Diffusion and Solvation of Radical Ions in an Ionic Liquid Studied by

Aug 26, 2014 - the MFE Probe. Tomoaki Yago, Yuya Ishii, and Masanobu Wakasa*. Department of Chemistry, Graduate School of Science and Engineering, ...
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Diffusion and Solvation of Radical Ions in an Ionic Liquid Studied by the MFE Probe Tomoaki Yago, Yuya Ishii, and Masanobu Wakasa* Department of Chemistry, Graduate School of Science and Engineering, Saitama University, 255 Shimo-okubo, Sakura-ku, Saitama-shi, Saitama 338-8570, Japan

ABSTRACT: Magnetic field effects (MFEs) on photoinduced electron transfer reaction between benzophenone (BP) and 1,4diazabicyclo [2.2.2] octane in an ionic liquid (IL) of N,N,N-trimethyl-N-propylammonium bis(trifluoromethanesulfonyl) amide were studied by a nanosecond laser flash photolysis technique. The escape yield of the benzophenone radical anion (BP•−) was increased with increasing magnetic field strength (B) of 0 T < B ≤ 0.1 T and almost saturated at 0.1 T < B ≤ 1.7 T. The observed MFEs were explained by the hyperfine coupling mechanism (HFCM) and the relaxation mechanism (RM). The large MFEs indicate the nanometer-scaled cage effects on the diffusion of the radical ion pairs (RIP) generated by the photoinduced electron transfer reaction in TMPA TFSA. The cage lifetime for the RIP was estimated to be 170 ns, which is much longer than that previously reported for the neutral radical pairs ( 0.6 μs were simply analyzed by the exponential function. Figure 4 shows a magnetic field dependence of the decay time constant (τ) obtained by the exponential fitting. In the magnetic field range of 0.08 T ≤ B, we could not obtain τ

Figure 4. Magnetic field dependence of the time constant (τ) obtained by the exponential fitting, A(t) = Af exp[−(1/τ)t] + As exp[−(1/τ′)t], for the first decay component observed at 690 nm. 22359

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dependences of the transient absorptions in the absence and presence of the magnetic field were simulated with the reaction scheme described in eqs 2−4. From the time dependence of the transient absorptions in the time range of 0 < t < 80 μs, the kbim values in eq 5 were roughly estimated to be 4 × 108 mol−1 dm3 s−1 with the assumption that the initial concentration of BP•− is on the order of 1 × 10−4 mol dm−3. With the use of these values, the effect of the bimolecular process on the dynamics of the geminate RIP can be estimated to be within a few percents. Thus, the bimolecular charge recombination reactions (eq 5) between the escaped radicals were not included in the calculations. In the reaction scheme of eqs 2−4, the charge recombination process involves the spin conversion from the triplet RIP to the singlet RIP. Thus, the rate constant (krec) for the charge recombination reaction is dependent on the magnetic field, generating the MFE. The RIPs can partially escape from the pair with the rate constant of kesc (eq 4), competing with the charge recombination reaction (eq 3). Thus, the following differential equations can be obtained from the reaction scheme of eqs 2−4,

