16794
J. Phys. Chem. 1996, 100, 16794-16800
Primary Photochemical Processes in Water A. Reuther, A. Laubereau,* and D. N. Nikogosyan† Physik-Department E11, Technische UniVersita¨ t Mu¨ nchen, D-85748 Garching, Germany ReceiVed: May 21, 1996; In Final Form: August 6, 1996X
The primary photochemical processes which occur in neat water after 282 nm high-intensity excitation via a two-photon mechanism were studied. Using probe pulses in UV, visible, and near-IR spectral ranges, the absorption process itself and the time evolution of the generated electrons and other photoproducts in the 0.1-80 ps scale were investigated. Different to previous femtosecond laser studies of water a quantitative analysis of the absorption process and yields of primary photoproducts was carried out. The two-photon absorption coefficient of liquid water for femtosecond pulses at 282 nm was measured to be β ) (1.9 ( 0.5) × 10-12 m/W, while the quantum yield of the hydrated electron at the same wavelength was determined to be Φ (eaq-) ) 0.11 ( 0.03. The results of the electron solvation and geminate recombination dynamics at 282 nm (excitation energy E2hν ) 8.8 eV) are in accordance with the findings of other groups for different excitation wavelengths. The numerical simulations of our data suggest that the energy threshold for H2O+ ion formation is above 8.8 eV.
Introduction Among all the solvents, water occupies an extraordinary position. Being the natural environment of such important biological molecules as nucleic acids and peptides, water is present in almost any living organism. Therefore, a detailed understanding of charge-transfer reactions initiated in water by light absorption and of light absorption processes in water itself is necessary for a proper description of photochemical experiments performed in water solution. It is well-known that at low intensities of light (below 1011 W/m2) the water is transparent for UV light with λ > 190 nm; i.e., the linear and nonlinear absorption is negligible. However, with intense UV light at λ > 190 nm, it is possible to excite a water molecule via a two-photon absorption (TPA) mechanism1 and initiate its chemical decomposition. It was shown in 1980 that under highintensity picosecond UV excitation with λ ) 266 nm the water molecule undergoes two-photon absorption2,3 with subsequent dissociation and ionization4
H2O + 2hν w H2O* w eaq-, H3O+, OH, H
(1)
experiments2-4
In the first the total two-photon energy value was Etotal ) 9.3 eV, and the ionization threshold for liquid water was determined to be Eion ) 6.5 ( 0.5 eV,4 consistent with earlier estimates of water ionization potential of 6.5 ( 0.15 and 6.0-6.5 eV.6 An updated value Eion ) 6.36-6.41 eV follows from recent experiments.7,8 The dissociation energy for neat water is reported to be Edis ) 6.41-6.71 eV.9 The development of high-intensity femtosecond laser systems made it possible to investigate the dynamics of primary photochemical reactions in water. Using the common pump and probe techniques with two-photon excitation in the UV and probing in the visible and near-IR ranges, the electron trapping and solvation as well as geminate recombination were studied by many experimental groups with time resolution up to 20 fs. In many of these investigations a colliding pulse mode-locked dye laser with second harmonic generation (SHG) was employed, yielding femtosecond UV pulses at 307,10 310,11-17 and * To whom all the correspondence should be addressed. † On leave from Institute of Spectroscopy, Russian Academy of Sciences, Troitzk, Moscow Region, 142092 Russia. X Abstract published in AdVance ACS Abstracts, October 1, 1996.
