J. Phys. Chem. 1996, 100, 17713-17715
17713
H2O/D2O Isotope Effect in Geminate Recombination of the Hydrated Electron Robert A. Crowell and David M. Bartels* Chemistry DiVision, Argonne National Laboratory, Argonne, Illinois 60439 ReceiVed: July 8, 1996X
Picosecond transient absorption measurements and simulations of the hydrated electron geminate recombination dynamics are presented for 4 eV multiphoton ionization of liquid H2O and D2O. To within the accuracy of the data and simulation, the isotope effect can be accounted for in terms of the decrease in the diffusion coefficients for eaq-, D3O+, and OD• and the eaq- + D3O+ f D reaction rate in D2O. TABLE 1: Simulation Parameters (X ) H, D)
Introduction
H2O
article,1
In the accompanying we presented the results of a study of eaq- recombination following picosecond multiphoton photolysis of water with photons in the 3.0-5.0 eV energy range. A major finding of that study is that the geminate dynamics of eaq- are independent of excitation energy between 7.8 and 9.0 eV (two-photon excitation) or across the first broad (1b1 f 3s/4a1) continuum in the water absorption spectrum. Because the recombination kinetics are very sensitive to the initial separation distance, the implication of our result is that eaq- is produced from the water excited state by a mechanism which does not impart excess kinetic energy to the electrons. In previous studies of the geminate recombination following 8 eV excitation,2,3 it was assumed that quasi-free electrons are produced, and the H2O/D2O isotope effect was explained in terms of the efficiency of electron energy loss to the solvent vibrational modes, to produce larger initial distances in D2O. This explanation of the isotope effect appears incompatible with the new results, so in this Letter we revisit the problem with a picosecond photolysis study and simulation of the isotope effect. We conclude that the isotope effect can be almost completely explained in terms of the change in diffusion coefficients and reaction rates of eaq- with its geminate partners. Experimental Section The details of the laser system and transient absorption spectrometer can be found in ref 1. The eaq- was generated through two-photon ionization at 310 nm (power density e∼1011 W/cm2) using the frequency-doubled output of an amplified dye laser, and its transient absorption was probed at 620 nm with the standard stroboscopic pump-probe technique. The maximum change in the optical density was less than 0.01. The instrument response (Gaussian fwhm ∼2 ps) for each transient was determined from the rise time of the eaqabsorption signal and was convolved with the results of the simulation. H2O was purified in a Barnstead Nanopure cartridge system to a resistivity of >18 MΩ/cm. D2O (Aldrich, 99.8%) was distilled twice and exposed to UV light for several hours prior to use. The water was flowed (∼1.5 L/min) through a 2 mm Suprasil cell and purged with argon prior to and throughout the course of the measurements. Simulation It is well-known that the creation of hydrated electrons implies the simultaneous generation of an (OH, H3O+) pair in water, because the H2O+ cation reacts immediately with a neighboring X
Abstract published in AdVance ACS Abstracts, October 15, 1996.
S0022-3654(96)02034-5 CCC: $12.00
-),
m2 s-1
D(e D(OX), m2 s-1 D(X3O+), m2 s-1 e- + X+ f X krxn, M s-1 rxn distance, nm a
D2O
4.89 × 2.8 × 10-9 9.0 × 10-9
[7]a [7] [7, 8]
3.88 × 10-9 2.2 × 10-9 6.66 × 10-9
[7] [6] [7, 8]
2.3 × 1010 0.54
[14] [4]
1.0 × 1010 0.54
[9] [4]
10-9
References are given in brackets.