There are two possibilities for the origin of the large MFEs observed in the present reaction in the IL. One is the cage effect for the radical ion diffusion in the IL as was reported in the micellar solutions. There are a number of studies that reported the MFEs larger than 160% in micellar solutions where the radical diffusion is restricted by the cage effects, which prolong the lifetime of the separated RPs.55 Another possibility for the origin of the large MFEs observed is a high viscosity of the IL (73 cP), which may also induce the long lifetime of the RIP, leading to the large MFEs. There are, however, few examples for the observation of the large MFE in highly viscous solvents. Levin et al. reported the MFE on RP generated by the photoinduced hydrogen abstract reaction between 3BP* and pcresol in grycerol, whose viscosity is as large as 1100 cP at room temperature.70 At the magnetic field of 0.34 T, the magnitude of the MFE on the yield of the escaped radicals was reported to be ca. 125%, which is much smaller than the MFE observed in the present study. As for the ET reaction systems, there are few MFE studies in highly viscous conventional solvents. In most of the highly viscous solvents, the origins of the high viscosities are aggregation of alkyl-chains. The polarities of the highly viscous solvents are generally low, which are disadvantages for the ET reactions. In the present ET reaction systems, we have tried to detect the MFE in highly viscous solvents such as silicon oils. However, we could not observe the clear MFEs due to the change of the reactivity of 3BP* and RIP. In the alcohol solvents with the viscosity of 15 cP, Kitahama et al. reported the long lifetime of the RIP on the order of microseconds by using the optically detected electron spin resonance.71 In the same ET reaction system, the magnitudes of the MFEs were reported to be about 20%, though the lifetime of the RIP is longer than that of the present RIP system.72 Thus, we concluded that the present large MFEs observed in TMPA TFSA were caused by the nanometer-scaled cage effects in TMPA TFSA rather than its high viscosity, as was previously proposed to explain the MFEs observed with the neutral RPs in ILs. The origin of the cage effect is supposed to be associated with the solvation dynamics of the ILs. After the generation of RIPs, the anion and cation IL molecules around the solutes should be reoriented, responding to the change of the charge distribution on the solute molecules. Since the solvent structure of ILs has the ordered structure with the size of 1−2 nm,20−34 the most stable intermediate is a solvent-separated RIP with the radical−radical distance (r) = 1−2 nm, where the spin conversions are efficient. In the RIPs with r < 1 nm, nanometer-scaled charge-ordering solvent structures cannot be completed around the radicals and the radicals are loosely solvated. Consequently, the radical can diffuse faster in the RIPs with r < 1 nm, and the fast diffusions of the radicals enhance the recombination reaction at the contact RIPs. The long lifetime of the solvent separated RIPs and the efficient recombination reaction in the solvent cage cause the large MFEs in the ILs. Dynamics of the MFEs on the Radical Ion Pairs. In the present study, the MFEs were found to have appeared immediately after the generation of BP•− as is shown in Figure 3. Moreover, the observed A(t) curves suggest that the generation and decay dynamics of BP•− is overlapped in the present photoinduced ET reaction. Thus, the simple fitting procedure with the exponential functions does not directly provide the kinetic parameters such as ket, krec, and kesc. To investigate the generation process of the MFEs in the RIP and to determine the kinetic parameters in the present system, time

d[3BP0*] = −ket[DABCO] dt

(6)

d⌊BP•−DABCO•+⌋ dt = ket[DABCO] − (k rec + kesc)[BP•−DABCO•+] d⌊BP•−⌋ = kesc[BP•−DABCO•+] dt

(7)

(8)

By solving the differential equations (eqs 6−8), one can obtain the following results for the time evolution of the concentration of BP•− after the photogeneration of 3BP*. [BP•−DABCO•+] + [BP•−] ⎧ k ′ − kesc k ′k = [3BP0*]⎨ et exp( −kett ) − et rec exp( −k 2t ) k1 k1k 2 ⎩ +

kesc ⎫ ⎬ k2 ⎭

(9a)

ket′ = ket[DABCO]

(9b)

k1 = −ket′ + k rec + kesc

(9c)

k 2 = k rec + kesc •−

(9d) •+

•−

Here [BP DABCO ], [BP ], and [ BP0*] represent the concentrations of BP•− in the RIP, the concentration of the escaped BP •−, and the initial concentration of 3BP*, respectively. In accordance with the Beer−Lambert law, the absorbance of the solute molecules is proportional to its concentration. The time profile [A(t)] of the transient absorption observed at 690 nm due to BP•− is therefore proportional to the concentration of BP•−, which can be calculated by eq 9. We assumed that the absorption coefficient of BP•− in the RIP and the escaped is the same. Time dependences of the concentrations of BP•− calculated by eq 9 in the absence and presence of 1.7 T are also shown in Figure 3. Here, the concentrations of BP•− were normalized by setting [3BP0*] to be unity. The calculated results were in good 22360

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agreement with the A(t) curves observed by the transient absorption measurements. The kinetic parameters for the geminate RIPs could be estimated (Table 1). ket was Table 1. Parameters Used for the Calculations: Electron Transfer Reaction Rate (ket[DABCO]) between 3BP* and DABCO, Charge Recombination Reaction Rate (krec) in RIP, and Escape Rate (kesc) from RIP magnetic field (T)

ket [DABCO] (s−1)

krec (s−1)

kesc (s−1)