S0022-3654(96)01462-1 CCC: $12.00
312.5 nm.18-22 The corresponding two-photon energies are 8.1, 8.0, and 7.9 eV, respectively. Other groups used femtosecond UV pulses at λ ) 248 nm23,24 (E2hν ) 10 eV) or at λ ) 390 nm.8,25,26 In the latter case the excitation of water molecule was achieved via the three-photon mechanism (E3hν ) 9.5 eV). Surprisingly, in all the above-mentioned femtosecond studies the absorption process was not quantitatively analyzed; e.g., the TPA coefficient was not determined. Such analysis is required to specify the excitation mechanism. Our experimental setup for femtosecond kinetic spectroscopy provides pumping at 282 nm (E2hν ) 8.8 eV) and probing not only in the visible and near-IR ranges but also in the ultraviolet range. This allowed us to monitor the two-photon absorption process in time with subsequent accurate measurement of the UV pump pulse duration. As a result, the two-photon absorption coefficient and the quantum yield of hydrated electron in water were determined. We have remeasured the time constants for the localization of the detached electrons and for the subsequent solvation. Our data obtained are in a good agreement with the results of several groups8,20,21 but at variance with other findings.11-15 The measurements with 450 nm probing and the numerical simulations performed give additional information on electron detachment process strongly suggesting that no water cations are generated at two-photon excitation of water molecule with Etotal e 8.8 eV. Experimental Section We start with a non-CW synchronously pumped dye laser emitting at 564 nm.27 After suitable amplification28 the femtosecond laser pulse is frequency-doubled to 282 nm in the 1 mm length ADP crystal29 (θ ) 68°, φ ) 45°). An energy conversion efficiency of 25% is accomplished, yielding pulses at 282 nm of approximately 10 µJ energy and 180 fs duration. The spectral bandwidth is estimated to be 7 nm and the repetition rate 15 Hz. The 282 nm femtosecond UV pulses serve as the pump radiation. When probing at the same wavelength, a weak reflection of the pump pulse is used for the probe. Different probing wavelengths are derived from continuum generation of the remainder of the fundamental laser pulse in a fused silica plate. For probing pulses in the visible and near-IR ranges, a frequency selection of the continuum output is carried out by © 1996 American Chemical Society
Primary Photochemical Processes in Water narrow-band interference filters (10 nm fwhm). The generation of probe pulses in the UV at 292 and 299 nm was achieved by SHG of the continuum radiation in a second ADP specimen of the same cut. The frequency selection is again performed by interference filters (6 nm fwhm). The duration of probe pulses (tpr, fwhm) is varied from 200 to 500 fs depending on wavelength. In the experiments the bidistilled deionized water, pH 6.8, was used; the sample thickness is 1 mm. In order to minimize the nonlinear effects,30,31 thin (1 mm) cell windows made from calcium fluoride (CaF2) are applied, giving an important improvement compared to fused silica. During the measurements the water cell is continuously moved in the plane perpendicular to the pump beam, avoiding undesirable thermal effects. The pump and probe beams were focused into the sample. The alignment of their spatial overlap is carried out with the help of a pinhole with 200 µm diameter. The beam waist of the pump radiation is varied in the range 80-320 µm using fused silica lenses of different focal length, giving the corresponding variation of the peak excitation intensity in the range I0 ) (20-200) × 1013 W/m2. The peak intensity values are obtained from careful measurements of the pulse energy, duration, and beam cross section and from an in situ technique described below which is based on the measured TPA coefficients. The energies of incident and transmitted probe pulses are monitored by silicon photodiodes. The sensitivity of the detection scheme allows to measure absorbance changes at any probing wavelength as low as ∆OD ) 5 × 10-4. All the results presented below refer to parallel polarization of the pump and probe beams. The duration of the UV pump pulse tp ) 180 ( 20 fs is measured by a TPA method monitoring the autocorrelation function between pump and probe 282 nm pulses in type IIa diamond32 or in water sample itself.33 A similar technique of the cross-correlation function measurement using TPA in water or diamond was used for the evaluation of probe pulse duration at 292 and 299 nm. For the determination of probe pulse duration in the visible and near-IR ranges the TPA in diamond was employed.33 The time resolution of our experimental setup is better than 30 fs when probing in the UV and about 50 fs using visible and near-IR probe pulses. All our experiments were done at room temperature (19 °C). Results and Discussion 1. Measurement of Two-Photon Absorption Coefficient. The knowledge of the TPA coefficient of water is of special interest, since it allows to describe quantitatively both the incident UV pump intensity and the number of photons absorbed by the sample. We recall that in previous femtosecond investigations of water8,10-26 quantitative data on pulse intensities and the quantum yields of the generated photoproducts are not reported. Under such conditions, for example, the relative role of higher-order excitation mechanisms is not known. The determination of two-photon absorption coefficient β for water at 282 nm was performed by intensity-dependent transmission measurements.32 Figure 1 presents the transmission data for the 282 nm femtosecond pulse propagating through the 1 mm water cell versus the incident intensity I0. The approximating curves in Figure 1 are calculated for different β values using the theoretical expression32
T(I,β) )
(1 - R)I(r,t) 1 - R +∞ ∫ 2πr∫-∞+∞1 + βl(1 - R)I(r,t) dr dt (2) E0 0
where T denotes the energy transmission of the input pulse with
J. Phys. Chem., Vol. 100, No. 42, 1996 16795
Figure 1. Two-photon absorption in neat water. The transmission of the 1 mm water sample is plotted versus the intensity of the femtosecond input pulse at 282 nm (tp ) 180 fs; experimental points, theoretical curves).
