Picosecond Pulse Radiolysis Study on the Distance Dependent

Article pubs.acs.org/JPCA

Picosecond Pulse Radiolysis Study on the Distance Dependent Reaction of the Solvated Electron with Organic Molecules in Ethylene Glycol Abdel Karim El Omar,† Uli Schmidhammer,† Pascal Pernot,† Shigeo Murata,‡ and Mehran Mostafavi*,† †

Laboratoire de Chimie Physique - ELYSE, UMR8000 CNRS-Université Paris Sud, 91405 Orsay, France National Institute of Advanced Industrial Science and Technology, AIST Tsukuba Central 5, 1-1-1 Higashi, Tsukuba 305-8565, Japan

‡

ABSTRACT: The decay of solvated electron es− is observed by nanosecond and picosecond pulsed radiolysis, in diluted and highly concentrated solutions of dichloromethane, CH2Cl2, trichloromethane, CHCl3, tribromomethane, CHBr3, acetone, CH3COCH3, and nitromethane, CH3NO2, prepared in ethylene glycol. First, second-order rate constants for the reactions between e−s and the organic scavengers have been determined. The ratio between the highest rate constant that was found for CH3NO2 and the lowest one that was found for acetone is 3. This difference in reactivity cannot be explained by the change of viscosity or the size of the molecules. Then, from the analysis of decay kinetics obtained using ultrafast pulse−probe method, the distance dependent first-order rate constant of electron transfer for each scavenger has been determined. The amplitude of the transient effect observed on the picosecond time scale differs strongly between these solvated electron scavengers. For an identical scavenger concentration, the transient effect lasts ≈650 ps for CH3NO2 compared to ∼200 ps for acetone. For acetone, the distance dependent first-order rate constant of electron transfer is decreasing very rapidly with increasing distance, whereas for nitromethane and tribromomethane the rate constant is decreasing gradually with the distance and its value remains non-negligible even at ∼10 Å. This rate constant is controlled mostly by the free energy of the reaction. For nitromethane and tribromomethane, the driving force is great, and the reaction can occur even at long distance, whereas for acetone the driving force is small and the reaction occurs almost at the contact distance. For nitromethane and acetone, the oneelectron reduction reaction needs less internal reorganization energy than for alkyl halide compounds for which the reaction occurs in concert with bond breaking and geometric adjustment.

I. INTRODUCTION Time resolved observations of solvated electron by pulse radiolysis techniques in 19621,2 opened the way to determine rate constants and establish the reaction mechanism for this transient species with a wide variety of solutes.3−7 The majority of these rate constants were determined directly from transient absorption measurements of the solvated electron decay or indirectly using competition methods.8 As in general for bimolecular electron transfer reactions in solution, the overall reaction of the solvated electron consists of two steps: the diffusive approach of reactants and the reduction. If the reduction rate is distinctly lower than the diffusion rate, the overall reaction kinetics is controlled by thermal activation. For diffusion controlled reaction, the time-resolved measurement does not reveal detailed information concerning the electron transfer process. The overall reaction can be even faster than diffusion controlled reaction if the electron transfer occurs at distances that are longer than the contact distance. In solutions at ambient temperature, the so-called “transient effect” can be observed on the subnanosecond scale, if a significant part of the reactants is already at distances for this long-range electron transfer without the need of diffusive approach. This condition © 2012 American Chemical Society

can be fulfilled by providing one reactant at appropriate high concentration in viscous solvent. Under these conditions, the kinetics deviates from an exponential function at short delay times, lasting usually a few hundred picoseconds. During the last 25 years, several photochemistry groups analyzed this transient effect on electron transfer reactions in solution, often by observing fluorescence quenching using time-resolved techniques such as single photon counting.9−22 Generally, such data were used to study the mechanism for electron transfer in liquid and solid solutions. The dependence of the rate constant on the donor−acceptor separation was taken into account using the Marcus equation23,24 or a phenomenological rate constant.25,26 To the best of our knowledge, the studies at room temperature were always performed with excited states of the molecules serving as either electron donor or acceptor. Here we study the electron transfer from the ground state of the solvated electron. Several studies during the 70s suggested that the Received: August 23, 2012 Revised: November 12, 2012 Published: November 14, 2012 11989

