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Solvated Electron Extinction Coefficient and Oscillator Strength in High Temperature Water† Patrick M. Hare,‡ Erica A. Price, Christopher M. Stanisky, Ireneusz Janik, and David M. Bartels* Radiation Laboratory, UniVersity of Notre Dame, Notre Dame, Indiana 46556 ReceiVed: October 12, 2009; ReVised Manuscript ReceiVed: December 3, 2009
The decadic extinction coefficient of the hydrated electron is reported for the absorption maximum from room temperature to 380 °C. The extinction coefficient is established by relating the transient absorption of the hydrated electrons in the presence of a scavenger to the concentration of stable product produced in the same experiment. Scavengers used in this report are SF6, N2O, and methyl viologen. The room temperature value is established as 22 500 M-1 cm-1, higher by 10-20% than values used over the last several decades. We demonstrate how previous workers arrived at a low value by incorrect choice of a radiolysis yield value. With this revision, the integrated oscillator strength, corrected by refractive index, is definitely (ca. 10%) larger than unity. This result is fully consistent with EPR and resonance Raman results which indicate mixing of the hydrated electron wave function with solvent electronic orbitals. Oscillator strength appears to be conserved vs temperature. I. Introduction The hydrated electron is the most strongly absorbing species formed by radiolysis or photolysis of water, so its extinction coefficient is extremely important to know for the quantitative interpretation of aqueous transient absorption experiments.1,2 The spectrum, in the form of relative absorption as a function of time, is quite easy to measure, given a stable source of radiation or photolysis.3-7 However, the precise determination of an absolute decadic extinction coefficient is a difficult challenge for such a reactive transient, particularly at very high temperatures. We recently published a Letter8 asserting that the room temperature extinction coefficient for the hydrated electron has been underestimated by 10-20% over the last 40 years. In this submission we confirm that result and present new measurements for temperatures up to 380 °C. The spectrum of this “simplest” aqueous anion has been the object of intense theoretical interest since its discovery9 in 1963 and is central to a debate over the solvation structure (solvent cavity vs solvent anion3,10,11) which continues to this day.12,13 Analysis of the spectral amplitude and shape indicates that total oscillator strength of the spectrum is conserved at all temperatures, as assumed for many years. We demonstrate here for the first time that the hydrated electron derives some of its oscillator strength from the water solvent. Assuming the validity of Beer’s Law, a transient absorption is related to a transient concentration (for path length l, and assuming uniform concentration) by A(t) ) εlC(t). In order to measure the extinction coefficient ε, the fundamental problem is to establish the transient concentration C(t). The first estimate of εe- for the hydrated electron by Rabani et al.1 was made by simultaneous measurements in a pulse radiolysis experiment of † The Notre Dame Radiation Laboratory is supported by the Office of Basic Energy Sciences at the United States Department of Energy. This is document number NDRL-4826 from the Notre Dame Radiation Laboratory. * Corresponding author. Phone: +1 574 631 5561. Fax: +1 574 631 8068. E-mail:
[email protected]. ‡ Present address: Department of Chemistry, Northern Kentucky University, Highland Heights, KY 41099.
hydrated electron absorption at 578 nm and of the 366 nm absorption of nitroform anion C(NO2)3-, the product from the scavenger tetranitromethane. This method makes a relative measurement of the initial hydrated electron absorption and the final product absorption and requires that all of the (e-)aq react to give the absorbing product. The extinction coefficient of the product must be accurately known for the conditions of interest (e.g., temperature) from some other experiment. Exactly the same strategy has been used for our recent reevaluation of εe(720 nm) using the methyl viologen scavenger.8 Based on this more recent experiment and the data shown below, the result of Rabani et al. was low by 20% (10% error was estimated). Subsequent estimates of the extinction coefficient by pulse radiolysis all made use of relative absorbance obtained in experiments on different chemical systems.14-17 The transient absorbance measured in pulse radiolysis can be written as A(t) ) D(t) × G(t) × εl, where D(t) is radiation dose (absorbed energy/volume) and G(t) is radiolysis yield (molecules/energy). It has long been established18-20 that in room temperature water, electron and gamma radiolysis yields of free radicals such as the hydrated electron are time-dependent due to recombination in “spurs”, but that by ca. 0.1-1.0 ms after a short radiolysis pulse, they asymptotically approach21,22 a limiting escape yield, G(∞). If one measures absorbance from a “standard” whose product Gε is known and then measures in the same cell and for the same dose the absorbance from the hydrated electron, one can obtain (approximately) Ge-(∞) × εe-. If Ge-(∞) is accurately known, e.g., from gamma radiolysis scavenging experiments, then εe- can be deduced. In 1967 Fielden and Hart14 published a study based on free radical scavenging in alkaline hydrogenated water, in which all radiolytically produced H and OH radicals are also converted to hydrated electron. Hydrated electron absorbance under these conditions was calibrated against alkaline hydrogenated KMnO4 solution, in which all radicals were converted to the product MnO42-, whose extinction coefficient is independently established. The extinction coefficient εe-(720 nm) ) 18 600 M-1 cm-1 was reported, which is 22% low compared to our recent
10.1021/jp909789b 2010 American Chemical Society Published on Web 01/08/2010
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report, but in good agreement with the earlier work of Rabani et al.1 This number was widely accepted for decades. In 1972, Jha et al.15 reported εe-(720 nm) ) 19 200 M-1 cm-1 by direct comparison of (e-)aq absorbance at ca. 100 ns after a radiolysis pulse, with absorbance from (SCN)2- in the standard oxygen-saturated thiocyanate dosimeter. This number is the same as the previous measurements, within error. However, Buxton and Stuart reported23 in 1995 that calibration of Gε for the standard thiocyanate dosimeter used by Jha et al. was incorrect (low) by ca. 10%. Most recently, Elliot et al.17 have reported εe-(720 nm) ) 21 000 M-1 cm-1 based on the corrected dosimeter calibration and based on Ge-(∞) ) 2.8 × 10-7 mol/J. The ratio of (e-)aq and (SCN)2- absorbance in their experiment is in good agreement with Jha et al., and we can demonstrate a similar result in our own apparatus (see Discussion, below). However, our recent independent room temperature result8 for εe-(720 nm) is still 8% higher than this number, suggesting that the thiocyanate dosimeter calibration might still be incorrect (Buxton and Stuart claim 2% accuracy23). We conclude from this brief history of the room temperature hydrated electron extinction coefficient that the methodology based on relative measurement with respect to a product absorption is an excellent strategy, but is limited by knowledge of the product extinction coefficient under the conditions of interest. At very high temperature such as in supercritical water, this is a severe problem. The methodology based on a “standard” dosimeter absorbance can be no better than the calibration of the dosimeter Gε product and the independent determination of Ge-. Moreover, the measurement is somewhat ill-determined by the fact that Ge- is time-dependent. Particularly at elevated temperature it can be experimentally difficult to separate the spur recombination kinetics from homogeneous recombination chemistry to approximate Ge-(∞). In order to overcome these limitations, we have invented the new more general approach described below. II. Approach We start with the idea that hydrated electrons will be generated in an optical cell with a pulse of radiation or photons. Subsequently they will recombine in geminate or quasi-geminate spur recombination or react with scavengers or impurities. Thus the concentration of electrons will be a function of time, C(t) ) D(t)G(t), where D(t) is radiation dose and G(t) is the timedependent “yield”. The absorbance of the electrons will be recorded as a function of time giving A(t) ) εlC(t). In order to determine the extinction coefficient ε, we must be able to relate the concentration C(t) to the concentration of some known product which can be measured reliably. In general we will add a scavenger S to the solution which will accomplish the reaction (e-)aq + S f P. The product P will be measured after the transient absorption experiment by some appropriate analytical technique. Ideally the scavenger S will react only with hydrated electrons and not with any other transient in the system. The product P, as well as the scavenger S, must be stable under the conditions of interest. Assuming pseudo-first-order scavenging kinetics characterized by rate constant kS, the final concentration of product P will be the integral over time
[P]∞ )
∫-∞∞ kS[S]C(t) dt
(1)
