for extracting excited-state decay rates from the time-resolved fluorescence data. The reduced χr2 values for the multiexponential fits lie almost entirely in the range from 1.00 to 1.07 for both Im2,1+/ NTf2− and CH3CN solutions, with outliers at the ends of the range being 0.993 and 1.097, respectively.

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RESULTS AND DISCUSSION Figure 3 shows representative fluorescence transients and spectra for quenching of 9,10-DCNA by C(CN)3− in Im2,1+/ NTf2− solution. These transients were measured for a range of C(CN)3− donor concentrations up to 0.23 M. They show a significant decrease of the 9,10-DCNA excited-state lifetime with increasing donor concentration. While the transients appear to be largely exponential, numerical analysis using convolute-and-compare algorithms show that two to four exponential components are required to achieve an acceptable fit. In contrast, the fluorescence quenching transients in CH3CN solutions are much closer to single exponential. The analysis of these data begins using a simple Stern−Volmer approach and proceeds to include a more sophisticated diffusion−reaction model to account for the higher quencher concentrations and higher viscosities in the IL. Stern−Volmer Analysis. Figure 4 shows both the timeresolved and steady-state Stern−Volmer plots for the same electron acceptor 9,10-DCNA quenched by the series of donors SeCN−, C(CN)3−, SCN−, N(CN)2−, and B(CN)4− in Im2,1+/ NTf2− solution. From these graphs, it is apparent that quenching of the 9,10-DCNA photoacceptor results when the SeCN−, C(CN)3−, SCN−, and N(CN)2− anions are used but no quenching is observed for B(CN)4−. For Im2,1+/NTf2− solutions, the Stern−Volmer plots for the electron-donating IL anions are nonlinear and were fit to the following quadratic equations as a function of the quencher concentration [Q]: I0/I = 1 + a1[Q] + a 2[Q]2 τ0/⟨τ ⟩ = 1 + b1[Q] + b2[Q]2

Figure 3. Time-resolved fluorescence transients (top) and steady-state fluorescence spectra (bottom) of 9,10-DCNA in Im2,1+/NTf2− with different concentrations of the C(CN)3− quencher at 298.15 K.

CH3CN. To facilitate comparison with the quenching rates observed by Liang et al. for neutral donors, we arbitrarily choose 0.1 M as the concentration at which Stern−Volmer nonlinearities become significant,23 and calculate values of kq from the slopes at this concentration: (steady state)

kqτ0 = b1 + b2(0.1 M)

(time resolved)

(2)

The nonlinearity of these Stern−Volmer plots results from transient effects in the fluorescence quenching. In typical neutral solvents such as CH3CN with much lower viscosities, the transient quenching effect is only observed at the earliest subpicosecond time scales and for the highest quencher concentrations. This effect also explains the single exponential decays observed for low viscosity neutral solvents, while the fluorescence decays become nonexponential in the higher viscosity ionic liquids. For higher quencher concentrations, some fraction of the electron transfer dynamics can become faster than the time resolution of the TCSPC instrument. The fraction of the ultrafast dynamics missed by using TCSPC can be judged by the difference between steady-state and time-resolved Stern− Volmer plots shown in Figure 4. The fraction of excited molecules observed to undergo quenching is calculated from f(SS) = 1 − I/I0 and f(TR) = 1 − / for steady-state and q q time-resolved measurements, respectively. The fraction of

(steady state) (time resolved)

kqτ0 = a1 + a 2(0.1 M)

(1)

For fluorescence transients in CH3CN solutions, the linear Stern−Volmer equations are sufficient, i.e., a2 = b2 = 0. (See Figure 3 of the Supporting Information.) The 9,10-DCNA acceptor lifetime τ0 is 13.8 ns in Im2,1+/NTf2− and 12.8 ns in 14792


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Table 2. Electron Transfer Quenching Parameters for 9,10DCNA in CH3CN at 293.2 K Obtained from Time-Resolved Fluorescence (TR) and Steady-State Fluorescence (SS)a donor −