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electron pulses with an energy of 7.2 MeV and a charge of ≈4 nC, at a repetition rate of 10 Hz. Single shot electro-optic sampling33 indicated that ELYSE provides in this configuration electron bunches with a typical pulse duration of ≈10 ps and shot-to-shot jitter 50 ps. It is well-known that in radiolysis, spurs with two or more electron−hole pairs are generated heterogeneously through the solvent. Tachiya’s model39 presented in section III.1 is not appropriate for treating reaction kinetics in such multiple pair spurs. The kinetics of geminate recombination of solvated electron described by S(t) can be changed when the solute is present at 0.4 M. In such a situation, the best way to treat the kinetic data would be to perform a Monte Carlo simulation. However, such a simulation code is at present impossible due to poor knowledge of spur structure and dynamics in EG. We limit our analysis to isolated pairs. Here it is important to note that the contribution of the decay of the solvated electron during the first hundreds of picoseconds is small compared to the scavenging reaction (Figure 1). Within the first 500 ps, less than 9% of the solvated electrons decay by geminate recombination in neat EG. This contribution of geminate kinetics is only reduced in the presence of scavenger. In contrast, adding 0.4 M of scavengers causes almost complete decay within a few nanoseconds. For example, in the presence of of 0.4 M CHCl3, 66% of solvated electrons disappear in less than 500 ps. Another observation is that, for acetone, even when 40% of presolvated electrons are scavenged by the solute, the transient effect is still weaker than for CH2Cl2 for which only 25% of presolvated electrons are scavenged. Therefore, the change of population distribution for geminate recombination cannot be responsible for the observed deviation from the pseudo-first-order kinetics, and we believe that the latter is indeed due to the transient effects in electron

Figure 4. Pulse−probe data obtained at 575 nm for the decay kinetics of the solvated electron in neat EG and solutions containing 0.4 M scavenger. The solid line for solvated electron decay in neat EG is obtained from eq 10, and other lines are the best fits obtained using the Bayesian method with parameters A and b reported in Table 3. The residuals are shown above.

indicate that the overall reaction is influenced by the electron transfer step. The fastest decay is observed for nitromethane and bromoform, and the lowest one for acetone. If we consider the time at which the concentration of solvated electron is reduced by half, this time is approximately 320, 480, 520, 830, and 930 ps for nitromethane, bromoform, chloroform, dichloromethane, and acetone, respectively. The magnitude of the transient effect is not the same for the different scavengers (Table 1) and its scale is estimated from the difference between the absorbance observed at 50 ps and that expected for a pseudo-first-order reaction. The latter is obtained by extrapolating the decay at longer delay time to the subnanosecond time domain (Figure 3). For nitromethane, the transient effect 11993

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Table 3. Kinetic Parameters A and b Obtained from Fits Shown in Figure 4 CH2Cl2 CHCl3 CHBr3 CH3COCH3 CH3NO2

reduction potentiala (VNHE)

estimated free energy, ΔG change (eV)

10−9A (s−1)

b (Å−1)

rmax (Å)

−0.8 −0.6 −0.46 −2.1 −0.8

2.1 2.3 2.4 0.8 2.1

1.61 ± 0.1 4.9 ± 1 1.51 ± 0.1 26.3 ± 1.3 2.7 ± 0.1

0.46 ± 0.02 0.7 ± 0.06 0.33 ± 0.01 4.53 ± 0.48 0.36 ± 0.01

6.2 6 7.8 5.5 7.9

Reduction potential for CHCl3, CH2Cl2, and CHBr3 were defined in dimethylformacide. The free energy change ΔG was estimated from these reduction potentials. a

