- Email: [email protected]
Formation and solvation dynamics of electrons in polyols
Journal of Molecular Liquids 141 (2008) 124 – 129 www.elsevier.com/locate/molliq
Formation and solvation dynamics of electrons in polyols I. Lampre ⁎, J. Bonin 1 , B. Soroushian, P. Pernot, M. Mostafavi Laboratoire de Chimie Physique/ELYSE, Univ Paris-Sud, UMR 8000, Bât. 349, Orsay, F-91405, France CNRS, Orsay, F-91405, France Available online 18 April 2008
Abstract Using pump-probe transient absorption spectroscopy we studied the solvation dynamics of the electron in liquid polyalcohols: ethane-1,2-diol, propane-1,2-diol, propane-1,3-diol and propane-1,2,3-triol. First, transmission measurements allowed us to assess that electrons were produced via two-photon ionization of the solvent with 263 nm femtosecond laser pulses, and to determine the two-photon absorption coefficient of the polyols. Second, time-resolved absorption spectra ranging from 440 to 710 nm were measured. Our study shows that the excess electron in the diols presents an intense and wide absorption band in the visible and near-IR spectral domain at early time after photoionization. Then, for the first tens of picoseconds the electron spectrum shifts toward the blue domain and its bandwidth decreases as the red part of the initial spectrum drops rapidly while the blue part hardly evolves. Using Bayesian data analysis method, the observed picosecond solvation dynamics were reconstructed with three models: a two-step mechanism and two continuous relaxation models. Comparison between the ability of models to reproduce the experimental kinetics is in favor of a heterogeneous continuous relaxation. Recent results obtained in propane-1,2,3-triol show that the electron solvation dynamics is very fast in this solvent despite its high viscosity and highlight the role of the OH group in that process. © 2008 Elsevier B.V. All rights reserved. Keywords: Solvated electron; Solvation dynamics; Photoionization; Alcohols
1. Introduction Since the optical characterization of the solvated electron by pulse radiolysis transient absorption measurements in water [1–4], a large number of time-resolved experiments were carried out to clarify the relaxation dynamics of the solvated electron. The first experimental studies of the formation dynamics of electrons in liquids started with electron pulse radiolysis experiments in alcohols, first in the nanosecond time range at low temperature [5] then, in the picosecond time range [6,7]. Picosecond laser studies of electron solvation in alcohols were also done [8–10] and thanks to the developments of laser techniques with a better time resolution, the ultrafast dynamics of the solvated electron was studied by femtosecond time⁎ Corresponding author. Laboratoire de Chimie Physique/ELYSE, Univ Paris-Sud, UMR 8000, Bât. 349, Orsay, F-91405, France. Tel.: +33 1 6915 4511; fax: +33 1 6915 6188. E-mail address: [email protected] (I. Lampre). 1 Present address: Laboratoire d'Electrochimie Moléculaire, Université Paris 7- Denis Diderot, 2 place Jussieu, 75251 Paris cedex 05, France. 0167-7322/$ - see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2008.01.017
resolved absorption spectroscopy with use of two-[11–25] or three-pulse sequences [26–30]. The pioneering work of Migus et al. [11] in water showed that the solvation process is complete in a few hundreds of picoseconds and hinted at the existence of short-lived precursors of the solvated electron, absorbing in the infrared spectral domain. Such precursors had already been suggested from picosecond experiments in alcohols [6]. So, subsequent studies often depicted the electron solvation process by stepwise mechanisms with several electron precursors, each precursor having a fixed, individual spectrum [10,12,13,15,16,24,26,30,31]. However, other works on electron solvation favored the so-called “continuous shift” model in which only one localized electron is considered but its spectrum, as a whole, shifts to the blue (short wavelengths) during the solvation [21–23]. In alcohols, the formation of the solvated electron is slower than in water; the duration increased with the size of the nalcohol molecule [6,7,15,20] but also depends on the number of OH groups [6]. So, to get a better insight into the solvation processes and precursor states, using femtosecond pump-probe spectroscopy we have investigated the solvation dynamics of
I. Lampre et al. / Journal of Molecular Liquids 141 (2008) 124–129
the electron in liquid polyols: ethane-1,2-diol (12ED, ethylene glycol), propane-1,2-diol (12PD, propylene glycol), propane-1, 3-diol (13PD, trimethylene glycol) and lately propane-1,2,3-triol (123PT, glycerol). The choice of the polyols comes from their relatively high viscosity, slowing down any diffusion controlled process, and the presence of several hydroxyl groups, allowing investigation of the influence of the number and the distance between hydroxyl groups on the electron solvation process. In addition, the absorption spectrum of the solvated electron in these solvents is localized in the visible spectral domain. To study the formation of the solvated electron in these alcohols, time-resolved absorption spectra from 440 to 710 nm were registered for the electron generated by photoionization of the solvent. In that paper, we resume our previous published works on ethane-1,2-diol [32] and both propanediols [33] and we report new results on propanetriol. We show that the photoinization of the polyols corresponds to a two-photon absorption process. Then, the temporal evolution of the recorded spectra is described and analyzed, in the case of the diols, with three solvation models: a two-step mechanism and two continuous relaxation models. The results obtained for the different polyols are compared and discussed. 2. Experimental method Experiments were performed using a system already described in details elsewhere [32]. Briefly, the output of an
125
amplified kilohertz femtosecond Ti:Sa laser system (Spectra physics) was split into two parts to generate the pump and probe pulses. The pump beam at 263 nm was produced by frequency doubling and sum-frequency mixing in two BBO crystals of 90% of the fundamental beam. It was then focused on a 300 μm thick liquid jet in order to produce electrons by photoionization of the solvent. The remaining 10% of the fundamental beam at 790 nm was directed to a variable optical delay line and focused on a 3 mm sapphire disk to generate a white-light continuum. The latter was then divided into a probe and a reference beam by a broad band beam-splitter. The probe beam was focused onto the liquid jet sample. Then, it was dispersed on a polychromator and detected on a CCD camera (Princeton Instrument) with a resolution of 0.2 nm per pixel, simultaneously with the reference beam to take into account any laser fluctuations. Time-resolved spectra were recorded from 440 to 720 nm and corrected for the group velocity dispersion. The pump pulse duration and energy was about 210 fs full width at halfmaximum and 20 μJ, respectively. The estimated diameter of the pump and probe beams on the jet was usually around 500 μm and 50 μm, respectively. Both pump and probe beams had the same vertical s-polarization. Ethane-1,2-diol, propane-1,2-diol and propane-1,2,3-triol from Aldrich (ACS Reagent) and propane-1,3-diol from Fluka (GC Grade) were used without further purification. Experiments were performed at 295 K except for propanetriol. The high viscosity of this solvent at room temperature (around 1000 cP)
Fig. 1. Transmittance of the 300 μm liquid jet versus the peak intensity of the 220 fs pump pulse at 263 nm for the four studied polyols: (a) ethane-1,2-diol, (b) propane1,2,3-triol, (c) propane-1,2-diol, (d) propane-1,3-diol (symbol, experimental data for different beam diameters; lines, calculated curves for different values of β).