Figure 2. Transient absorption in a 1 mm cell of neat water for highintensity femtosecond excitation (I0 ) 2.15 × 1015 W/m2) at 282 nm and also probing at 282 nm (experimental points, theoretical curves). The thick line corresponds to the sum of all contributions, and the thin line represents the calculated contribution of water photolysis products.
energy E0, R denotes the reflection loss of the front and back surfaces of the cell, and l is the length of water layer. The pulse shape I(r,t) used in calculations is assumed to be
I(r,t) ) I0 sech2(1.763 t/tp) exp(-2r2/r02)
(3)
This means the sech2 shape in time with tp pulse duration (fwhm) and Gaussian shape in space with r0 radius of electromagnetic field at the e-1 level. The curves in Figure 1 strongly support the TPA mechanism; a contribution of three-photon absorption is not indicated. From the comparison of the experimental and theoretical data in Figure 1 the two-photon absorption coefficient for neat water is determined to be β(282 nm + 282 nm) ) (1.9 ( 0.5) × 10-12 m/W. This value is somewhat higher than the value determined earlier using picosecond UV laser pulses (λ ) 281 nm, tp ) 36 ps).4 The discrepancy observed may be due to the different situation, i.e., due to the contribution of photoproducts to the observed intensity dependence. However, for the femtosecond pulses studied here the contribution by UV absorption of photoproducts is negligible. This conclusion follows from Figure 2 where the experimental kinetics of induced absorption in pure neat water (λpump ) λprobe ) 282 nm) together with the results of numerical simulations is depicted. The thick line in Figure 2 corresponds to the sum of all signal contributions, including the two-photon convolution of pump and probe pulses and absorption of water photoproducts (thin line in Figure 2). It is readily seen that the two-photon absorption signal strongly dominates around zero delay time. As mentioned above, the two-photon absorption peak can be used to measure the UV pulse duration. From the data of Figure
16796 J. Phys. Chem., Vol. 100, No. 42, 1996
Reuther et al.
Figure 3. Transient absorption in a 1 mm sample cell of neat water for femtosecond excitation at 282 nm and probing at different wavelengths: (a) pump intensity I0 ) 1.0 × 1015 W/m2 and probing at 292 nm; (b) pump intensity I0 ) 0.45 × 1015 W/m2 and probing at 299 nm (experimental points, theoretical curves). The meaning of thick and thin lines is the same as in Figure 2.
(or hydration) with characteristic time τhyd producing the hydrated electron (eaq-), and geminate recombination with parent positive ion H3O+ (see refs 11-13, 19, and 20); the second route via H2O*(2) could be called dissociation channel (lefthand side of Figure 4) and includes the formation of an intermediate state (designated as (x) in Figure 4) which is populated with characteristic time τ1 and depopulated with characteristic time τ2 (1/τ2 ) 1/τ′2 + 1/τ′2′) via the relaxation to the ground state of water molecule with time constant τ′2 or the dissociation reaction (x) w OH + H with time constant τ′2′ (see refs 16 and 17). The branching ratio of the two channels is governed by the probability 2Φeaq- for the conversion of H2O* to H2O*(1), while the subsequent yield of solvated electrons is denoted by (1 - η). The level H2O*(2), on the other hand, is formed with (1 - 2Φeaq-) probability and leads to H atoms with a (1/τ′2′)/(1/τ′2 + 1/τ′2′) yield. It is assumed that the possible intermediate states involved in the branching are extremely short-lived, with lifetime well below the time resolution of our experimental apparatus. As a result, the conversion of H2O* to H2O*(1) and to H2O*(2) is practically instantaneous. Using the notations introduced in the Appendix, we can write the following system of differential equations for the primary events in water induced by two-photon absorption:
ionization channel: Ipu2(z′,t′) nH2O*(1)(z′,t′) ∂ (4) nH2O*(1)(z′,t′) ) 2Φeaq-βpu ∂t′ 2pωpu τtr nH2O*(1)(z′,t′) newet-(z′,t′) ∂ newet-(z′,t′) ) ∂t′ τtr τhyd
(5)
t′ < 100 fs: Figure 4. Model of primary events in pure liquid water at two-photon excitation.