0 1.7

4.0 × 107 4.0 × 107

4.5 × 106 9.0 × 105

6.0 × 106 6.0 × 106

independent of the magnetic field while krec depended on the magnetic field, reflecting the magnetic field dependent spin conversion between the triplet and the singlet RIP. In the absence of the magnetic field, krec was estimated to be 4.5 × 106 s−1 but decreased to 9.0 × 105 s−1 in the presence of the magnetic field of 1.7 T. These results indicate that the spin conversions are inhibited by the Zeeman splitting. kesc is independent of the magnetic field and associated with the cage lifetime of TMPA TFSA for RIP. From the obtained kesc value of 6.0 × 106 s−1, the cage lifetime (τcage = 1/kesc) was estimated to be as long as 170 ns. The cage lifetime observed in the RIP are compared with that observed in the neutral RPs produced by the photoinduced hydrogen abstract reactions. In TMPA TFSA, we previously observed the MFE due to the transverse spin relaxation caused by the large anisotropy of the g value (δg). The characteristic of this MFE is quite similar to the MFE due to the Δg mechanism. The generation of the observed MFEs require the fast recombination reaction and the fast escape rate from the pair because the spin relaxation caused by δg is fast in the presence of the magnetic field. In TMPA TFSA, the cage lifetime was estimated to be shorter than 20 ns from the generation dynamics of the MFE with the neutral RP.54 In the present study, the estimated τcage value of 170 ns is much longer than that obtained for the neutral RP in TMPA TFSA. The difference in τcage values suggests that the solvation dynamics of the charged molecules are largely different from that of neutral molecules in the IL. When the solute molecules possess the charge, the solute molecules are rigidly solvated by the IL molecules due to the strong Coulomb interaction between the solute and solvent molecules. As a result, the lifetime of the solvent separated RIP becomes longer than that of the solvent separated neutral RPs. The large MFEs with the long lifetime of the RIP were therefore observed in the present photoinduced ET reaction in TMPA TFSA. This conclusion is consistent with the molecular diffusion studies in ILs in which the ionic molecules were found to diffuse slower than the neutral molecules.35−39 To obtain the further information on the MFE dynamics and the solvation dynamics in TMPA TFSA, we also look at the time dependence of the R(B) curve in detail. Figure 6 shows magnetic field dependence of R(B) obtained at the delay time from 50 to 500 ns. The magnitude of R(B) was increased with increasing the delay time, which was consistent with the time evolution of the MFE shown in Figure 3. Moreover, we found that the shape of the R(B) curve is also dependent on the delay time. The magnetic field for the saturation of R(B) is varied with the delay time. In addition to that, we observed the anomalous dips at the magnetic fields of 0.3 and 1 T when the delay time is shorter than 100 ns. The observed dips can be

Figure 6. Magnetic field dependence of the yield of the escaped BP•− [R(B) = A (t ns, B T)/A (t ns, 0 T)] observed at the delay time of 50 (red), 100 (blue), 200 (green), and 500 ns (black) after the laser excitation. R(B) values observed at lower fields (≤0.2 T) (top).

explained by the MFE due to the LCM and will be discussed in the next section. In this section, we focus the time dependence of the saturation behavior of R(B). At the delay time of 50 ns, the R(B) was saturated at the magnetic field below 0.01 T. The magnetic field for the saturation of R(B) was increased with the increase of delay time. At the delay time of 500 ns, the R(B) is saturated at the magnetic field above 0.1 T (Figure 7). These results are reasonably interpreted by the change of the MFE mechanism from the HFCM to the RM with the increase of delay time. The magnetic field for the saturation of the MFE due to the HFCM can be estimated from the HFC constants of the RP (radicals a and b). The half-field value (B1/2), in which the magnitude of the MFE is half of the saturated magnetic field, is represented as follows,73 B1/2 =

2(Ba2 + Bb2 ) Ba + Bb

1/2 ⎡ l ⎛ A i ⎞2 ⎤ ⎢ ⎥ BR = ∑ li(li + 1)⎜ ⎟ ⎢⎣ i ⎝ gβ ⎠ ⎥⎦

22361

(10a)

(R = a and b) (10b)

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Figure 7. Normalized magnetic field dependence of the yield of the escaped BP•− [R(B) = A (t ns, B T)/A (t ns, 0 T)] observed in the low-field region (≤0.2 T) at the delay time of 50 (red) and 500 (black) ns. The solid lines are guides for the eyes. The arrows indicate the magnetic fields where the R(B) values are saturated.

Figure 8. Magnetic field dependence of the yield of the escaped BP•− [R(B) = A (t ns, B T)/A (t ns, 0 T)] observed at the delay time of 50 ns after the laser excitation. The solid line is a guide for eyes. The red dotted circles indicate the magnetic fields where the MFE due to the LCM are observed.