126
I. Lampre et al. / Journal of Molecular Liquids 141 (2008) 124–129
Table 1 Two-photon absorption coefficient β at 263 nm of the four polyols deduced from the data in Fig. 1 Solvent − 11
β (10
−1
mW )
12ED
12PD
13PD
123PT
2.1 ± 0.2
2.0 ± 0.3
2.4 ± 0.3
3.5 ± 0.5
made it impossible to form a liquid jet with our circulating system; so, propanetriol was heated up to 333 K to reduce its viscosity down to 76 cP and to create the jet. 3. Results and discussion As electrons generated by different photo-processes have different thermalization and geminate recombination, it is worth identifying the number of photons involved in the ionization of the polyols in our experiments. The ionization threshold of the studied polyols is around 8.2 eV [34]. Since the energy of 263 nm photons is 4.7 eV, the ionization should occur by a two-photon absorption mechanism. The transmittance of the liquid jet versus the peak power of the 263 nm pump beam presents a similar evolution for the four alcohols (Fig. 1) and is characteristic of a single-beam two-photon absorption. From the fit of the data, we determine the two-photon absorption coefficient β of the polyols at 263 nm (Table 1). The values obtained for the diols are very similar and slightly lower than the value found for the propanetriol. These values are of the same order of magnitude than that found for water (β = (1.8 ± 0.1) × 10− 11 m W− 1) at 266 nm with 100 fs pulses [35].
Fig. 2 depicts the time evolution of the absorption spectra recorded in the four polyols after photoionization of the solvent at 263 nm. At very short time delay after the pump pulse, the excess electron in 12ED presents a very broad absorption band in the visible and near-IR domain with a peak maximum around 675 nm (Fig. 2a). The red part of the spectrum then drops rapidly for the first 5 ps while the blue part increases slightly, leading to a blue shift of the absorption maximum down to 590 nm. The absorbance on the red side of the spectrum follows its decrease while the absorbance on the blue side remains nearly constant. Consequently, the absorption band maximum continues to shift toward shorter wavelengths and, 50 ps after the pump pulse, is around 570 nm, the position of the absorption band maximum of the equilibrated solvated electron in 12ED. The excess electron in both 12PD and 13PD shows a similar behaviour as that in 12ED but on a longer time scale. Indeed, the excess electron in both PD presents a wide absorption band in the visible and near-IR domain at very short time delays after the pump pulse (Fig. 2c and d). The time-resolved spectra reveal that the main change also occurs in the red part of the absorption spectra and indicate that a localized electron, absorbing in the blue spectral domain, is promptly formed and relaxes to the equilibrated solvated electron in a couple of tens of picoseconds. In contrast to the diols, even at very short time after the pump pulse, no significant absorption in the IR domain is observed in the case of 123PT, as the absorption band maximum is already located in the visible domain. The maximum is around 580 nm, very close to the position of the absorption band
Fig. 2. Time evolution of the absorption spectrum obtained in the four studied polyols upon two-photon ionization of the solvent at 263 nm (peak intensity around 0.05 TW cm− 2): (a) ethane-1,2-diol, (b) propane-1,2,3-triol, (c) propane-1,2-diol, (d) propane-1,3-diol (solid lines through experimental points are guides for the eyes).
I. Lampre et al. / Journal of Molecular Liquids 141 (2008) 124–129
127
Table 2 Comparison between the three models used to fit the experimental data on the solvation of electron in ethane-1,2-diol and propanediols Solvent 12ED
12PD
13PD
Model name
Scheme
Comments
Nθa
Rms (10− 3)b
IBc
STEP3P CREX2 CRELH STEP3P CREX2 CRELH STEP3P CREX2 CRELH
e−wb→e−sb→e−s e−wb– – →e−s e−wb– – →e−s e−wb→e−sb→e−s e−wb– – →e−s e−wb– – →e−s e−wb→e−sb→e−s e−wb– – →e−s e−wb– – →e−s
Two-step process Bi-exponential relaxation Heterogeneous relaxation Two-step process Bi-exponential relaxation Heterogeneous relaxation Two-step process Bi-exponential relaxation Heterogeneous relaxation
9 10 10 10 12 10 10 12 10
2.56 2.47 2.50 4.45 4.12 4.39 3.24 3.15 3.18
13,509 13,846 13,730 7409 8010 7517 10,332 10,575 10,490
a
Number of adjusted parameters; broot mean square; cBayes Information criterion.