Further, C(t) can be written as C°(t) exp(-kS[S]t), where the superscript ° denotes the time-dependent (e-)aq concentration in
the absence of the scavenger S. (It is important to note that C°(t) is completely arbitrary and may include other first-order scavenger or impurity reactions in addition to geminate or spur recombination. It includes the convolution of the radiation pulse D(t) with the response function G(t). However, it should not include second-order radical recombination reactions, so that low enough concentration should be generated experimentally to avoid any dose effect on the shape of the kinetics. Scavenger concentration should be low enough to avoid any effect of presolvated electron scavenging.24) Substituting, we arrive at
[P]∞ ) kS[S]
∫-∞∞ Co(t) exp(-kS[S]t) dt
(2)
Thus we need to relate the integral of the time-dependent concentration to the transient absorption A(t). If we integrate A(t), we have
Aint )
∫-∞∞ A(t) dt ) εl ∫-∞∞ Co(t) exp(-kS[S]t) dt (3)
Now by elimination of the integral over C(t) in eqs 2 and 3 we arrive at a simple relationship between product concentration and time-integrated absorbance:
εl[P]∞ ) kS[S]Aint
(4)
Regardless of the actual form of C°(t), integration of the transient absorbance and comparison of this integral with the final product yield allows determination of the extinction coefficient. It is not necessary to know the actual form of G(t), and one does not need to estimate the limiting escape yield G(∞). It is necessary to know the “scavenging power” kS[S], but this can most often be determined “in situ” by fitting the tail of the absorbance kinetics. The best practice will be to measure a suitable range of concentrations [S] and determine the scavenging rate constant under the conditions of the experiment. The advantage of this approach over those used in the past is that no radiation or photolysis dose needs to be measured. The product yield is directly compared to the absorbance in the same experiment, for whatever dose has been applied. Propagation of errors in measurement is correspondingly reduced. This is a significant advantage for radiolysis work at high temperatures where dose measurement is difficult, and one typically relies on dosimetry done at ambient conditions followed by an assumption of inverse proportionality to the fluid density to obtain the high temperature dose. The fluid density itself may fluctuate significantly in supercritical fluid experiments, and calculation of the density from equations of state requires very accurate measurement of both temperature and pressure. It is interesting to consider that measurement of the absorbance integral Aint also greatly reduces demands on the detector time response. A slow detector may not correctly resolve high frequency components of the function A(t), but the same fraction of photons is intercepted by the sample in an absorbance experiment regardless of the detector. The integrated transmittance change ∆(It/Io) must be conserved if the detector response is linear. Use of a slower but more sensitive detector may be very advantageous in improving the signal-to-noise ratio of the measurement.
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III. Experimental Section Radiolysis experiments were performed with 2-10 ns electron pulses from the 8 MeV Titan Beta linear accelerator at the Notre Dame Radiation Laboratory. A high pressure, high temperature cylindrical flow cell made of high nickel Hastelloy 276C alloy with 3 mm thick sapphire windows was employed in all experiments.25,26 The light path is 1.2 cm and the diameter of the cylinder is 4.00 mm, giving a total volume of 0.15 cm3. The electron pulse of approximately Gaussian cross section with 1 cm fwhm irradiates the cell perpendicular to the light path through a section of the cell body that is thinned to 2 mm thickness. SF6, 8% N2O in Ar, and Ar were all ultrahigh purity, obtained from Mittler Supply, Inc. Phenol and the disodium salt of methyl viologen were obtained from Sigma. KOH was obtained from Fisher. All chemicals were used as received. Type-I ASTM purified water (resistivity 18 MΩ cm, total organic carbon 0.7, and the similarity of this quantity to that of solvated electrons in ammonia was cited as proof that
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the absorbing species in water is also a solvated electron.3 Calculation of the experimental oscillator strength uses the relation (for decadic extinction coefficient in units of M-1 cm-1)
f)
4mec2ε0 2
NAe
(
× 2.303 × 103
) (
cm3 m × 10-2 L cm
) ∫ ε dν˜ ν˜
(12) f ) 4.32 × 10-9
∫ εν dν˜ ˜
(13)