2 the value of tp ) 180 ( 20 fs is found, assuming a shape of laser pulse. In addition, the knowledge of two-photon absorption coefficient β allows the in situ determination of pump pulse intensity from the peak amplitude of the induced probe absorption (∝βI0).33 In all measurements discussed below this TPA technique was applied for a simple and reliable estimation of the irradiation intensity. The observed induced absorption kinetics in the case of 292 and 299 nm probing are similar to that at 282 nm (Figure 3). A quantitative analysis reveals a smaller value of the two-photon absorption coefficient. From several measurements with probing at 299 nm and independent determination of the pump intensity at 282 nm, we find a value of β(282 nm + 299 nm) ) (1.0 ( 0.4) × 10-12 m/W. By linear interpolation we estimate the TPA value for 292 nm probing to be β(282 nm + 292 nm) ) (1.3 ( 0.5) × 10-12 m/W. 2. Primary Events in Pure Water after Two-Photon Excitation. By absorption of two light quanta with λ ) 282 nm a water molecule acquires an energy of 8.8 eV, which is significantly higher than ionization and dissociation threshold energies presented above. As a consequence, the molecule should ionize and dissociate. A schematic picture of primary events is presented in Figure 4. Two-photon excitation promotes a water molecule to an excited state H2O*. There are two different channels for relaxation of excited water molecule: the first one which could be called ionization channel (right-hand side of Figure 4) proceeds via H2O*(1) and includes the processes of electron detachment, localization (or trapping into the preexisting traps) with characteristic time τtr forming the socalled wet electron in the prehydrated state (ewet-), solvation
newet-(z′,t′) ∂ neaq-(z′,t′) ) ∂t′ τhyd
sech2
t′ g 100 fs:
(6)
( x)
newet-(z′,t′) ∂ ∂ gr - negraq-(z′,t′) neaq-(z′,t′) ) η erf ∂t′ τhyd ∂t′ newet-(z′,t′) ∂ ll neaq-(z′,t′) ) (1 - η) ∂t′ τhyd
Tj t′
(7)
(8)
dissociation channel: Ipu2(z′,t′) nH2O*(2)(z′,t′) ∂ nH2O*(2)(z′,t′) ) (1 - 2Φeaq-)βpu φ∂t′ 2pωpu τ1 (9) nH2O*(2)(z′,t′) nx(z′,t′) ∂ nx(z′,t′) ) ∂t′ τ1 τ2
(10)
Following previous investigations,12,24 the geminate recombination process is described in eq 7 by the error function. In order to avoid numerical problems around zero delay time, the computation includes the (slow) geminate recombination only for time t′ g 100 fs. It was checked that this treatment does not influence the numerical results. Since the hydrated electrons may escape the geminate recombination, the number density of hydrated electron neaq- is divided into two parts: the longliving part nellaq- ) (1 - η)neaq- and the fraction negraq- ) ηneaq-, which undergoes geminate recombination. The general descrip-
Primary Photochemical Processes in Water
J. Phys. Chem., Vol. 100, No. 42, 1996 16797
Figure 5. Transient absorption in a 1 mm cell of neat water for femtosecond excitation at 282 nm (I0 ) 0.77 × 1015 W/m2) and probing at 650 nm (tpr ) 300 fs) (experimental points, theoretical curves). The thick line represents the numerically simulated signal, and the thin lines indicate the contributions of ewet- and eaq-.