SeCN C(CN)3− SCN− N(CN)2− DMAc

kq(TR)

kq(SS)

kdb

kq(TR)/kd

kq(SS)/kd

2.54 2.37 2.28 1.03 3.10

2.90 2.26 2.12 1.03 4.44

1.85 1.80 1.88 1.84 1.94

1.37 1.31 1.21 0.56 1.60

1.56 1.26 1.13 0.56 2.29

a Rates are in units of 1010 M−1 s−1. bDiffusion rate calculated using Smoluchowski equations and diffusion coefficients from Stokes− Einstein equation. cThe quenching of 9,10-DCNA* in acetonitrile from Liang et al., at 298 K.23

Table 3. Electron Transfer Quenching Parameters for 9,10DCNA in Im2,1+/NTf2− at 298.2 K Obtained from TimeResolved Fluorescence (TR) and Steady-State Fluorescence (SS)a donor −

SeCN C(CN)3− SCN− N(CN)2− DMAc

kq(TR)

kq(SS)

kdb

kq(TR)/kd

kq(SS)/kd

10.5 9.20 6.50 4.91 23

14.0 12.2 7.79 4.90 45

3.13 3.05 3.20 3.12 2.6

3.35 3.01 2.03 1.57 9.4

4.47 4.00 2.43 1.57 18

a Rates are in units of 108 M−1 s−1. bDiffusion rate calculated using Smoluchowski equations and diffusion coefficients from Table 4. cThe estimation of quenching rate by DMA in a 31 cP viscosity ionic liquid in the literature. It is the average of quenching rate in Pyrr4,1+/NTf2− at 313 and 333 K, where viscosities are 41 and 21 cP, respectively.

Table 2 presents the quenching rate constants between the cyano anion donors and the photoexcited 9,10-DCNA* acceptor in solutions of CH3CN at 293.2 K. Table 3 shows the comparable data in solutions of Im2,1+/NTf2− at 298.2 K. The values for quenching of 9,10-DCNA by the neutral donor molecule DMA are extrapolated from the values published by Liang et al. For CH3CN solutions, the values are scaled for the differences in viscosity at 293.2 vs 298.2 K.23 The rate parameter kq(TR) is obtained from the Stern−Volmer analysis of the time-resolved quenching data, while kq(SS) is obtained from integrated steady-state fluorescence spectra, both at 0.1 M via eq 2. The predicted diffusion-limited rates kd are calculated from the molecular sizes and diffusivities using the Smoluchowski equation, kd = 4π × 10−7NA(RD + RA)(DD + DA), where NA is Avogadro’s constant, RD and RA are the radii of donor and acceptor, and DD and DA are the diffusion coefficients. The factor of 10−7 is applied to maintain units of M−1 s−1 for distances in Å and diffusion coefficients in m2 s−1. The diffusivities DD and DA are in turn calculated from the temperature, solution viscosity η, and sizes using the Stokes− Einstein equation, D = kBT/(6πηR). Comparing kq and kd in Table 2, we find that quenching by neutral donor DMA and electron donating anions behave very differently in CH3CN and Im2,1+/NTf2− solutions. In solutions of CH3CN, the quenching of photoexcited 9,10-DCNA by either a neutral donor or charged donors is similar to the diffusion-limited rate. In contrast, for solutions of all four cyano anion donors in Im2,1+/NTf2−, the observed quenching rates are well above the predicted diffusion-limited rates, as shown in Table 3, though they are significantly slower than for quenching by neutral DMA. Generally, fluorescence quenching rates for the cyano anion donors are 1.5−4.5 times faster than the

Figure 4. Stern−Volmer representations of quenching data (points) with quadratic fits (curves) using steady-state fluorescence (top) and time-resolved fluorescence (bottom) data for 9,10-DCNA quenched by the SeCN−, C(CN)3−, SCN−, and N(CN)2− donors in solutions of the Im2,1+/NTf2− IL. Note that no quenching is observed for B(CN)4−.