maximum of the equilibrated solvated electron in 123PT at 333 K (∼ 550 nm) [36]. From 1 to 100 ps, a decrease in the red part of the spectrum occurs without any significant change in the blue side. At longer time (N 50 ps for 12ED, N 100 ps for 12PD, 13PD and 123PT), the position and the shape of the electron spectrum in each solvent hardly change but its whole intensity diminishes due to geminate recombination. Many models have been proposed to explain experimental results on the electron solvation and relaxation. In our study on the solvation dynamics of the electron in 12ED [32], we analyzed our spectro-kinetics signals with various approaches and tested eleven models based on sequential stepwise mechanisms, continuous relaxation or combination of both processes. For the analysis of the data obtained in both PD [33], we retained only the three models which had given a good quality fit with a minimum number of adjustable parameters i.e. a two-step model (STEP3P), a heterogeneous continuous relaxation model (CRELH) and a bi-exponential continuous relaxation model (CREX2). The data analysis was performed over the first 50 ps or 100 ps for 12ED and both PD, respectively, in order to neglect geminate recombination. Consequently, in the models, the solvated electron, the final species is considered to be stable with an infinite lifetime and its spectrum is explicitly introduced. For the sequential stepwise mechanism (STEP3P), only two steps and three species are necessary but sufficient to accurately fit − the data: a weakly-bound electron, ewb , converts into a strongly − bound electron, esb, which gives the solvated electron es−. Each considered species is supposed to have a time-dependent concentration ck(t) and a fixed and individual spectrum εk(E) modeled by a lognormal shape function S: ek ð E Þ ¼ ek S E; Emax;k ; Xk ; gk
t0(E) corresponds to the group velocity dispersion curve in energy space and G (t;t0,γ,α) denotes a generalized Gaussian function: a t t0 G ðt; t0 ; g; aÞ ¼ exp g
where S is parameterized by the peak position in energy Emax, the full width at half-maximum Ω and the asymmetry factor γ. So, the time-dependent absorbance is written:
CREX2
3 pffiffiffiffiffiffiffiffiffi X Aðt; E Þ ¼ G t; t0 ð EÞ; r= 4ln2; 2 ck ð t Þ e k ð E Þ k¼1
pffiffiffiffiffiffiffiffiffi where G t; t0 ð EÞ; r= 4ln2; 2 represents the instrumental response function and ⊗ stand for the convolution operator;
j
j
The continuous relaxation models consider a single species whose spectrum undergoes a continuous evolution. In our models, not only the position but also the shape of the absorption spectrum may change during the solvation process. The time-dependent absorption spectrum is then described by a lognormal function with time-dependent parameters: pffiffiffiffiffiffiffiffiffi Aðt; E Þ ¼ G t; t0 ð E Þ; r= 4ln2; 2 ½c0 eðt Þ S ð E; Emax ðtÞ; Xðt Þ; gðt ÞÞ
The time-dependence of each parameter (x = ε, Emax, Ω, γ) is modeled either by a bi-exponential function (CREX2): xðt Þ ¼ xl þ Dx;1 G t; 0; sx;1 ; 1 þ Dx;2 G t; 0; sx;2 ; 1 Or by a stretched exponential function (CRELH): xðt Þ ¼ xl þ Dx G ðt; 0; sx ; bx Þ;
0 b bx V 1
The results of the Bayesian data analysis with the different models are reported in Table 2. The three models provide good fits of our spectro-kinetics signals for all the diols (rms b 4.5 × 10− 3). Table 3 Comparison between the characteristic times obtained by STEP3P and CREX2 models used to fit the experimental data on the solvation of electron in ethane-1,2-diol and propanediols Solvent
12ED
12PD
13PD
Viscosity (cP)
η = 16
η = 40
η = 39
1.3 ± 0.1 25.0 ± 0.2 1.0 ± 0.1 1.7 ± 0.1 25.5 ± 0.3 22.5 τEmax1 τEmax2 23.5 τEmax1 τEmax2 24.5
4.5 ± 0.1 54.6 ± 0.5 5.6 ± 0.1 0.6 ± 0.1 27.5 ± 0.7 25.3 1.0 ± 0.1 75.9 ± 3.5 72.5 19.8 ± 1.0 – 19.8
3.2 ± 0.1 34.6 ± 0.7 2.9 ± 0.1 0.2 ± 0.1 20.6 ± 0.7 19.6 2.6 ± 0.6 40.5 ± 1.4 39 13.6 ± 1.6 – 13.6
STEP3P
e−wb e−sb
ε Emax Ω γ
τ1 (ps) τ2 (ps) τε (ps) τEmax1 (ps) τEmax2 (ps) bτEmaxN (ps) τΩ1 (ps) τΩ2 (ps) bτΩ1N (ps) τγ1 (ps) τγ2 (ps) bτγ1N (ps)
128
I. Lampre et al. / Journal of Molecular Liquids 141 (2008) 124–129
As the number of adjustable parameters is not identical for the three models, the Bayes criteria, IB, confirms that the best fit of our data is obtained with CREX2 whatever the diol. Even if stretched exponential functions are often used to describe nonexponential behavior of complex dynamics found in liquids or glasses, the physical meaning of the parameters (relaxation time tx and heterogeneity constant βx) and the derived average times is not obvious. Consequently, hereafter, we will focus only on the results of STEP3P and CREX2 (Table 3). Both models indicate, as expected from the experimental observation, that the electron solvation dynamics is faster in 12ED than in PD. In the case of 12ED, the CREX2 model leads to the same two characteristic times for the parameters Emax, Ω and γ, except ε which follows a mono-exponential evolution with a time constant of 1 ps. The two time constants (τEmax1 = τΩ1 = tγ1 = 1.7 ps and τEmax2 = τΩ2 = tγ2 = 25.5 ps) are close to the lifetimes of the intermediate species found with STEP3P (τ1 = 1.3 ps and τ2 = 25.0 ps). So, it is possible to extract two characteristic times for the electron solvation in 12ED. In the case of both PD, as for 12ED, the kinetics of ε appear to be mono-exponential with a time constant τε of 5.6 and 2.9 ps for 12PD and 13PD, respectively. These values are close to the lifetime τ1 determined by STEP3P (4.5 and 3.2 ps for 12PD and 13PD, respectively). Unlike 12ED, for the other parameters, the adjustments by CREX2 do not lead to similar characteristic times. The asymmetry factor γ evolves according a monoexponential with a time constant of 19.8 and 13.6 ps for 12PD and 13PD, respectively. The behaviors of Emax and Ω are bi-exponential with time constants τEmax1 = 0.6 ps, τEmax2 = 27.5 ps, τΩ1 = 1.0 ps, τΩ2 = 75.9 ps for 12PD, and τEmax1 = 0.2 ps, τEmax2 = 20.6 ps, τΩ1 = 2.6 ps and τΩ2 =40.5 ps for 13PD. For both PD, the τx1 values are short, lower than the lifetime τ1 obtained by STEP3P, while the τx2 values surround the lifetime τ2: τEmax2 b τ2 b τΩ2. However, whatever the parameter, the average lifetime bτxN is longer for 12PD than for 13PD, indicating a faster solvation process in 13PD compared to 12PD. That difference cannot be related to viscosity as the two solvents have almost the same viscosity at room temperature (39 and 40 cP, respectively), but must involve the molecular structure. The slower solvation dynamics corresponds to the vicinal diol 12PD. That suggests greater molecular changes in close proximity to the electron site, which have longer range effects. For instance, that may indicate a different number of first-solvation shell molecules, insofar as only one or both of the OH groups of the diol molecule may be involved in the electron cavity. The Bayesian data analysis of the signals obtained in 123PT is in progress and characteristic times should be published soon. Nevertheless, from the experimental data (Fig. 2) if we compare the time evolution of the excess electron absorption band for the four polyols, we observe that, in spite of the higher viscosity of 123PT at 333 K (76 cP) than that of both PD at room temperature, the solvation dynamics is faster in 123PT than in PD. In particular, the position of the absorption band maximum of the fully solvated electron is reached much more rapidly in the case of 123PT compared to the other diols, even 12ED. These observations clearly show that the solvation dynamics in the polyols cannot be explained by the viscosity alone but greatly depends on the molecular structure of the solvent.