where me is the mass of the electron, c is the speed of light, εo is the permittivity of free space, NA is Avogadro’s number, e is the charge of the electron, and the integral is over the absorption spectrum in wavenumbers.42,43 Determination of the total oscillator strength requires both a complete spectrum to integrate from zero to infinity and an absolute value for εe-. At room temperature the (e-)aq spectrum is described well by a Gaussian on the low energy side and a Lorentzian on the high energy side of the absorption maximum.5,7 Approximations must be used to calculate contributions from the last measured points of the spectrum to zero and to infinity.44,45,5,46,7 The most recent estimate of f for (e-)aq by Jou and Freeman yielded a value of 0.76 at room temperature, arrived at using εe-(720 nm) ) 19 000 M-1 cm-1.45,5 It has not been generally appreciated that the oscillator strength formula (eq 12) assumes unit refractive index; i.e., it is strictly valid only for gas phase species. Following earlier work of Dexter47,43 on atomic and color center absorption in crystals, Golden and Tuttle derived a one-electron model for the solvated electron absorption which relates moments of the spectrum to thermally averaged properties of the electron wave function.48 According to the moment analysis, the M(-1), M(0), and M(1) moments of the spectrum γ(ω) can be characterized with the following relationships (in atomic units):
M(-1) ) n0
∫0∞ ω-1γ(ω) dω ) 32 〈r2〉
M(0) ) n0
∫0∞ γ(ω) dω ) f ) 1
M(+1) ) n0
(14)
∫0∞ ωγ(ω) dω ) 34 〈T〉
〈r2〉 ) 〈|rav - r|2〉 is the thermally averaged dispersion in position or (squared) radius of gyration for the electron about its average position, n0 is the refractive index of the medium (averaged over the spectrum), and 〈T〉 is the corresponding kinetic energy. Thus, the oscillator strength integral (zeroth moment of the spectrum) requires a refractive index factor to correct for attenuation of the optical-frequency electric field by polarization of the medium. (The factor naturally falls out when the Einstein B-coefficient is derived in a dielectric medium.43) With the data available at the time, Golden and Tuttle determined that this relation holds, within error, for (e-)s in a variety of solvents, providing strong ex post facto justification of the one-electron treatment.48 Using a value of 1.3 for no and 0.76 for fvac (i.e., fvac is the result of eq 12) gives approximately unity for the product nofvac of the hydrated electron spectrum, in perfect agreement with the model of Golden and Tuttle. Using Jou and Freeman’s fitting functions and parameters,45,5 but our revised εe-(720 nm), we calculate fvac ) 0.85, which gives f ) nofvac ) 1.1. Even
truncating the integration at the end of the measured data (at 270 nm or 3.6 eV) yields fvac) 0.81 and thus a minimum value for nofvac of 1.08. A slightly more accurate (and rigorous) way of calculating Golden and Tuttle’s relationship is to include the refractive index inside the M(0) integral over γ(ω) rather than using an average value. This change will account for wavelengthdependent variations of no that might not be insignificant given the breadth of (e-)aq’s absorption spectrum. Using refractive index data from Harvey et al.49 and the fitting functions from Bartels et al.7 yields an integrated value of M(0) ) f ) 1.14. Consequently, we can now with complete confidence state that the integrated oscillator strength for the hydrated electron spectrum (properly corrected for the dielectric medium) is greater than unity. This can only happen if intensity is “borrowed” from the solvent electronic transitions, and it means that a correct description of the absorption spectrum is inherently a multielectron problem. This revelation may have more psychological than practical importance, as it merely confirms what is already obvious from the EPR resonance of the hydrated electron.50-52 The single motional-narrowed X-band resonance is shifted from the freeelectron position (g-factor 2.0005 rather than 2.0023), which can only come from mixing of the unpaired electron wave function with p-orbitals on water molecules in the solvation shell.51 It was estimated using model ab initio calculations that on the order of 10% of spin density must be shared by orbitals of the surrounding water molecules.51 Recently Shkrob and coworkers have reviewed the magnetic resonance, resonance Raman, and optical absorption evidence regarding electrons solvated in both amines and water.12,13 The thesis advanced is that in all cases the proper description of solvated electrons is of a multimer radical anion, with charge and spin shared between several solvent molecules. In water, much of the charge density resides in a “cavity” between the solvent molecules, but in amines the situation is more complicated. One-electron models which have been widely used for the