TABLE 1: Kinetic Parameters of Electron Solvation Process λpump (nm)
Etotal (eV)
τtr (fs)
τhyd (fs)
ref
312.5 310 282 390
7.9 8.0 8.8 9.5
180 ( 40 110 180 ( 50 150 ( 50
540 ( 50 240 540 ( 80 500 ( 150
20, 21 11, 12, 13, 14 this work 8
tion of the solution of the rate equation system and of the assumptions involved is presented in the Appendix. 3. Formation of Hydrated Electron and (x) State. After two-photon ionization and dissociation, one should expect the formation of different radicals and ions such as detached electron e-, hydroxyl radical OH•, hydrogen atom H, and hydronium ion H3O+ (for details see refs 4, 12, and 13). Indeed, in the induced absorption experiments with UV probing (see Figure 3) after the end of two-photon absorption peak one observes a long-lived absorption tail which can be attributed to linear absorption of above-mentioned particles. Among the mentioned particles only the hydrated electron displays strong absorption in the visible and near-IR ranges with the maximum positioned at λ ) 720 nm.5,34,35 The previous time-resolved measurements8,10-14,20,21 have shown that the hydrated electron is formed on a subpicosecond time scale via an intermediate state, the so-called “wet electron” (ewet-, see Figure 5). On the other hand, the lifetime of the hydrated electron in water with normal oxygen content is about 0.3 µs.4 So the processes expected to appear in the probe absorption in the visible and near-IR within the first 100 ps are the formation and geminate recombination of the hydrated electron. An example is shown in Figure 5. The kinetics in neat water for pumping at 282 nm and probing at 650 nm is displayed in the time interval 0-5 ps. The fast signal rise is due to the solvation process. The numerical analysis of the signal transient reveals that an intermediate absorbing state, ewet-, has to be introduced. We recall that the pulse durations and the zero setting of the time scale are determined by TPA reference measurements in the same experimental runs. The numerical fitting of the computed data to the experimental points yields the time constants for electron localization, τtr ) 180 ( 50 fs, and electron solvation, τhyd ) 540 ( 80 fs. The variation of the probe wavelength in the range 450-750 nm has no influence on the measured time constants. In Table 1 our data on the electron solvation process are compared with other investigations. It is seen that our values agree well with the results of two groups8,20,21 but are at variance with refs 11-14. It should be noted that the relaxation time of the excited hydrated electron in the so-called p state, τrel ) 550 ( 170 fs, measured by a different technique in ref 25, is consistent with our findings.
Figure 6. Transient absorption data for a 1 mm cell of neat water with fs excitation at 282 nm (I0 ) (0.5-2.0) × 1015 W/m2) and probing at different wavelengths: (a) 450, (b) 525, (c) 588, (d) 650, and (e) 750 nm (experimental points, theoretical curves). Thick lines represent the numerically simulated signal.
The derived theoretical models suggest that the prehydrated state (ewet-) and the first excited state of the hydrated electron (p state) are identical.36 The comparison between the computed and measured data also yields some values of the absorption cross section of the “wet” electron relative to that of hydrated electron. We have found for the ratio σ(ewet-)/σ(eaq-) the values 0.62, 0.77, and 0.74 at the wavelengths 525, 588, and 650 nm, respectively. The data obtained agree satisfactorily with previous results.20,21 Similar to the measurements of ref 16, we have observed at 750 nm probing the evidence of an additional short-lived (τ ∼ 1 ps) IR-absorbing kinetic component (data not shown). However, its interpretation was not attempted in present work. 4. Geminate Recombination and Quantum Yield of eaq-. The observed induced absorption kinetics for longer times up to 80 ps are depicted in Figure 6 for pumping at 282 nm and probing at five wavelengths in the range 450-650 nm. The signal curves first rise to a maximum close to 1 ps and then decay rather slowly to a long-lived absorption change. This picosecond relaxation is explained by geminate recombination of the hydrated electron with parent positive ion. Knowing the number of absorbed 282 nm photons from a quantitative analysis of the excitation process and the absorption cross section of hydrated electron at the respective probing wavelength (refs 33, 5, and 34), it is possible to determine the quantum yield of hydrated electron as a function of time. For the maximum of generated hydrated electrons (delay time ≈1 ps) we find Φemax -(282 nm) ) 0.11 ( 0.03. aq Let us return to the geminate recombination kinetics. For times t > 2 ps, when the primary processes have terminated, the number density of hydrated electrons escaping the geminate recombination is given by the expression (see eqs 4-8)
16798 J. Phys. Chem., Vol. 100, No. 42, 1996
Reuther et al.