scavenging reactions. From the analysis of this effect we can find the information about the kinetics of electron transfer, as we reported in our previous work.29 According to the equations given in section III.1, three parameters D, A, and b need to be determined for simulation of decay kinetics. In the previous work, D was considered as an adjustable parameter varying from 0.03 × 10−5 to 0.34 × 10−5 cm2 s−1 and we found that D = 0.12 × 10−5 and 0.15 × 10−5 cm2 s−1 were the best estimates for EG solutions containing CuII and PbII, respectively. The viscosity of EG solutions used in this study was determined for each scavenger (Table 1) to be ∼21 cP at 0.4 M compared to 24 cP for a metal cation solution of the same concentration. Our simulations indicate that the diffusion coefficient in the present system should be higher than for metal cation systems. On the basis of the value previously estimated for D and adjusted by the viscosity and the simulations (not reported here), we fixed the diffusion coefficient D to 0.18 × 10−5 cm2 s−1. This value is in agreement with the estimated mutual diffusion coefficient obtained for the reaction of solvated electron with silver ions in EG that is 0.19 × 10−5 cm2 s−1, which was estimated from the value of the rate constant of 3 × 109 mol L−1 s−1 by assuming a reaction radius of 3 Å.50 Consequently, only two kinetics parameters, A and b were determined in the present study. Decay kinetics calculated using eqs 1−3 were fit to the experimental kinetics using eqs 5−8, and the best fits (solid lines) and residuals are shown in Figure 4. The fits reproduce the decay kinetics very well. The residuals are very low, confirming again that the method used to follow the kinetics of transient effect of the solvated electron by picosecond pulse radiolysis is sound. The parameters A and b of the first-order rate constant (distance dependent) are deduced from the fits and reported in Table 3. The rate k(r) obtained from (eq 3) is shown in Figure 6. The profile of k(r) depends strongly on the scavenger. For acetone, the rate constant decreases very steeply with increasing distance. The electron transfer reaction can be considered to occur at contact distance. In contrast, for nitromethane and bromoform, k(r) decreases gradually. So the reaction still proceeds even at 10 Å. For halocarbon scavengers, k(r) plots cross each other. For CH2Cl2, k(r) is the lowest one for r < 8.5 Å. k(r) is almost the same at 7.5 Å for chloroform and bromoform. At r < 7.5 Å, k(r) is larger for CHCl3 than CHBr3 and at r > 7.5 Å it is the other way around. The curves for CuII and PbII obtained in the previous work are also reported for comparison. The time dependent distribution distance (Y(r,t), not reported here) indicates that at short time, close solvated electron−scavenger pairs react first, as k(r) is greater at these short distances. Later on, the fraction of such pairs decreases, and the distribution of reaction distances shifts to pairs separated by the final distance at which Y(r) is maximum ∼8 Å

Figure 6. Distance dependence of the first-order rate constant k(r) for reaction of the solvated electron and dichloromethane, trichloromethane, tribromomethane, acetone, and nitromethane in EG. For comparison, the data for PbII and CuII are also reported from ref 29.

The distance of maximum reaction probability rmax (Figure 7) varies greatly for different scavengers. For acetone, as

Figure 7. Distribution of reaction distances Y(r) calculated at 0.4 M scavenger. The contact distance is 4 Å. Note a break in the vertical axis.

expected from the value of k(r), the reaction occurs in contact pairs. For nitromethane and CHBr3, rmax is reached at ∼8 Å. For CHCl3 the distribution reaction distance is different. It is significant at short distance and weak at longer distance. It is interesting to note that our model shows that even if the reaction of solvated electron is faster with nitromethane than with bromoform (Figure 4), the distribution of reaction distances is slightly wider for the latter. Finally, the distribution distance is wider for CH2Cl2 than for CHCl3. In fact, the value of the rate constant at distance larger than 9 Å is higher for CH2Cl2 than for CHCl3. 11994