initially excited molecules that are quenched on time scales faster than can be observed in the TCSPC transients is given by f(SS) − f(TR) . Thus, we can calculate that the fraction of q q quenching events observable using the TCSPC experiment is fobs = 1 − f(SS) + f(TR) = 1 + (I/I0) − (/). The q q parameters from the Stern−Volmer analyses and the observed quenching fractions fobs (at [0.1 M] quencher) are contained in Table 1 and show that for each of the four quenchers we have captured nearly all of the quenching dynamics. Similar values of fobs are also obtained for other quencher concentrations. For CH3CN solutions, the value of fobs is unity. Table 1. Stern−Volmer Parameters for Quenching of 9,10DCNA by SeCN−, C(CN)3−, SCN−, and N(CN)2− in Im2,1+/ NTf2− Solutions at 298.2 K quencher −

SeCN C(CN)3− SCN− N(CN)2−

a1

a2

b1

b2

fobs

9.32 10.80 7.45 5.82

100.7 60.81 32.96 9.40

14.22 12.67 8.63 6.69

2.01 0.284 3.32 0.00

0.89 0.90 0.91 0.97 14793


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donors, and the time-dependent reaction rate coefficient is 2 given by k(t) = 4π∫ ∞ 0 kET(r) p(r,t)r dr. The rate k(t) is related to the electron donor and acceptor pair distribution p(r,t) which is determined from the spherically symmetric reaction− diffusion equation

diffusion-limited rate, while the previous studies showed rate enhancements for the neutral donor DMA in the range of 10− 100.18,23 We note that the viscosity ratio for Im2,1+/NTf2− to CH3CN at 298 K is 33.0/0.341.48 As explained by Liang et al.,23 the dramatic rate enhancements sometimes observed for electron-transfer reactions in ionic liquids result from two contributions. First, as also discussed by Koch et al.,24 the high viscosities of ionic liquids result in slower diffusion and, as a result, much of the quenching occurs during the transient portion of the reaction where electron transfer is faster than under stationary reaction conditions. In addition, neutral quenchers often diffuse much more rapidly than expected based on a simple viscosity scaling of the diffusion rates in conventional solvents.21 In the present case, both of these factors are muted to some extent, first through use of a less viscous ionic liquid than used in other studies and second by the fact that the quenchers used here are charged. Vieira and Falvey18 and Liang et al. used ILs such as Im4,1+/PF6−, which have viscosities that are an order of magnitude higher than that of Im2,1+/NTf2−, and so should display larger rate enhancements. Charged solutes do not show enhanced diffusion in ionic solvents to nearly the extent that neutral quenchers do, and for small enough ionic solutes diffusion can be much slower than simple hydrodynamic predictions.21,49 Several studies have demonstrated that self-diffusivities for neutral species in ILs are faster than those for similarly sized ions. Kaintz et al. used pulsed field gradient spin-echo (PG-SE) NMR methods to show that neutral DMA diffusivities were at least an order of magnitude faster than those of IL anions or cations.21 These methods were also applied to show much faster diffusivity for hexane50 or water51,52 relative to the IL anions or cation in mixtures of these solvents with ILs. An explanation for how and why neutral species exhibit greater self-diffusivities than the ionic species in IL solutions was given by Araque et al.49 They explored the self-diffusion of the isoelectronic and isostructural pair, NH4+ and CH4, to find that the caging is about an order of magnitude longer and that the rate of the diffusive jumps is also slower for ammonium relative to methane.49 Diffusion−Reaction Modeling. A number of research groups have made significant progress in understanding the nonexponential kinetics that result from the initial portions of photoinduced bimolecular electron-transfer reactions.24,42,53−65 The diffusion−reaction equation can be solved numerically as was done by Angulo et al.,61 who compared electron-transfer quenching in imidazolium-based ILs with reactivity in organic solvents including CH3CN, DMSO, and glycerol.24 This approach helped to explain the apparently larger rates for bimolecular reactions observed in IL solutions. Here we follow the approach introduced by Liang et al.,23 who used an approximate solution to the Smoluchowski diffusion−reaction equation proposed by Dudko and Szabo.39 This approach combines a modified Smoluchowski equation40 with an approximate distance dependent Marcus equation for electron-transfer rates.41,66 The transient emission intensity is given by I (t ) = exp{−k 0t − [Q] I(0)