water molecule.1-5 Hydrated electrons react at near-diffusionlimited rates with both species, so the geminate kinetics becomes a three-body problem with no simple analytical solution.4,5 Our simulations are performed using the independent pairs approach of Pimblott,4 which is very easy to evaluate. Briefly, approximate analytical solutions for geminate reaction of eaq- with OH and H3O+ are calculated separately, and the joint survival probability is taken as the product of those for the independent pairs. We refer the reader to ref 4 for details of the theory and calculation. Goulet and Jay-Gerin5 carried out a more rigorous random-flights Monte Carlo simulation of this problem, and their results are in good agreement with those of Pimblott.4 The simulation parameters used here are listed in Table 1. The light water parameters are taken from Pimblott.4 The diffusion of OD is presumed to be 20% slower than OH, based on the H2O/D2O viscosity ratio.6 Diffusion of D3O+ and eaqin D2O is derived from conductivity measurements,7,8 while reaction of eaq- with D3O+ was recently remeasured by Elliot in a pulse radiolysis experiment.9 The model calculation assumes that OX radical and X3O+ ion (X ) H, D) are initially separated by 2.85 Å at the origin, while the hydrated electron coordinates are randomly chosen from a Gaussian distribution centered at the origin: P(r) ∝ exp[-r2/2σ2]. Observed kinetics are then calculated by Monte Carlo integration using the independent pairs assumption. It should be emphasized that the Gaussian distance probability distribution for eaq- about its geminate partners is merely the simplest reasonable choice for a model. Goulet and Jay-Gerin recommend P(r) ∝ exp(-r/b) as a possibly more realistic distribution.5 Pimblott found both distributions worked equally well, and the measurable experimental quantity is roughly the initial root-mean-square displacement.4 Realizations in which the solvated electron is initially within the reaction distance of OX or X3O+ are presumed to recombine “immediately” and so do not contribute to the observed kinetics. Details of the calculation can be found in ref 4. Uncertainties in σ were estimated graphically, all other errors were calculated using a t-distribution at the 90% confidence limit. © 1996 American Chemical Society
17714 J. Phys. Chem., Vol. 100, No. 45, 1996
Letters
Results The transient absorption decays, which are a direct measure of the hydrated electron survival probability, are shown along with the simulation results in Figure 1. After 70 ps the signal has decayed to 69.6 ( 0.5% of its initial amplitude for H2O and 73.7 ( 0.3% for D2O. Before convolution with the instrument response the simulations indicate that the survival probability for the hydrated electron is 60 ( 1% in H2O and 64 ( 1% in D2O after the first 70 ps. These results are in good agreement with the femtosecond work of Gauduel et al.2 and the previous simulation of Pimblott.4,10 Table 1 contains the parameters used in the simulation curves. The D2O data are best fit with a Gaussian distribution of σ ) 6.40 ( 0.15 Å while the H2O results are best described with σ ) 6.25 ( 0.15 Å . Simulation of the light water recombination dynamics using σ ) 6.40 Å indicates that 85% of the isotope effect at 70 ps is due to the difference in the diffusion and reaction parameters of Table 1. To within the validity of the independent pairs model, the accuracy of the measured reaction and diffusion parameters, and the noise in the transient absorption data, the initial electron distributions can be considered the same for H2O and D2O. Discussion Previous investigators2,3 have explained the isotope effect in terms of a larger thermalization distance for the ejected quasifree electron in D2O relative to H2O. If one assumes that the main channel for electron thermalization is through the transfer of translational energy of the ejected electron to quantized vibrational modes of the solvent molecules, then a greater thermalization distance in D2O can be rationalized in terms of the less energetic vibrational modes of D2O relative to H2O. This effect is most likely to play an important role in water radiolysis where quasi-free electrons are generated with a large amount of excess energy. Indeed, the isotope effect in the spur kinetics of water radiolysis was interpreted in this way in ref 11 where it was estimated that the initial spatial distribution for the electron should be 1.18-1.41 times larger in D2O than in H2O.12 If the electron thermalization mechanism were correct for water photolysis as well, then the initial geminate distribution should become larger as excitation energy is increased. This prediction was found not to hold for two-photon excitation between 7.8 and 9.0 eVsgeminate kinetics are invariant over this range of the first continuum absorption and begin to change only at higher energies where other electronic transitions begin to contribute.1 Consequently, with 8 eV excitation the electrons are not ejected with significant excess energy, and a different explanation for the H2O/D2O isotope effect must be found. Within ∼2 ps following the photoionization of water the electron has become thermalized, and the overall reaction for the generation of hydrated electrons is described by
H2O f H3O+ + OH + eaq-
(R1)
Once thermalized, the picosecond decay in the population of hydrated electrons is a result of the two geminate recombination reactions:
eaq- + H3O+ f Haq + H2O
(R2)
eaq- + OH f OH-
(R3)
If both reactions were diffusion-limited, then the H2O/D2O isotope effect would consist merely of a ca. 20% slower recombination in D2O due to the difference in diffusion
Figure 1. Picosecond transient absorption decays of eaq- following photolysis at 310 nm (4.0 eV) for D2O (upper curve) and H2O (lower curve). Simulations with σ ) 6.4 Å for D2O (dashed curve) and σ ) 6.25 Å for H2O (dotted curve) are also shown. The parameters used in the simulations are shown in Table 1.