Indeed, 123PT is a highly viscous solvent but with a high hydrogen bond density since the molecule has three hydroxyl groups in vicinity in its molecular structure. Theoretical works have pointed out the role of the microscopic structure of the liquid [37] and the importance of the coupling between the excess electron and the solvent intramolecular modes on the absorption band of the excess electron both in the visible and near-IR domain [38–41]. So, the solvated electron dynamics is mainly governed by the vibrational properties of matrices in which the electron is trapped. Recent results on resonance Raman experiments also support this description [42–44]. The theoretical approaches lead to two kinds of trapped electrons in alcohols, already postulated [6,45,46]: visible absorbing electrons associated with hydroxyl traps and IR-absorbing electrons trapped by the alkyl group. Their existence, respectively where the paraffinic and the hydroxyl groups are locally concentrated, had been evidenced at 77 K for monohydroxy-alcohols but not for polyhydroxyalcohols, indicating that, in the latter solvents, the phase is not segregated into polar and non-polar regions owing to the abundance of the H-bonds [45]. Consequently, we can consider that the time evolution of the spectra of excess electrons we observed in polyols is not due to a conversion from an electron trapped by alkyl groups to an electron trapped by hydroxyl groups but it is related to vibronic coupling and vibrational relaxation in the first-solvation shell molecules. That is corroborated by the results in 123PT. In that solvent, any significant absorption band in the near-IR is observed indicating a strong association of the electron with the hydroxyl traps. To conclude, our results on the solvation dynamics of electrons in polyols give evidence of the continuous character of the solvation process. The main kinetic factor is not the viscosity but the molecular structure of the solvent; in particular, the OH group density appears to be an important parameter. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
E.J. Hart, J.W. Boag, J. Am. Chem. Soc. 84 (1962) 4090. J.W. Boag, E.J. Hart, Nature 197 (1963) 45. J.P. Keene, Nature 197 (1963) 47. E.J. Hart, M. Anbar, The Hydrated Electron, 1970 New-York. J.H. Baxendale, P. Wardman, Nature 230 (1971) 449. W.J. Chase, J.W. Hunt, J. Phys. Chem. 79 (1975) 2835. G.A. Kenney-Wallace, C.D. Jonah, J. Phys. Chem. 86 (1982) 2572. F. Wang, R. Pottel, U. Kaatze, J. Phys. Chem., B 101 (1997) 922. H. Miyasaka, H. Masuhara, N. Mataga, Laser Chem. 7 (1987) 119. Y. Hirata, N. Mataga, J. Phys. Chem. 94 (1990) 8503. A. Migus, Y. Gauduel, J.L. Martin, A. Antonetti, Phys. Rev. Lett. 58 (1987) 1559. F.H. Long, H. Lu, K.B. Eisenthal, Phys. Rev. Lett. 64 (1990) 1469. M. Sander, U. Brummund, K. Luther, J. Troe, Ber. Bunsenges. Phys. Chem. 96 (1992) 1486. C. Pépin, T. Goulet, D. Houde, J.-P. Jay-Gerin, J. Phys. Chem. 98 (1994) 7009. X. Shi, F.H. Long, H. Lu, K.B. Eisenthal, J. Phys. Chem. 99 (1995) 6917. A. Reuther, A. Laubereau, D.N. Nikogosyan, J. Phys. Chem. 100 (1996) 16794. R.A. Crowell, D.M. Bartels, J. Phys. Chem. 100 (1996) 17940. L. Turi, P. Holpar, E. Keszei, J. Phys. Chem., A 101 (1997) 5469. C. Pépin, T. Goulet, D. Houde, J.-P. Jay-Gerin, J. Phys. Chem., A 101 (1997) 4351.
I. Lampre et al. / Journal of Molecular Liquids 141 (2008) 124–129 [20] T. Goulet, C. Pépin, D. Houde, J.-P. Jay-Gerin, Radiat. Phys. Chem. 54 (1999) 441. [21] A. Hertwig, H. Hippler, A.-N. Unterreiner, Phys. Chem. Chem. Phys. 1 (1999) 5633. [22] D. Madsen, C.L. Thomsen, J. Thogersen, S.R. Keiding, J. Chem. Phys. 113 (2000) 1126. [23] J.A. Kloepfer, V.H. Vilchiz, V.A. Lenchenkov, A.C. Germaine, S.E. Bradforth, J. Chem. Phys. 113 (2000) 6288. [24] T. Scheidt, R. Laenen, Chem. Phys. Lett. 371 (2003) 445. [25] R. Lian, R.A. Crowell, I.A. Shkrob, J. Phys. Chem., A 109 (2005) 1510. [26] M. Assel, R. Laenen, A. Laubereau, J. Chem. Phys. 111 (1999) 6869. [27] C. Silva, P.K. Walhout, P.J. Reid, P.F. Barbara, J. Phys. Chem., A 102 (1998) 5701. [28] C. Silva, P.K. Walhout, K. Yokoyama, P.F. Barbara, Phys. Rev. Lett. 80 (1998) 1086. [29] M.F. Emde, A. Baltuska, A. Kummrow, M.S. Pshenichnikov, D.A. Wiersma, Phys. Rev. Lett. 80 (1998) 4645. [30] A. Thaller, R. Laenen, A. Laubereau, J. Chem. Phys. 124 (2006) 024515. [31] P. Holpar, T. Megyes, E. Keszei, Radiat. Phys. Chem. 55 (1999) 573. [32] B. Soroushian, I. Lampre, J. Bonin, P. Pernot, S. Pommeret, M. Mostafavi, J. Phys. Chem., A 110 (2006) 1705.
129
[33] J. Bonin, I. Lampre, P. Pernot, M. Mostafavi, J. Phys. Chem., A 111 (2007) 4902. [34] J.-M. Jung, in, University Louis Pasteur, Strasbourg I, France, 2003. [35] S. Pommeret, F. Gobert, M. Mostafavi, I. Lampre, J.-C. Mialocq, J. Phys. Chem., A 105 (2001) 11400. [36] N. Chandrasekhar, P. Krebs, A.-N. Unterreiner, J. Chem. Phys. 125 (2006) 164512-164511–164512-164517. [37] M. Hilczer, M. Steblecka, Radiat. Phys. Chem. 67 (2003) 263. [38] H. Abramczyk, J. Phys. Chem. 95 (1991) 6149. [39] H. Abramczyk, J. Kroh, J. Phys. Chem. 95 (1991) 6155. [40] H. Abramczyk, J. Kroh, Radiat. Phys. Chem. 39 (1992) 99. [41] H. Abramczyk, J. Kroh, Radiat. Phys. Chem. 43 (1994) 291. [42] M.J. Tauber, R.A. Mathies, Chem. Phys. Lett. 354 (2002) 518. [43] M.J. Tauber, R.A. Mathies, J. Am. Chem. Soc. 125 (2003) 1394. [44] M.J. Tauber, C.M. Stuart, R.A. Mathies, J. Am. Chem. Soc. 126 (2004) 3414. [45] T. Shida, S. Iwata, T. Watanabe, J. Phys. Chem. 76 (1972) 3683. [46] M. Ogasawara, K. Shimizu, H. Yoshida, Radiat. Phys. Chem. 17 (1981) 331.