∫0

⎡ −w(r ) ⎤ ⎡ −w(r ) ⎤ ∂ ∂p(r , t ) ⎛ 1 ∂ 2 r exp⎢ = ⎜⎜D 2 ⎥ ⎥ exp⎢ ∂t ⎣ kBT ⎦ ∂r ⎣ kBT ⎦ ⎝ r ∂r ⎞ − kET(r )⎟⎟p(r , t ) ⎠

where r is the distance between the donor and acceptor, D is the relative diffusion coefficient, w(r) is the potential of mean force between the donor and acceptor, and kET(r) is the distance-dependent electron-transfer rate. This rate constant is assumed to be of the form given by Rips and Jortner67 1 1 1 = + kET kNA k SC

(5)

with kNA, the rate constant of the classical Marcus theory for nonadiabatic electron transfer,41,66,68−70 given by kNA =

1/2 ⎛ (ΔG + λ)2 ⎞ 2πHDA 2 ⎡ 1 ⎤ ⎥ exp⎜ ⎢ ⎟ ℏ ⎣ 4πλkBT ⎦ ⎝ 4λkBT ⎠

(6)

The solvent-controlled rate of electron transfer, kSC, as given by Zusman is71 k SC =

1/2 ⎛ ΔG * ⎞ 1⎛ λ ⎞ SC ⎟ ⎜ ⎟ exp⎜ k T τs ⎝ 16πkBT ⎠ ⎝ B ⎠

(7)

In these expressions HDA is the electronic coupling, λ is the reorganization energy, ΔG is the driving force, and ΔGSC * is the barrier height, which in principle all depend on the donor− acceptor distance, and τs is the solvation time, which is independent of distance. Details of how these quantities are determined are provided in the Supporting Information. Here we mainly note that this approach departs from the original one used by Liang et al.23 in that the former work assumed that kET = kNA.72 One key determinant of the bimolecular quenching rates is the relative diffusion coefficient of the donor−acceptor pair, D = DA + DD. We fit the above model to the data using D as an adjustable parameter. For comparison to the fit values, the estimated diffusion coefficients Di of all species in these experiments are provided in Table 4. The value for the 9,10DCNA acceptor is estimated from the empirical correlation ln(D/T) = −12.2436 − 3.5046 ln(Vu) + 0.8080 ln(Vv) − 0.9244 ln(η), where Vu is the volume of solute, Vv is the volume of solvent (Vv = (Vcation + Vanion)/2), and η is the viscosity of the solvent.21 The van der Waals volumes and the spherical radii they imply via Ri = (3Vi/(4π))1/3 are also provided in Table 4. For the electron-donating anions, we scale the diffusivities reported by Tokuda et al.73 for the NTf2− anion in Im2,1+/NTf2− by using the effective spherical radii that are obtained from the molecular van der Waals volumes, via D1/D2 = R2/R1. In addition to the diffusivities, a number of other parameters are included in the diffusion−reaction model. As there are far more parameters than can be determined from the present data, most parameters were fixed at values determined from other experiments or to physically reasonable values, as described in

t

k(t ′) dt ′}

(4)

(3)

where [Q] is the concentration of the electron donors, k0 is the fluorescence decay rate constant in the absence of electron 14794


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the Supporting Information. Ultimately we fit each set of data for a given solvent and quencher using only two freely adjustable parameters: the relative diffusion coefficient, D, and the value of the electronic coupling at contact, V0. Rather than fit the decay data directly, we used multiexponential fits of the data after deconvolution (compiled in Table 1 in the Supporting Information) as inputs to the reaction−diffusion model. In addition, the fluorescence decays of 9,10-DCNA in Im2,1+/NTf2− are not purely single exponential. As shown in Table 1 in the Supporting Information, there is a rise time in each data set of about 0.5−1.0 ns that does not vary with emission wavelength. Indeed, this rise time fluctuates randomly as the quencher concentration is varied. To account for the nonexponential fluorescence kinetics, instead of fitting I(t)/I(0) to eq 3, we divided the decay profile at each nonzero value of the quencher concentration [Q] by the zero-quencher profile and fit