coefficients in the two solvents. A difference in limiting escape yields would imply a difference in the initial distance distributions. (For diffusion-limited recombination, escape probability is independent of diffusion rate.13) Part of the isotope effect apparent in Figure 1 and in refs 2 and 3 reflects the fact that the data have not been recorded to long enough time to determine limiting escape yields. But while reaction R3 is essentially diffusion limited at room temperature, the reaction rate for R2 is only about two-thirds the value predicted for a diffusion-limited reaction in H2O, and in D2O is much slower still, reflecting the large reorganization involved in converting eaq- to Haq. The competition between (R2) and (R3) consequently produces a 2-3% isotope effect in limiting escape yield as well, even with identical initial distance distributions. As demonstrated in the Results section, the entire H2O/D2O isotope effect in this water photolysis experiment might be explained by the reaction and diffusion rates, without any difference in initial electron distance distribution. Nevertheless, a slightly larger distribution in D2O could still be present. As already pointed out by Goulet and Jay-Gerin,5 this might arise from diffusion of the H2O+ holes by resonance charge transfer, in competition with the proton transfer reaction of H2O+ with water molecules on a femtosecond time scale. One expects that D2O+ will live slightly longer than H2O+ and so will have more opportunity to diffuse away from its geminate eaq- partner. Very precise experiment and simulation would apparently be necessary to prove this effect. Conclusion We have measured and simulated the isotope effect on the geminate recombination dynamics of the hydrated electron following 8 eV photoionization. It is concluded that over the first 70 ps following photoionization the difference in the dynamics is primarily due to the isotope effect on reactions R2 and R3: specifically, the difference in the diffusion coefficients in H2O and D2O and the significant difference in the reaction of eaq- with hydronium (deuteronium) ion. Consequently, the electron “thermalization distance” in D2O need not be greater than in H2O as previously suggested2,3 for 8 eV water photolysis. It should be reemphasized that for water radiolysis, or higher energy photolysis excitation, the thermalization distance in D2O may be genuinely greater than in H2O because the electrons are ejected with much larger excess energy. Acknowledgment. This work was performed under the auspices of the Office of Basic Energy Sciences, Division of Chemical Science, US-DOE, under Contract W-31-109-ENG38. References and Notes (1) Crowell, R. A.; Bartels, D. M. J. Phys. Chem. 1996, 100, xxxx.
Letters (2) Gauduel, Y.; Pommeret, S.; Migus, A.; Antonetti, A. J. Phys. Chem. 1991, 95, 533. Gauduel, Y. In Ultrafast Dynamics of Condensed Systems; Simon, J. D., Ed.; Kluwer Academic Publishers: Dordrecht, 1994; pp 81136. Gauduel, Y.; Pommeret, S.; Migus, A.; Antonetti, A. Chem. Phys. 1990, 149, 1. (3) Lu, H.; Long, F. H.; Bowman, R. M.; Eisenthal, K. B. J. Phys. Chem. 1989, 93, 27. Long, F. H.; Lu, H.; Eisenthal, K. B. Chem. Phys. Lett. 1989, 160, 464. (4) Pimblott, S. M. J. Phys. Chem. 1991, 95, 6946. (5) Goulet, T.; Jay-Gerin, J.-P. J. Chem. Phys. 1992, 96, 5076. (6) The diffusion of OD is presumed to be 20% slower than OH, based on the H2O/D2O viscosity ratio; CRC Handbook of Chemistry and Physics; Weast, R. C., Astle, M. J., Eds.; CRC Press: Boca Raton, FL, 1981; p F-42. Millero, F. J.; Dexter, R.; Hoff, E. J. Chem. Eng. Data 1971, 16, 85. Drost-Hansen, W.; Millero, F. J. J. Phys. Chem. 1969, 73, 34. (7) Schmidt, K. H.; Han, P.; Bartels, D. M. J. Phys. Chem. 1992, 96, 199. (8) Gierer, A. Z. Naturforsch. 1950, 5A, 581. (9) Elliot, J. A. AECL Whiteshell Laboratories, report in preparation.
J. Phys. Chem., Vol. 100, No. 45, 1996 17715 (10) Note that in our accompanying paper1 convolutions were performed to mimic a ca. 4 ps instrument response, and somewhat noisier data were fit out to 3 ns using σ ) 7.3 Å. The present data and convolution agree quite well with the simulation of Pimblott,4 whose fit of the data in ref 2 was somewhat forced with σ ) 5.8 Å. Clearly, the independent pairs approximation is flawed for quantitative treatment of the early time kinetics, just as discussed in refs 4 and 5, but this does not affect our qualitative conclusions. (11) Chernovitz, A. C.; Jonah, C. D. J. Phys. Chem. 1988, 92, 5946. Jonah, C. D.; Chernovitz, A. C. Can. J. Phys. 1990, 68, 935. (12) The thermalization distance derived from the radiolysis experiments is 6-7 times greater (∼40 Å), indicating significantly more excess energy than that measured in our photolysis work.1 (13) Diffusion-Limited Reactions; Rice, S. A., Ed.; Elsevier: New York, 1985. (14) Buxton, G. V.; Greenstock, C. L.; Helman, W. P.; Ross, A. B. J. Phys. Chem. Ref. Data 1988, 17, 513.
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