Formation and solvation dynamics of electrons in polyols I. Lampre ⁎, J. Bonin 1 , B. Soroushian, P. Pernot, M. Mostafavi Laboratoire de Chimie Physique/ELYSE, Univ Paris-Sud, UMR 8000, Bât. 349, Orsay, F-91405, France CNRS, Orsay, F-91405, France Available online 18 April 2008
Abstract Using pump-probe transient absorption spectroscopy we studied the solvation dynamics of the electron in liquid polyalcohols: ethane-1,2-diol, propane-1,2-diol, propane-1,3-diol and propane-1,2,3-triol. First, transmission measurements allowed us to assess that electrons were produced via two-photon ionization of the solvent with 263 nm femtosecond laser pulses, and to determine the two-photon absorption coefficient of the polyols. Second, time-resolved absorption spectra ranging from 440 to 710 nm were measured. Our study shows that the excess electron in the diols presents an intense and wide absorption band in the visible and near-IR spectral domain at early time after photoionization. Then, for the first tens of picoseconds the electron spectrum shifts toward the blue domain and its bandwidth decreases as the red part of the initial spectrum drops rapidly while the blue part hardly evolves. Using Bayesian data analysis method, the observed picosecond solvation dynamics were reconstructed with three models: a two-step mechanism and two continuous relaxation models. Comparison between the ability of models to reproduce the experimental kinetics is in favor of a heterogeneous continuous relaxation. Recent results obtained in propane-1,2,3-triol show that the electron solvation dynamics is very fast in this solvent despite its high viscosity and highlight the role of the OH group in that process. © 2008 Elsevier B.V. All rights reserved. Keywords: Solvated electron; Solvation dynamics; Photoionization; Alcohols
1. Introduction Since the optical characterization of the solvated electron by pulse radiolysis transient absorption measurements in water [1–4], a large number of time-resolved experiments were carried out to clarify the relaxation dynamics of the solvated electron. The first experimental studies of the formation dynamics of electrons in liquids started with electron pulse radiolysis experiments in alcohols, first in the nanosecond time range at low temperature [5] then, in the picosecond time range [6,7]. Picosecond laser studies of electron solvation in alcohols were also done [8–10] and thanks to the developments of laser techniques with a better time resolution, the ultrafast dynamics of the solvated electron was studied by femtosecond time⁎ Corresponding author. Laboratoire de Chimie Physique/ELYSE, Univ Paris-Sud, UMR 8000, Bât. 349, Orsay, F-91405, France. Tel.: +33 1 6915 4511; fax: +33 1 6915 6188. E-mail address: [email protected] (I. Lampre). 1 Present address: Laboratoire d'Electrochimie Moléculaire, Université Paris 7- Denis Diderot, 2 place Jussieu, 75251 Paris cedex 05, France. 0167-7322/$ - see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2008.01.017
resolved absorption spectroscopy with use of two-[11–25] or three-pulse sequences [26–30]. The pioneering work of Migus et al. [11] in water showed that the solvation process is complete in a few hundreds of picoseconds and hinted at the existence of short-lived precursors of the solvated electron, absorbing in the infrared spectral domain. Such precursors had already been suggested from picosecond experiments in alcohols [6]. So, subsequent studies often depicted the electron solvation process by stepwise mechanisms with several electron precursors, each precursor having a fixed, individual spectrum [10,12,13,15,16,24,26,30,31]. However, other works on electron solvation favored the so-called “continuous shift” model in which only one localized electron is considered but its spectrum, as a whole, shifts to the blue (short wavelengths) during the solvation [21–23]. In alcohols, the formation of the solvated electron is slower than in water; the duration increased with the size of the nalcohol molecule [6,7,15,20] but also depends on the number of OH groups [6]. So, to get a better insight into the solvation processes and precursor states, using femtosecond pump-probe spectroscopy we have investigated the solvation dynamics of
I. Lampre et al. / Journal of Molecular Liquids 141 (2008) 124–129
the electron in liquid polyols: ethane-1,2-diol (12ED, ethylene glycol), propane-1,2-diol (12PD, propylene glycol), propane-1, 3-diol (13PD, trimethylene glycol) and lately propane-1,2,3-triol (123PT, glycerol). The choice of the polyols comes from their relatively high viscosity, slowing down any diffusion controlled process, and the presence of several hydroxyl groups, allowing investigation of the influence of the number and the distance between hydroxyl groups on the electron solvation process. In addition, the absorption spectrum of the solvated electron in these solvents is localized in the visible spectral domain. To study the formation of the solvated electron in these alcohols, time-resolved absorption spectra from 440 to 710 nm were registered for the electron generated by photoionization of the solvent. In that paper, we resume our previous published works on ethane-1,2-diol [32] and both propanediols [33] and we report new results on propanetriol. We show that the photoinization of the polyols corresponds to a two-photon absorption process. Then, the temporal evolution of the recorded spectra is described and analyzed, in the case of the diols, with three solvation models: a two-step mechanism and two continuous relaxation models. The results obtained for the different polyols are compared and discussed. 2. Experimental method Experiments were performed using a system already described in details elsewhere [32]. Briefly, the output of an
125
amplified kilohertz femtosecond Ti:Sa laser system (Spectra physics) was split into two parts to generate the pump and probe pulses. The pump beam at 263 nm was produced by frequency doubling and sum-frequency mixing in two BBO crystals of 90% of the fundamental beam. It was then focused on a 300 μm thick liquid jet in order to produce electrons by photoionization of the solvent. The remaining 10% of the fundamental beam at 790 nm was directed to a variable optical delay line and focused on a 3 mm sapphire disk to generate a white-light continuum. The latter was then divided into a probe and a reference beam by a broad band beam-splitter. The probe beam was focused onto the liquid jet sample. Then, it was dispersed on a polychromator and detected on a CCD camera (Princeton Instrument) with a resolution of 0.2 nm per pixel, simultaneously with the reference beam to take into account any laser fluctuations. Time-resolved spectra were recorded from 440 to 720 nm and corrected for the group velocity dispersion. The pump pulse duration and energy was about 210 fs full width at halfmaximum and 20 μJ, respectively. The estimated diameter of the pump and probe beams on the jet was usually around 500 μm and 50 μm, respectively. Both pump and probe beams had the same vertical s-polarization. Ethane-1,2-diol, propane-1,2-diol and propane-1,2,3-triol from Aldrich (ACS Reagent) and propane-1,3-diol from Fluka (GC Grade) were used without further purification. Experiments were performed at 295 K except for propanetriol. The high viscosity of this solvent at room temperature (around 1000 cP)
Fig. 1. Transmittance of the 300 μm liquid jet versus the peak intensity of the 220 fs pump pulse at 263 nm for the four studied polyols: (a) ethane-1,2-diol, (b) propane1,2,3-triol, (c) propane-1,2-diol, (d) propane-1,3-diol (symbol, experimental data for different beam diameters; lines, calculated curves for different values of β).