Table 4. Calculated Molecular Sizes and Diffusivities of the Relevant Molecules in Im2,1+/NTf2− at 298.15 Ka molecule Im2,1+ NTf2− −

SeCN SCN− N(CN)2− C(CN)3− B(CN)4− 9,10-DCNA

volume (Å3)a

radius (Å)

D (×10−11 m2 s−1)

116.5 158.7 53.1 42.3 56.0 78.8 138.1 204.6

3.03 3.36 2.33 2.16 2.37 2.66 3.21 3.66

4.95b 3.09b 4.44c 4.80c 4.37c 3.90c 3.23c 2.4821

a

The vdW radii of the cations and anions are calculated from the van der Waals volume increments approach of Edward.74 The atomic volumes for Se and B were obtained from the study by Zhao et al.75 b From Tokuda et al.73 cScaled from the value for NTf2− calculated using the Stokes−Einstein equation.

Figure 5. Fits to the diffusion−reaction model given by eq 4 for 9,10-DCNA fluorescence dynamics in Im2,1+/NTf2− solution. From top to bottom, the quenchers are SeCN−, SCN−, C(CN)3−, and N(CN)2−. The left and center columns of plots provide two different semilogarithmic representations of the scaled transients with data shown as points (×), and the reaction−diffusion model fits as smooth curves. The right column is F(t) from eq 9 illustrating the degree to which the data conforms to the expectation of independent quenchers. In the left panel only one out of five data points used in the fitting is shown. 14795


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The Journal of Physical Chemistry B fobs ([Q])

[I(t )/I(0)][Q] [I(t )/I(0)][Q] = 0

= exp{−[Q]

∫0

Table 5. Parameters of the Reaction−Diffusion Model

t

k(τ ) dτ }

SeCN−

(8)

⎪

⎪

⎪

⎪

∫0

C(CN)3−

Fixed Parameters 6.0 5.8 6.3 1.5 1.5 1.5 50 50 50 −1.4 −0.8 −0.7 IL Fit Parameters (τs = 10 ps) V0 (cm−1)c 118 80 288 D (10−11 m2 s−1) 6.7 6.5 6.3 CH3CN Fit Parameters (τs = 0.2 ps) V0 (cm−1)c 30 52 53 D (10−11 m2 s−1) 547 532 451 IL Contact Values g 35 16 220 ΔG*/(kBT) 0 0.89 0.06 kET (1010 s−1) 9.2 3.7 8.7 CH3CN Contact Values g 0.1 0.1 0.2 ΔG*/(kBT) 0.33 1.04 1.21 kET (1010 s−1) 15 20 18

r0 (Å) βel (Å−1)a ϵDA (kBK)b ΔG0 (eV)

All such data recorded in the IL solvent are shown as the points (×) in the two left panels of Figure 5. Note that the steady-state quenching results are implicitly included in these fits by virtue of the fact that each data set is normalized by fobs, the fraction of the decay captured by the TCSPC experiment. Also shown as the rightmost panels in Figure 5 are the quantities ⎧ [I(t )/I(0)][Q] ⎫ 1 ⎬ F(t ) = ln⎨fobs ([Q]) =− [I(t )/I(0)][Q] = 0 ⎭ [Q] ⎩

SCN−

t

k(τ ) dτ (9)