where I and A are the spin angular momentum quantum number and the HFC constant for the kth nucleus, respectively. In the present photoinduced ET reaction, B1/2 is estimated to be 3.3 mT from the HFC constants of BP•−74 and DABCO•+.75 The MFEs due to the HFCM are therefore expected to be saturated at the magnetic field lower than 0.01 T. Moreover the time needed for the S−T conversion by the hyperfine coupling is on the order of 10 ns. Thus, the MFE due to the HFCM, which are saturated at the magnetic field below 0.01 T, are generated within a few tens of nanoseconds after the generation of the RIP. On the other hand, the MFE due to the RM is not saturated at the low magnetic field such as 0.01 T. In the micellar solutions, for example, the MFEs due to the RM is not saturated even in the presence of the magnetic field of 1 T because of the extremely long lifetime of RP.56 The time needed for the spin conversion by the spin relaxation is on the order of 100 ns at the low magnetic field. The MFE due to the RM is unsaturated at the magnetic field below 0.01 T and is generated with the delay time of a few hundred nanoseconds after the born of RIP. To summarize this section, the magnetic field for the saturation of the R(B) increased with increasing delay time. This is because the MFE mechanism is changed from the HFCM to the RM. At the delay time of 50 ns, the observed MFEs are explained by the HFCM and LCM (discussed in the next section). The major feature of the MFEs can be explained by the RM at the delay time of 500 ns. MFEs Due to the LCM. As can be seen in Figure 8, the anomalous dips are observed at the magnetic fields of 0.3 and 1 T when the delay time is shorter than 100 ns. These dips are unclear in the R(B) curves observed at the delay times of 200 and 500 ns. The observed dips can be interpreted with the efficient S−T conversion caused by the LCM.55,56 In accordance with the LCM, the dips are observed with RPs in which the singlet and one of the triplet sates (T+1 or T−1) are energetically degenerated. The degeneracy is provided by the canceling of the S−T energy gap (exchange interaction) with the Zeeman interaction, causing efficient S−T conversion. The observation of the MFE due to the LCM is an indication that the RP with specific r has a long lifetime. The MFE due to the LCM have been mainly observed in the biradical system where the two radicals were connected by the chemical bond.55

In the homogeneous solutions where the radicals diffuse freely in three-dimensional space, the LCM cannot be observed. In the present study, the observation of the MFEs due to the LCM implies that organized solvent structures, which stabilize the specific RIPs, are involved for the generation of the RIP in TMPA TFSA. The schematic view of the possible solvent and RIP structures in TMPA TFSA is depicted in Figure 9 with the

Figure 9. Schematic view of the solvent structure of TMPA TFSA together with RIP produced by the photoinduced ET reaction to explain the observed MFE due to the LCM.

fixed BP•− position. Here we assumed that solute and solvent molecules are hard spheres with the radius of 0.3 nm and the plus and minus charged molecules in alternating positions. The charge ordering structures are common in ILs and have been reported by the X-ray and neutron scattering measurements and molecular dynamics simulations.20,23−25 In the presence of the charge ordering structure in IL, the structures of the RIP generated by the photoinduced ET reactions are stabilized when the positions of TMPA cation and TFSA anion are occupied by DABCO•+ and BP•−, respectively. In Figure 9, the representative RIP structures with r ≤ 1.5 nm are shown. We can find three RIP with different r where cations occupy site I, site II, and site III. The RIP with site I is a contact RIP with r = 0.6 nm. The RIP with site II and site III are solvent-separated 22362

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solvents, the value of β ≈ 1 Å−1 has been typically used.80,83 In solutions, the solvent molecules play an important role in determining the β value via the super exchange mechanism. In the super exchange mechanism, the ET reactions occur through the virtual states where the solvent molecules are reduced or oxidized.84 When the solvent molecules are easily reduced or oxidized, the β value is decreased, resulting in the efficient longrange ET reactions. The reduction potentials of TMPA TFSA are however expected to be not much different from the aromatic organic solvents.85 Katoh et al. reported that in TMPA TFSA, the solvated electron does not react with the solvent molecules and is stable with the lifetime of a few hundred nanoseconds.86 The observation indicates that the energy level of the solvated electron is lower than that of the reduced form of TMPA and TFSA. Thus, the solvated electron rather than solvent molecule works as a virtual state for the ET reactions in TMPA TFSA. Although the solvated electrons are not generated in the present study, the solvated electron-mediated ET reactions are possible in TMPA TFSA. The small β-values suggested in the present study can be ascribed by the solvatedelectron mediated superexchange mechanism. The obtained small β-value does not directly represent efficient ET reactions in IL. This is because the ET reactions in ILs are generally adiabatic and solvent controlled.45,46 The ET reaction dynamics in IL is dominated by the solvent dynamics rather than the magnitude of the electronic coupling. The LCM MFEs were clearly observed at the delay times of 50 and 100 ns, whereas they become unclear at the delay times of 200 and 500 ns. The dips observed around 0.3 T were completely diminished at the delay time of 500 ns, probably because of the overlap of the RM MFE. The results indicate that the LCM MFE was generated just after the formation of the RIP but was not generated after the delay time of 200 ns. From these observations, we presume that the long-range charge separation and recombination occurs in sites II and III without molecular diffusion. After the formation 3BP*, longrange charge separation generates triplet RIP when the sites II or III are occupied by DABCO. The part of the triplet RIP is converted to the singlet RIP by the efficient spin state mixing in LCM. The long-range charge recombination from the singlet RIP generates the MFE on the yield of radical ions. When the radicals in RIP start to diffuse, the charge-ordering structure around the RIP are destroyed and sites II and III cannot be found. Thus, the LCM MFE was only observed at the early time while the contribution of the MFE due to the RM increased with increasing the delay time. Diffusion and Solvation Dynamics of RIPs. In the present study, we have observed the MFEs due to the HFCM, RM, and LCM. So far, we tried to explain the mechanism of the MFE observed. Here, we intend to shed some light on the diffusion and solvation dynamics of the RIP based on the observed MFEs, though a part of the content in this section may be overlapped with that in the previous sections. The reaction scheme obtained by the present MFE study is summarized in Scheme 3. By the photoinduced ET reactions, the contact RIPs are produced as a major chemical intermediate. The contact RIP diffuses and is solvated individually, resulting in the formation of the solvent separated RIP with r ≥ 2 nm. The large MFEs due to the RM and HFCM are generated by the efficient S−T mixing in the solvent separated RIP and the subsequent charge recombination reaction at the contact RIP. From the decay of the RIP, the lifetime of the RIP (or lifetime of the solvent cage) is estimated