126
I. Lampre et al. / Journal of Molecular Liquids 141 (2008) 124–129
Table 1 Two-photon absorption coefficient β at 263 nm of the four polyols deduced from the data in Fig. 1 Solvent − 11
β (10
−1
mW )
12ED
12PD
13PD
123PT
2.1 ± 0.2
2.0 ± 0.3
2.4 ± 0.3
3.5 ± 0.5
made it impossible to form a liquid jet with our circulating system; so, propanetriol was heated up to 333 K to reduce its viscosity down to 76 cP and to create the jet. 3. Results and discussion As electrons generated by different photo-processes have different thermalization and geminate recombination, it is worth identifying the number of photons involved in the ionization of the polyols in our experiments. The ionization threshold of the studied polyols is around 8.2 eV [34]. Since the energy of 263 nm photons is 4.7 eV, the ionization should occur by a two-photon absorption mechanism. The transmittance of the liquid jet versus the peak power of the 263 nm pump beam presents a similar evolution for the four alcohols (Fig. 1) and is characteristic of a single-beam two-photon absorption. From the fit of the data, we determine the two-photon absorption coefficient β of the polyols at 263 nm (Table 1). The values obtained for the diols are very similar and slightly lower than the value found for the propanetriol. These values are of the same order of magnitude than that found for water (β = (1.8 ± 0.1) × 10− 11 m W− 1) at 266 nm with 100 fs pulses [35].
Fig. 2 depicts the time evolution of the absorption spectra recorded in the four polyols after photoionization of the solvent at 263 nm. At very short time delay after the pump pulse, the excess electron in 12ED presents a very broad absorption band in the visible and near-IR domain with a peak maximum around 675 nm (Fig. 2a). The red part of the spectrum then drops rapidly for the first 5 ps while the blue part increases slightly, leading to a blue shift of the absorption maximum down to 590 nm. The absorbance on the red side of the spectrum follows its decrease while the absorbance on the blue side remains nearly constant. Consequently, the absorption band maximum continues to shift toward shorter wavelengths and, 50 ps after the pump pulse, is around 570 nm, the position of the absorption band maximum of the equilibrated solvated electron in 12ED. The excess electron in both 12PD and 13PD shows a similar behaviour as that in 12ED but on a longer time scale. Indeed, the excess electron in both PD presents a wide absorption band in the visible and near-IR domain at very short time delays after the pump pulse (Fig. 2c and d). The time-resolved spectra reveal that the main change also occurs in the red part of the absorption spectra and indicate that a localized electron, absorbing in the blue spectral domain, is promptly formed and relaxes to the equilibrated solvated electron in a couple of tens of picoseconds. In contrast to the diols, even at very short time after the pump pulse, no significant absorption in the IR domain is observed in the case of 123PT, as the absorption band maximum is already located in the visible domain. The maximum is around 580 nm, very close to the position of the absorption band
Fig. 2. Time evolution of the absorption spectrum obtained in the four studied polyols upon two-photon ionization of the solvent at 263 nm (peak intensity around 0.05 TW cm− 2): (a) ethane-1,2-diol, (b) propane-1,2,3-triol, (c) propane-1,2-diol, (d) propane-1,3-diol (solid lines through experimental points are guides for the eyes).
I. Lampre et al. / Journal of Molecular Liquids 141 (2008) 124–129
127
Table 2 Comparison between the three models used to fit the experimental data on the solvation of electron in ethane-1,2-diol and propanediols Solvent 12ED
12PD
13PD
Model name
Scheme
Comments
Nθa
Rms (10− 3)b
IBc
STEP3P CREX2 CRELH STEP3P CREX2 CRELH STEP3P CREX2 CRELH
e−wb→e−sb→e−s e−wb– – →e−s e−wb– – →e−s e−wb→e−sb→e−s e−wb– – →e−s e−wb– – →e−s e−wb→e−sb→e−s e−wb– – →e−s e−wb– – →e−s
Two-step process Bi-exponential relaxation Heterogeneous relaxation Two-step process Bi-exponential relaxation Heterogeneous relaxation Two-step process Bi-exponential relaxation Heterogeneous relaxation
9 10 10 10 12 10 10 12 10
2.56 2.47 2.50 4.45 4.12 4.39 3.24 3.15 3.18
13,509 13,846 13,730 7409 8010 7517 10,332 10,575 10,490
a
Number of adjusted parameters; broot mean square; cBayes Information criterion.
maximum of the equilibrated solvated electron in 123PT at 333 K (∼ 550 nm) [36]. From 1 to 100 ps, a decrease in the red part of the spectrum occurs without any significant change in the blue side. At longer time (N 50 ps for 12ED, N 100 ps for 12PD, 13PD and 123PT), the position and the shape of the electron spectrum in each solvent hardly change but its whole intensity diminishes due to geminate recombination. Many models have been proposed to explain experimental results on the electron solvation and relaxation. In our study on the solvation dynamics of the electron in 12ED [32], we analyzed our spectro-kinetics signals with various approaches and tested eleven models based on sequential stepwise mechanisms, continuous relaxation or combination of both processes. For the analysis of the data obtained in both PD [33], we retained only the three models which had given a good quality fit with a minimum number of adjustable parameters i.e. a two-step model (STEP3P), a heterogeneous continuous relaxation model (CRELH) and a bi-exponential continuous relaxation model (CREX2). The data analysis was performed over the first 50 ps or 100 ps for 12ED and both PD, respectively, in order to neglect geminate recombination. Consequently, in the models, the solvated electron, the final species is considered to be stable with an infinite lifetime and its spectrum is explicitly introduced. For the sequential stepwise mechanism (STEP3P), only two steps and three species are necessary but sufficient to accurately fit − the data: a weakly-bound electron, ewb , converts into a strongly − bound electron, esb, which gives the solvated electron es−. Each considered species is supposed to have a time-dependent concentration ck(t) and a fixed and individual spectrum εk(E) modeled by a lognormal shape function S: ek ð E Þ ¼ ek S E; Emax;k ; Xk ; gk