As indicated by eq 9, if the underlying assumption of quencher independence is valid, F(t) should be identical for all [Q]. Although we do not anticipate that quencher−quencher interactions should be a complicating factor in the concentration range studied, [Q] < 0.4 M, Figure 5 reveals some departure from this expectation over the time windows fit (times when I(t)/I(0) ≥ 10−3). Similar plots using the raw decay data prior to fitting are shown as Figure 5 in the Supporting Information. The origins of this imperfect agreement among quencher concentrations are not known, but it limits the precision with which the reaction−diffusion model is able to reproduce the quenching data. Best fits of the quenching data in Im2,1+/NTf2− are shown as the continuous curves in the two left sets of panels in Figure 5. (Corresponding plots of the quenching data in CH3CN are provided in Figure 6 in the Supporting Information). For a given donor, the model decays at all concentrations derive from a single F(t) function, shown as the dashed pink curve in the rightmost panel, which represents the best compromise given the variation in the experimental data. The model parameters required to obtain these best fits are summarized in Table 5. Because the reactions studied here are all largely diffusion controlled, the diffusion coefficients are well-determined by the fits and are all close to the expected values. The quenching data in Im2,1+/NTf2− yield fitted values of D within 15% of the estimated values of DA + DD provided in Table 4 except in the case of the N(CN)2− quencher, where the fit value is ∼40% smaller than expected. The fitted diffusion coefficients from quenching in CH3CN are comparable to those estimated from DA + DD in Table 4 when scaled by the relative viscosities of CH3CN and Im2,1+/NTf2− (×1/87). The fit values are an average of 16% smaller. Thus, apart from quenching by N(CN)2− in Im2,1+/NTf2−, values of D required to fit the quenching data are within the expected accuracy with which these diffusion coefficients can be estimated. It would be interesting to measure the diffusion coefficients of the donors directly from independent experiments, for example by pulsed field gradient NMR experiments. Unfortunately, attempts to do so in the ionic liquid were thwarted by overlap of the 13C signals of these cyano-substituted donors with the signal from the NTf2−. (This problem was also noted by Solangi et al. in the case of SeCN−.45) The other parameter allowed to vary in these fits is the electronic coupling at contact, V0. The electronic coupling between two proximate molecules is expected to be a strong function of both the relative placement and orientations of the donor and acceptor,63,76−78 making V0 as employed here

N(CN)2− 6.0 1.5 50 −0.4 509 4.0 149 472 657 2.36 0.90 1.1 4.16 4

a

Distance dependence of electron coupling. bThe potential well depth between the donor and acceptor assuming a Lennard-Jones potential. c The donor and acceptor electronic coupling at contact.

effectively an averaged value over the course of a donor− acceptor encounter. The values of V0 are not as well determined by the fits as are the diffusion coefficients, because they depend more strongly on the choice of a number of other model parameters, for example βel, ΔG0, and τs. Neither the variations with donor nor the ∼3-fold difference between the values in Im2,1+/NTf2− and CH3CN is easy to rationalize. At this point the most that can be said about the values of V0 in Table 5 is that they are plausible based on averages calculated over first solvation shell quenchers surrounding coumarin 152 (∼200 cm−1)76 and oxazine 1 (∼300 cm−1)77 in neat dimethylaniline using semiempirical electronic structure methods. Finally, it is useful to consider what the fits indicate about other electron-transfer parameters when the donor and acceptor are in contact. Three relevant quantities are shown in the lower part of Table 5. The adiabaticity parameter g is defined as g = kNA/kSC, and it controls the relative contributions of the nonadiabatic and solvent-controlled mechanisms via kET = kNA/(1 + g). (If the modification of the barrier height by HDA (eq SI-1) is neglected, g = 4πHDA2τs/ℏ.67) The present modeling places the reaction in the solvent controlled regime in Im2,1+/NTf2− and in the nonadiabatic limit or close to the nonadiabatic limit in CH3CN given the values of τs chosen, values which are intermediate between the likely limits of this parameter (0.75−93 ps and 0.12−0.26 ps for the two solvents; see the discussion in the Supporting Information). This situation is unchanged even using the limiting values for τs; however, we find that use of the integral solvation time 93 ps for Im2,1+/NTf2−79 significantly degrades the quality of the fits. Of course the value of HDA varies significantly from V0 as the donor−acceptor separation increases. By the second solvation shell (r ∼ 2r0) g ≪ 1 and the electron transfer falls well within the nonadiabatic regime in all cases. In both solvents, the barriers to electron transfer at contact, ΔG*, are calculated to be comparable to thermal energies, which means that neither eq 6 nor eq 7 can be expected to be completely accurate. The 14796


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results using a homologous series of cationic electron donors with which to compare the present results using anionic donors.