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V. DISCUSSION AND CONCLUDING REMARKS Electron transfer reactions studied are of two types. The reaction of halocarbon is an electron transfer concerted with bond breaking: RX n + es− → RX n − 1• + X−

reorganization energy, and the value of reorganization energy is almost imposed by the solvent. In contrast for alkyl, the internal reorganization energy should be more important than for acetone and nitromethane as one bond is dissociated and other bonds are readjusted. Moreover, four of the five reactions could be in the inverted region, where the driving force exceeds the total reorganization energy. Neglecting quantum effects, in the inverted region the ET rates speed up when the reorganization energy increases. The outer sphere reorganization energy increases when the separation distance r between the solvated electron and its partner increases, so the distance dependence of λs can contribute to the observed distance dependence of electron transfer. This study demonstrated that solvated electron reactions with organic molecules in EG exhibit the transient effect on a subnanosecond time scale. Our simulation of decay kinetics yielded distance-dependent rate constants of electron transfer in the systems. In combination with our previous study we can conclude that the solvated electron can react at distances as long as 10 Å with both charged and uncharged species. Moreover, a large variety of electron acceptors can be used as scavenger; i.e., a large range of free energy of reactions can be accessed. This case of access can be useful for mechanistic studies of electron transfer. Finally, we note that a more accurate analysis of the experimental data in the future will use a Monte Carlo code for EG radiolysis. The development of such a code will bring more information on spur reactions and electron transfer kinetics.

(11)

whereas acetone and nitromethane react by electron attachment: (CH3)2 CO + es− → (CH3)2 CO•−

(12)

CH3NO2 + es− → CH3NO2•−

(13)

Kinetics of electron transfer are usually described by the Marcus51,52 equation, with electron transfer rate k(r): 2π 2 J exp[−β(r − r0)] ℏ 0 ⎡ (ΔG + λ)2 ⎤ 1 exp⎢ − ⎥ 4λkBT ⎦ ⎣ 4πλkBT

k(r ) =

(14)

where J0 is the electronic coupling matrix element at r = r0, β is the attenuation coefficient, ΔG is the free energy change, and λ is the reorganization energy. According to this equation ΔG, λ, J0, and β are the main parameters determining the electron transfer rate constant. The reorganization energy includes the solvent and internal reorganization energies. The former can be estimated from λs =

e 2 ⎛⎜ 1 1 ⎞⎟⎛ 1 1 2⎞ − − ⎟ ⎜ + ⎜ ⎟ 2 ⎝ εop εs ⎠⎝ ra rb r⎠

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AUTHOR INFORMATION

Corresponding Author

(15)

*E-mail: [email protected].

where e is electron charge, a and b are donor and acceptor radii, and εOP and εS are the solvent’s optical and static dielectric constants. However, the sizes of the scavengers used in this study are not very different. The greatest one is CHBr3 (2.7 Å), and the smallest is CH2Cl2 (2.4 Å), as estimated using the method of Edward.53 So, λs’s for different scavengers are not very different, but the internal reorganization energy could be different. In a first approximation, the free energy change can be expected to have a major effect on the dynamic of electron transfer. The standard reduction potential for (CH3)2CO/ (CH3)2CO•−; CH2Cl2/CH2Cl•, Cl−; CHCl3/CHCl2•, Cl−; CHBr3/CHBr2•, Br−; CH3NO2/CH3NO2•− varies as −2.1,54 −0.8,55 −0.6,57 −0.46,57 and −0.8 VNHE,56,57 respectively, in organic solutions (Table 3). The redox potential of solvated electron is quite low −2.87 V (in aqueous solutions).56 The lowest −ΔG of the electron transfer reaction is for acetone (0.7 eV), and the highest one is for bromoform (2.4 eV). Thus, the driving force for the bromoform is so large that the electron transfer occurs even at a large distance, whereas for acetone, the driving force is significantly lower and the reaction occurs almost upon contact. Taking a closer look at Figure 4 reveals that the reaction rate increases as (CH3)2CO < CH2Cl2 < CHCl3 < CHBr3 < CH3NO2, which is not fully in agreement with the order of increasing −ΔG’s. So, even if the free energy change is not more favorable than for bromoform, dichloromethane, and chloroform, the reaction is fastest for nitromethane. Apparently, ΔG is not the only parameter in play. For acetone and nitromethane, the reduction does not imply bond dissociation, then it does not need the important change of internal

Notes

The authors declare no competing financial interest.

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REFERENCES

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