t0(E) corresponds to the group velocity dispersion curve in energy space and G (t;t0,γ,α) denotes a generalized Gaussian function: a t t0 G ðt; t0 ; g; aÞ ¼ exp g
where S is parameterized by the peak position in energy Emax, the full width at half-maximum Ω and the asymmetry factor γ. So, the time-dependent absorbance is written:
CREX2
3 pffiffiffiffiffiffiffiffiffi X Aðt; E Þ ¼ G t; t0 ð EÞ; r= 4ln2; 2 ck ð t Þ e k ð E Þ k¼1
pffiffiffiffiffiffiffiffiffi where G t; t0 ð EÞ; r= 4ln2; 2 represents the instrumental response function and ⊗ stand for the convolution operator;
j
j
The continuous relaxation models consider a single species whose spectrum undergoes a continuous evolution. In our models, not only the position but also the shape of the absorption spectrum may change during the solvation process. The time-dependent absorption spectrum is then described by a lognormal function with time-dependent parameters: pffiffiffiffiffiffiffiffiffi Aðt; E Þ ¼ G t; t0 ð E Þ; r= 4ln2; 2 ½c0 eðt Þ S ð E; Emax ðtÞ; Xðt Þ; gðt ÞÞ
The time-dependence of each parameter (x = ε, Emax, Ω, γ) is modeled either by a bi-exponential function (CREX2): xðt Þ ¼ xl þ Dx;1 G t; 0; sx;1 ; 1 þ Dx;2 G t; 0; sx;2 ; 1 Or by a stretched exponential function (CRELH): xðt Þ ¼ xl þ Dx G ðt; 0; sx ; bx Þ;
0 b bx V 1
The results of the Bayesian data analysis with the different models are reported in Table 2. The three models provide good fits of our spectro-kinetics signals for all the diols (rms b 4.5 × 10− 3). Table 3 Comparison between the characteristic times obtained by STEP3P and CREX2 models used to fit the experimental data on the solvation of electron in ethane-1,2-diol and propanediols Solvent
12ED
12PD
13PD
Viscosity (cP)
η = 16
η = 40
η = 39
1.3 ± 0.1 25.0 ± 0.2 1.0 ± 0.1 1.7 ± 0.1 25.5 ± 0.3 22.5 τEmax1 τEmax2 23.5 τEmax1 τEmax2 24.5
4.5 ± 0.1 54.6 ± 0.5 5.6 ± 0.1 0.6 ± 0.1 27.5 ± 0.7 25.3 1.0 ± 0.1 75.9 ± 3.5 72.5 19.8 ± 1.0 – 19.8
3.2 ± 0.1 34.6 ± 0.7 2.9 ± 0.1 0.2 ± 0.1 20.6 ± 0.7 19.6 2.6 ± 0.6 40.5 ± 1.4 39 13.6 ± 1.6 – 13.6
STEP3P
e−wb e−sb
ε Emax Ω γ
τ1 (ps) τ2 (ps) τε (ps) τEmax1 (ps) τEmax2 (ps) bτEmaxN (ps) τΩ1 (ps) τΩ2 (ps) bτΩ1N (ps) τγ1 (ps) τγ2 (ps) bτγ1N (ps)
128
I. Lampre et al. / Journal of Molecular Liquids 141 (2008) 124–129
As the number of adjustable parameters is not identical for the three models, the Bayes criteria, IB, confirms that the best fit of our data is obtained with CREX2 whatever the diol. Even if stretched exponential functions are often used to describe nonexponential behavior of complex dynamics found in liquids or glasses, the physical meaning of the parameters (relaxation time tx and heterogeneity constant βx) and the derived average times is not obvious. Consequently, hereafter, we will focus only on the results of STEP3P and CREX2 (Table 3). Both models indicate, as expected from the experimental observation, that the electron solvation dynamics is faster in 12ED than in PD. In the case of 12ED, the CREX2 model leads to the same two characteristic times for the parameters Emax, Ω and γ, except ε which follows a mono-exponential evolution with a time constant of 1 ps. The two time constants (τEmax1 = τΩ1 = tγ1 = 1.7 ps and τEmax2 = τΩ2 = tγ2 = 25.5 ps) are close to the lifetimes of the intermediate species found with STEP3P (τ1 = 1.3 ps and τ2 = 25.0 ps). So, it is possible to extract two characteristic times for the electron solvation in 12ED. In the case of both PD, as for 12ED, the kinetics of ε appear to be mono-exponential with a time constant τε of 5.6 and 2.9 ps for 12PD and 13PD, respectively. These values are close to the lifetime τ1 determined by STEP3P (4.5 and 3.2 ps for 12PD and 13PD, respectively). Unlike 12ED, for the other parameters, the adjustments by CREX2 do not lead to similar characteristic times. The asymmetry factor γ evolves according a monoexponential with a time constant of 19.8 and 13.6 ps for 12PD and 13PD, respectively. The behaviors of Emax and Ω are bi-exponential with time constants τEmax1 = 0.6 ps, τEmax2 = 27.5 ps, τΩ1 = 1.0 ps, τΩ2 = 75.9 ps for 12PD, and τEmax1 = 0.2 ps, τEmax2 = 20.6 ps, τΩ1 = 2.6 ps and τΩ2 =40.5 ps for 13PD. For both PD, the τx1 values are short, lower than the lifetime τ1 obtained by STEP3P, while the τx2 values surround the lifetime τ2: τEmax2 b τ2 b τΩ2. However, whatever the parameter, the average lifetime bτxN is longer for 12PD than for 13PD, indicating a faster solvation process in 13PD compared to 12PD. That difference cannot be related to viscosity as the two solvents have almost the same viscosity at room temperature (39 and 40 cP, respectively), but must involve the molecular structure. The slower solvation dynamics corresponds to the vicinal diol 12PD. That suggests greater molecular changes in close proximity to the electron site, which have longer range effects. For instance, that may indicate a different number of first-solvation shell molecules, insofar as only one or both of the OH groups of the diol molecule may be involved in the electron cavity. The Bayesian data analysis of the signals obtained in 123PT is in progress and characteristic times should be published soon. Nevertheless, from the experimental data (Fig. 2) if we compare the time evolution of the excess electron absorption band for the four polyols, we observe that, in spite of the higher viscosity of 123PT at 333 K (76 cP) than that of both PD at room temperature, the solvation dynamics is faster in 123PT than in PD. In particular, the position of the absorption band maximum of the fully solvated electron is reached much more rapidly in the case of 123PT compared to the other diols, even 12ED. These observations clearly show that the solvation dynamics in the polyols cannot be explained by the viscosity alone but greatly depends on the molecular structure of the solvent.