rates of electron transfer at contact are such that reaction is predicted to occur in 5−20 ps in most cases and as slow as ∼100 ps only in the case of N(CN)2− in Im2,1+/NTf2−. The values of kET are an average of 3-fold faster in CH3CN compared to Im2,1+/NTf2−. This difference might be related to reacting pairs being able to explore orientational space more rapidly in the less viscous solvent.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.5b09216. Preparation of Im2,1+/SeCN−; background on Marcus electron-transfer theory; absorption and emission spectra of electron-donor solutions; example of TCSPC data and analysis; multiexponential vs distributed exponential fitting of TCSPC data; Stern−Volmer graphs for CH3CN solutions; testing the independence of observed kinetics on quencher concentration; diffusion−reaction analysis for CH3CN solutions; viscosities of Im2,1+/ NTf2− solutions with added cyano anion quenchers; cyclic voltammetry of donors (PDF)

■

CONCLUSIONS Bimolecular photoinduced electron-transfer reactions between the S1 state of 9,10-DCNA and a series of anionic donors were studied in solutions of a representative ionic liquid, Im2,1+/ NTf2−, and compared with the same reaction in a strongly dipolar solvent, CH3CN. Stern−Volmer analysis of the concentration-dependent fluorescence quenching showed that, in CH3CN solutions, the cyano-substituted donor anions SeCN−, SCN−, and C(CN)3− quench 9,10-DCNA at diffusionlimited rates, while quenching by the N(CN)2− anion was slightly slower. B(CN)4− showed no reactivity in either solvent. In Im2,1+/NTf2− solutions, all four anionic donors showed rates significantly higher than those predicted for a diffusion-limited reaction. Rates in both solvents varied in the order SeCN− > C(CN)3− > SCN− > N(CN)2−. With the exception of SCN− these rates are ordered according to the estimated driving force ΔG0 for the electron transfer in this series of anions. Previous reports on ionic liquids have shown that electron transfer between neutral donors and acceptors proceeds at rates that are typically 1−2 orders of magnitude faster than the simple diffusion-limited rate predicted by the Smoluchowski equation.18,23 Quenching rates for the anionic donors are only 1.5−4.5 times faster than the predicted quenching rate in Im2,1+/NTf2− solutions. Our analysis indicates that two factors contribute to this difference. First, fewer reactive events occur in the transient regime for the lower viscosity Im2,1+/NTf2− relative to higher viscosity ILs studied previously, such as Im4,1+/PF6−. Second, the diffusion of neutral donors is considerably faster than that of charged donors. One of the similarities of the present results to those of prior studies is the observation of linear Stern−Volmer plots and nearly exponential emission transients in CH3CN but nonlinear Stern−Volmer plots and significantly nonexponential transients in Im2,1+/NTf2−. This more complex quenching behavior reflects the importance of the transient regime in ionic liquids. To describe these phenomena, we employed an analysis based on a spherically symmetric reaction−diffusion equation and a simplified electron-transfer model as in our previous work.23 The main result of such modeling was to demonstrate that, with only two adjustable parameters (D and V0), the data in both solvents are understandable within such a theoretical framework. Relative diffusion coefficients, D, derived from fitting the quenching data are consistent with expectations for this neutral acceptor and anionic donors. The values required to fit the data for the electronic coupling at contact, V0, are in a plausible range but vary in a manner not easily rationalized in terms of donor structure. We are presently expanding on this work in several ways. We are beginning computational work on the species involved in hopes of gaining a better understanding of what the variations in V0 deduced here might indicate about the electron transfer. By using a series of other cyano-substituted anthracenes, we are exploring the full range of the Rehm−Weller curves with the current set of cyano anion donors. Lastly, we have obtained

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (M.M.). *E-mail: [email protected] (E.W.C.). Present Address

M.L.: Avon Research and Development, Avon, 1 Avon Pl, Suffern, NY 10901, USA. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge funding for this research from the Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences under Contract No. DE-SC0001780 at Rutgers and Contract No. DE-SC0008640 at Penn State.

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