RIP with r = 1 and r = 1.3 nm, respectively. Importantly, one can estimate the magnitudes of the S−T energy gaps in RPs from the magnetic fields where the dips caused by the LCM MFE are observed.55,56 The S−T energy gap in RIP was calculated to connect the observed LCM MFE and the RIP model depicted in Figure 9. It has been well-known that the S− T energy gap in RIPs are directly related with the electronic coupling (V) for the ET reactions.76−78 When the photoinduced ET reactions proceed from the triplet excited state, the singlet RIP interacts with the singlet ground state. The S−T energy gap (JCT) is represented with V, charge recombination reaction free energy (ΔGCR), and reorganization energy (λ) as follows,77 JCT (r ) =

V (r )2 ΔGCR + λ

⎡ β ⎤ V (r ) = V0 exp⎢ − (r − d)⎥ ⎣ 2 ⎦

(11a)

(11b)

where V0 is an electronic coupling between donor and acceptor molecules at the closest distance d. β is a falloff parameter for the r dependence of the JCT. The r dependence of the JCT is dominated by the exponential decay of V as is represented with eq 11b. We made the approximation that ΔGCR and λ are independent of r. The values of ΔGCR = 2.51 eV77 and λ = 1.0 eV46 were employed for the calculation. V and β values have been estimated from the analysis on the ET reactions. Typical values in conventional polar solvents are V0 ≈ 300 cm−1, β ≈ 1 Å−1, and d ≈ 6 Å.79−83 However, the r dependence of the JCT calculated with the above parameter set did not reproduce the experimental results with the model presented in Figure 9. Thus, we treated β as an adjustment parameter, while the V0 was fixed to 300 cm−1. Figure 10 shows r dependence of the JCT

Figure 10. Radical−radical distance dependence of the exchange interaction calculated by eq 11 with the parameters of V0 = 300 cm−1 and β = 0.5 Å−1. The red circles represent corresponding JCT and r positions for the generation of the LCM MFE.

calculated by eq 11 with β = 0.5 Å−1. The JCT values are calculated to be 1 T at r = 10 Å (site II) and 0.2 T at r = 13 Å (site III), which correspond to the magnetic fields for LCM MFE. In site I, the JCT value was calculated to be 8 T, which is beyond the range of the magnetic field in the present study and we could not observed the LCM MFE associated with site I. By using β = 0.5 Å−1, we can interpret the observed LCM MFE with the model depicted in Figure 9. In conventional organic 22363

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Scheme 3. Reaction Scheme for Photo-Induced ET Reaction between BP and DABCO Obtained by the Present MFE Studya

a

CR denotes the charge recombination reaction.

RIP to the contact RIP. In these processes, the solvations of the radical ions are not completed in TMPA TFSA. The radical ions are not rigidly solvated and can diffuse faster. Such fast diffusions enable the efficient charge recombination reactions and also contribute to the generation of the large MFEs. The observed MFE dynamics indicates that the nature of the radical ion diffusion is inhomogeneous in the IL and the radical ions fluctuate between the slow and fast diffusions. The averaged diffusion process is comparable or faster than the prediction of the Stokes−Einstein equation.

to be 170 ns in TMPA TFSA, which is 1 order of magnitude longer than that observed with neutral RP (