last two decades, consisting of a quantized electron interacting via a pseudopotential with a classical MD solvent bath, omit any mixing of electron and solvent wave function by design.53-55 Such models are inadequate to describe the structural details revealed by magnetic resonance, particularly in ammonia, although in water these models seem to qualitatively capture many aspects of the system. The danger is that even in the most favorable water case, we train ourselves to think about the solvated electron in an oversimplified and perhaps even qualitatively incorrect way. Thus, our discovery of oscillator strength larger than unity serves to reinforce the conclusion that multielectron models56,57,13 are essential for a full understanding of the solvated electron properties. At the same time, a mere 10% deviation from unity probably does not invalidate the approximate measurements of hydrated electron radius of gyration and kinetic energy which have been derived from the moment theory.48,11,58,7 A further test of the optical spectrum and its implications comes from the temperature dependence of oscillator strength. That is, in the one-electron model the moment M(0) is assumed to remain constant as a function of temperature, which implies a change in εe at the absorption maximum as the spectrum shifts. One can calculate from the spectrum what εe- needs to be in order for M(0) to be conserved. Using the fit functions reported in ref 7, we calculated the spectra up to 350 °C. Above 250 °C in H2O, the red edge of the spectrum is significantly obscured, and therefore the Gaussian width from a fit of the spectrum in D2O was used. A power law with exponent -3.5 was used to extrapolate the spectrum at energies above 3.6 eV.59 Spectra
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were multiplied by the refractive index given in ref 49, and the results were integrated from 0.4 to 6.5 eV to obtain the mediumcorrected oscillator strength f. Oscillator strengths were normalized to the 25 °C value, and εe-’s at the absorption maximum were calculated. The resulting predicted epsilon is included in Figure 4 as the black diamonds. The agreement with experiment is exceptional over the entire temperature range. Because of the large number of parameters in the spectral fitting function, the prediction from oscillator strength conservation has considerable uncertainty to it, especially at higher temperatures. To estimate the possible error, extremes in the Gaussian width, cut-on energy of the power law, and power law exponent that could provide reasonable fits to the data were chosen by eye, with the resulting range of εe- shown as the gray region in Figure 4. Overall, the good agreement between the best guess from the spectrum shape and the experimental values suggests that total oscillator strength is indeed conserved to high temperatures. An attempt was made to fit spectra in the supercritical regime in order to determine if the oscillator strength continues to be conserved here as well. One might expect a change in the nature of the solvated electrons, from bulk species at high density to “surface” species at low density. Perhaps the simple bulk refractive index correction of the optical electric field is no longer adequate. Spectra in D2O from ref 7 were calculated using the fit function from the same reference. The resulting predictions for ε(1000 nm) are found as the line in Figure 5. However, the mismatch between D2O and H2O in this regime and the poor coverage of spectra mean that little can be concluded from this comparison. More data in the supercritical regime (both measurements and full spectra) are required. VI. Conclusion Measurement of the hydrated electron extinction coefficient at the absorption maximum has been carried out up to 350 °C, independent of any assumed radiation or photochemical yields. The room temperature result is 10-20% higher than numbers which have been accepted in previous decades,14,15 and results for higher temperatures are similarly larger than those reported previously.16,17 We demonstrate that use of a correct radiolysis escape yield rather than scavenged product yield for the hydrated electron to interpret earlier experiments is consistent with our measurement; this independently confirms the system of dosimetry revised by Buxton and Stuart,23 which is now in common use for pulse radiolysis experiments. Determination of εe- over a large temperature range opens up the use of (e-)aq as a dosimeter in high temperature and pressure water and allows the accurate determination of second-order recombination reaction rates.41 The total oscillator strength of the hydrated electron spectrum at room temperature, corrected for the refractive