Indeed, 123PT is a highly viscous solvent but with a high hydrogen bond density since the molecule has three hydroxyl groups in vicinity in its molecular structure. Theoretical works have pointed out the role of the microscopic structure of the liquid [37] and the importance of the coupling between the excess electron and the solvent intramolecular modes on the absorption band of the excess electron both in the visible and near-IR domain [38–41]. So, the solvated electron dynamics is mainly governed by the vibrational properties of matrices in which the electron is trapped. Recent results on resonance Raman experiments also support this description [42–44]. The theoretical approaches lead to two kinds of trapped electrons in alcohols, already postulated [6,45,46]: visible absorbing electrons associated with hydroxyl traps and IR-absorbing electrons trapped by the alkyl group. Their existence, respectively where the paraffinic and the hydroxyl groups are locally concentrated, had been evidenced at 77 K for monohydroxy-alcohols but not for polyhydroxyalcohols, indicating that, in the latter solvents, the phase is not segregated into polar and non-polar regions owing to the abundance of the H-bonds [45]. Consequently, we can consider that the time evolution of the spectra of excess electrons we observed in polyols is not due to a conversion from an electron trapped by alkyl groups to an electron trapped by hydroxyl groups but it is related to vibronic coupling and vibrational relaxation in the first-solvation shell molecules. That is corroborated by the results in 123PT. In that solvent, any significant absorption band in the near-IR is observed indicating a strong association of the electron with the hydroxyl traps. To conclude, our results on the solvation dynamics of electrons in polyols give evidence of the continuous character of the solvation process. The main kinetic factor is not the viscosity but the molecular structure of the solvent; in particular, the OH group density appears to be an important parameter. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
E.J. Hart, J.W. Boag, J. Am. Chem. Soc. 84 (1962) 4090. J.W. Boag, E.J. Hart, Nature 197 (1963) 45. J.P. Keene, Nature 197 (1963) 47. E.J. Hart, M. Anbar, The Hydrated Electron, 1970 New-York. J.H. Baxendale, P. Wardman, Nature 230 (1971) 449. W.J. Chase, J.W. Hunt, J. Phys. Chem. 79 (1975) 2835. G.A. Kenney-Wallace, C.D. Jonah, J. Phys. Chem. 86 (1982) 2572. F. Wang, R. Pottel, U. Kaatze, J. Phys. Chem., B 101 (1997) 922. H. Miyasaka, H. Masuhara, N. Mataga, Laser Chem. 7 (1987) 119. Y. Hirata, N. Mataga, J. Phys. Chem. 94 (1990) 8503. A. Migus, Y. Gauduel, J.L. Martin, A. Antonetti, Phys. Rev. Lett. 58 (1987) 1559. F.H. Long, H. Lu, K.B. Eisenthal, Phys. Rev. Lett. 64 (1990) 1469. M. Sander, U. Brummund, K. Luther, J. Troe, Ber. Bunsenges. Phys. Chem. 96 (1992) 1486. C. Pépin, T. Goulet, D. Houde, J.-P. Jay-Gerin, J. Phys. Chem. 98 (1994) 7009. X. Shi, F.H. Long, H. Lu, K.B. Eisenthal, J. Phys. Chem. 99 (1995) 6917. A. Reuther, A. Laubereau, D.N. Nikogosyan, J. Phys. Chem. 100 (1996) 16794. R.A. Crowell, D.M. Bartels, J. Phys. Chem. 100 (1996) 17940. L. Turi, P. Holpar, E. Keszei, J. Phys. Chem., A 101 (1997) 5469. C. Pépin, T. Goulet, D. Houde, J.-P. Jay-Gerin, J. Phys. Chem., A 101 (1997) 4351.
I. Lampre et al. / Journal of Molecular Liquids 141 (2008) 124–129 [20] T. Goulet, C. Pépin, D. Houde, J.-P. Jay-Gerin, Radiat. Phys. Chem. 54 (1999) 441. [21] A. Hertwig, H. Hippler, A.-N. Unterreiner, Phys. Chem. Chem. Phys. 1 (1999) 5633. [22] D. Madsen, C.L. Thomsen, J. Thogersen, S.R. Keiding, J. Chem. Phys. 113 (2000) 1126. [23] J.A. Kloepfer, V.H. Vilchiz, V.A. Lenchenkov, A.C. Germaine, S.E. Bradforth, J. Chem. Phys. 113 (2000) 6288. [24] T. Scheidt, R. Laenen, Chem. Phys. Lett. 371 (2003) 445. [25] R. Lian, R.A. Crowell, I.A. Shkrob, J. Phys. Chem., A 109 (2005) 1510. [26] M. Assel, R. Laenen, A. Laubereau, J. Chem. Phys. 111 (1999) 6869. [27] C. Silva, P.K. Walhout, P.J. Reid, P.F. Barbara, J. Phys. Chem., A 102 (1998) 5701. [28] C. Silva, P.K. Walhout, K. Yokoyama, P.F. Barbara, Phys. Rev. Lett. 80 (1998) 1086. [29] M.F. Emde, A. Baltuska, A. Kummrow, M.S. Pshenichnikov, D.A. Wiersma, Phys. Rev. Lett. 80 (1998) 4645. [30] A. Thaller, R. Laenen, A. Laubereau, J. Chem. Phys. 124 (2006) 024515. [31] P. Holpar, T. Megyes, E. Keszei, Radiat. Phys. Chem. 55 (1999) 573. [32] B. Soroushian, I. Lampre, J. Bonin, P. Pernot, S. Pommeret, M. Mostafavi, J. Phys. Chem., A 110 (2006) 1705.
129
[33] J. Bonin, I. Lampre, P. Pernot, M. Mostafavi, J. Phys. Chem., A 111 (2007) 4902. [34] J.-M. Jung, in, University Louis Pasteur, Strasbourg I, France, 2003. [35] S. Pommeret, F. Gobert, M. Mostafavi, I. Lampre, J.-C. Mialocq, J. Phys. Chem., A 105 (2001) 11400. [36] N. Chandrasekhar, P. Krebs, A.-N. Unterreiner, J. Chem. Phys. 125 (2006) 164512-164511–164512-164517. [37] M. Hilczer, M. Steblecka, Radiat. Phys. Chem. 67 (2003) 263. [38] H. Abramczyk, J. Phys. Chem. 95 (1991) 6149. [39] H. Abramczyk, J. Kroh, J. Phys. Chem. 95 (1991) 6155. [40] H. Abramczyk, J. Kroh, Radiat. Phys. Chem. 39 (1992) 99. [41] H. Abramczyk, J. Kroh, Radiat. Phys. Chem. 43 (1994) 291. [42] M.J. Tauber, R.A. Mathies, Chem. Phys. Lett. 354 (2002) 518. [43] M.J. Tauber, R.A. Mathies, J. Am. Chem. Soc. 125 (2003) 1394. [44] M.J. Tauber, C.M. Stuart, R.A. Mathies, J. Am. Chem. Soc. 126 (2004) 3414. [45] T. Shida, S. Iwata, T. Watanabe, J. Phys. Chem. 76 (1972) 3683. [46] M. Ogasawara, K. Shimizu, H. Yoshida, Radiat. Phys. Chem. 17 (1981) 331.