index of solvent, is estimated to be 1.14 and appears to be conserved to high temperature. Even when the room temperature spectrum is truncated at an observation limit of 3.6 eV, the observed partial oscillator strength is 1.08. We can assert with perfect confidence that the oscillator strength is greater than unity, which means that intensity is “borrowed” from electrons of the solvent. It is interesting to contemplate whether this realization would have made a difference in the long-running debate concerning the “cavity” vs “solvent anion” nature of hydrated electrons, if the correct extinction coefficient had been reported in the 1960s. Virtually every model of solvated electron which has ever been presented was justified by its ability to reproduce the optical absorption spectrum,60,61,48,62,54,63 but a cavity model, or a modern single electron/pseudopotential model, clearly cannot produce
Hare et al. oscillator strength greater than unity. The result reinforces the arguments recently presented by Shkrob and co-workers on the basis of the magnetic resonance evidence,12,13 that all solvated electrons, even in water, should really be viewed as multimersolvent anions. Acknowledgment. The authors acknowledge valuable conversations with Dr. Daniel Chipman of the Notre Dame Radiation Laboratory and with Dr. Ilya Shkrob of Argonne National Laboratory. References and Notes (1) Rabani, J.; Mulac, W. A.; Matheson, M. S. J. Phys. Chem. 1965, 69, 53. (2) Marin, T. W.; Takahashi, K.; Jonah, C. D.; Chemerisov, S. D.; Bartels, D. M. J. Phys. Chem. A 2007, 111, 11540. (3) Hart, E. J.; Anbar, M. The Hydrated Electron; Wiley-Interscience: New York, 1970. (4) Michael, B. D.; Hart, E. J.; Schmidt, K. H. J. Phys. Chem. 1971, 75, 2798. (5) Jou, F. Y.; Freeman, G. R. J. Phys. Chem. 1979, 83, 2383. (6) Wu, G. Z.; Katsumura, Y.; Muroya, Y.; Li, X. F.; Terada, Y. Radiat. Phys. Chem. 2001, 60, 395. (7) Bartels, D. M.; Takahashi, K.; Cline, J. A.; Marin, T. W.; Jonah, C. D. J. Phys. Chem. A 2005, 109, 1299. (8) Hare, P. M.; Price, E. A.; Bartels, D. M. J. Phys. Chem. A 2008, 112, 6800. (9) Boag, J. W.; Hart, E. J. Nature 1963, 197, 45. (10) Hameka, H. F.; Robinson, G. W.; Marsden, C. J. J. Phys. Chem. 1987, 91, 3150. (11) Tuttle, T. R.; Golden, S. J. Phys. Chem. 1991, 95, 5725. (12) Shkrob, I. A. J. Phys. Chem. A 2007, 111, 5223. (13) Shkrob, I. A.; Glover, W. J.; Larsen, R. E.; Schwartz, B. J. J. Phys. Chem. A 2007, 111, 5232. (14) Fielden, E. M.; Hart, E. J. Radiat. Res. 1967, 32, 564. (15) Jha, K. N.; Bolton, G. L.; Freeman, G. R. J. Phys. Chem. 1972, 76, 3876. (16) Elliot, A. J.; Ouellette, D. C. J. Chem. Soc., Faraday Trans. 1994, 90, 837. (17) Elliot, A. J.; Ouellette, D. C.; Stuart, C. R. The Temperature Dependence of the Rate Constants and Yields for the Simulation of the Radiolysis of HeaVy Water; Report AECL-11658, AECL: Chalk River, Ontario, Canada, 1996. (18) Draganic, I. G.; Draganic, Z. D. The Radiation Chemistry of Water; Academic Press: New York, 1971. (19) Radiation Chemistry: Principles and Applications; Farhataziz; Rogers, M. A. J., Eds.; VCH Publishers: New York, 1987. (20) Spinks, J. W. T.; Woods, R. J. An Introduction to Radiation Chemistry, 3rd ed.; Wiley Interscience, New York, 1990. (21) Laverne, J. A.; Pimblott, S. M. J. Phys. Chem. 1991, 95, 3196. (22) Bartels, D. M.; Cook, A. R.; Mudaliar, M.; Jonah, C. D. J. Phys. Chem. A 2000, 104, 1686. (23) Buxton, G. V.; Stuart, C. R. J. Chem. Soc., Faraday Trans. 1995, 91, 279. (24) Jonah, C. D.; Miller, J. R.; Matheson, M. S. J. Phys. Chem. 1977, 81, 1618. (25) Takahashi, K.; Cline, J. A.; Bartels, D. M.; Jonah, C. D. ReV. Sci. Instrum. 2000, 71, 3345. (26) Bonin, J.; Janik, I.; Janik, D.; Bartels, D. M. J. Phys. Chem. A 2007, 111, 1869. (27) Janik, I.; Bartels, D. M.; Jonah, C. D. J. Phys. Chem. A 2007, 111, 1835. (28) Cline, J. A.; Jonah, C. D.; Bartels, D. M. ReV. Sci. Instrum. 2002, 73, 3908. (29) Janik, D.; Janik, I.; Bartels, D. M. J. Phys. Chem. A 2007, 111, 7777. (30) Buxton, G. V.; Greenstock, C. L.; Helman, W. P.; Ross, A. B. J. Phys. Chem. Ref. Data 1988, 17, 513. (31) Czapski, G.; Peled, E. Isr. J. Chem. 1968, 6, 421. (32) Takahashi, K. J.; Ohgami, S.; Koyama, Y.; Sawamura, S.; Marin, T. W.; Bartels, D. M.; Jonah, C. D. Chem. Phys. Lett. 2004, 383, 445. (33) Lian, R.; Crowell, R. A.; Shkrob, I. A. J. Phys. Chem. A 2005, 109, 1510. (34) Asmus, K. D.; Gruenbein, W.; Fendler, J. H. J. Am. Chem. Soc. 1970, 92, 2625. (35) Cline, J.; Takahashi, K.; Marin, T. W.; Jonah, C. D.; Bartels, D. M. J. Phys. Chem. A 2002, 106, 12260. (36) Solar, S.; Solar, W.; Getoff, N.; Holcman, J.; Sehested, K. J. Chem. Soc., Faraday Trans. 1 1982, 78, 2467.
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JP909789B