TABLE 2: Parameters of Geminate Recombination Process λpump (nm)
Etotal (eV)
Tj (ps)
η
ref
310 282 248
8.0 8.8 10.0
1.2 ( 0.1 2.7 ( 0.5 12.2 ( 2.2
0.55 0.43 ( 0.04 0.30 ( 0.02
12, 13 this work 23, 24
neaq-(t) ) neaq-(t)0){(1 - η) + η erf(Tj/t)1/2}
(11)
where neaq-(t)0) is the (extrapolated) initial number density and 1/Tj is the jump rate of electron. The fraction of electrons undergoing the geminate recombination is denoted by η, while (1 - η) is the probability to escape geminate recombination. From the signal transients of Figure 6, we deduce the probability of geminate recombination η ) 0.43 ( 0.04 and time constant Tj ) 2.7 ( 0.5 ps. The data obtained are listed in Table 2 together with the results of previous experiments. The good agreement of our results (which were obtained under welldefined conditions) with data of other femtosecond works is noteworthy and gives experimental support to their interpretation in terms of dominating two-photon excitation mechanism. It is interesting also to compare our data with the results of earlier picosecond investigations. In ref 4 the quantum yield of hydrated electrons escaping geminate recombination at 200 ps time delay after 282 nm high-intensity excitation was found ps to be Φe200 - (282 nm) ) 0.07. In order to estimate from this aq value the maximal value Φemax -(282 nm), it is necessary to aq combine it with the probability (1 - η) to escape the geminate recombination, i.e. 200 ps Φemax - ) Φe - /(1 - η) aq aq
(12)
Using our value η ) 0.43, we estimate Φemax -(282 nm) ) 0.12, aq in nice agreement with our value 0.11 ( 0.03. 5. Additional Intermediate Observed in Blue Spectral Range. In the femtosecond investigation of water13 with 310 nm pumping and 410-460 nm probing a distinct absorption maximum around 150 fs time delay with a subsequent quick decay within several hundred femtoseconds to a longer-lived component with amplitude depending of probing wavelength was discovered. The absorption peak was assigned as H2O+ (see Figure 2 of ref 13). We have also performed measurements with probing in blue spectral range at 450 nm. An example of the signal transient is shown in Figure 7. A different time evolution was observed without a pronounced maximum at short delay time. The numerical analysis of the data reveals that an additional blue-absorbing component has to be included (dotted curve in Figure 7) besides the prehydrated and hydrated electron (dashed and thin lines in Figure 7). However, the relative contribution of the additional species appears to be considerably weaker than observed in ref 13. For the interpretation of the various findings, the different excitation conditions should be taken into account, e.g., probe pulse durations (about 500 fs in our case and possibly smaller duration in ref 13), pump pulse intensities, and wavelengths (approximately 1016 W/m2 at 310 nm in ref 13 and 2 × 1015 W/m2 at 282 nm in the present work). Let us consider three possible schemes for the explanation of the additional ultrafast intermediate in the blue: (a) It could be the H2O+ ion, as previously proposed; its time evolution should follow the occupation of the H2O*(1) state of the ionization channel introduced above (see Figure 4), from which the electron thermalization with subsequent solvation takes place. The quantum yield of H2O+ should be equal to the quantum yield of hydrated electron Φeaq-; as a consequence, the relative contributions of the new species and of the generated electrons should not depend on excitation wavelength.
Figure 7. Transient absorption in a 1 mm sample cell of neat water for femtosecond excitation at 282 nm (I0 ) 2 × 1015 W/m2) and probing at 450 nm (tpr ) 470 fs) (experimental poins, theoretical curves). The thick line represents the numerically simulated signal; the other curves respectively indicate the contributions of eaq- (thin), of ewet- (dashed), and of an additional fast, blue-absorbing component (dotted).
(b) The additional signal contribution may be related to the dissociation channel of water, i.e., the occupation of H2O*(2) state with subsequent population of (x) state (see Figure 4). The quantum yield of this state is equal to (1 - 2Φeaq-)/2; therefore, the relative contributions of the new species and of the electrons should depend on excitation wavelength, since Φeaq- varies with excitation wavelength. (c) The fast absorption feature around zero delay time could represent a TPA signal due to simultaneous absorption of pump and probe photons. The total energy of two photons (282 + 450 nm) is about 7.15 eV, which is significantly higher than ionization limit (≈6.4 eV, see above). The total energy of two photons used in ref 13 is again higher than the ionization threshold (E310 nm+460 nm ) 6.7 eV, E310 nm+410 nm ) 7.0 eV). The drastically different signal transients for excitation at 310 nm (Figure 2 from ref 13) and 282 nm (Figure 7) immediately exclude mechanism (a), whereas the explanation (b) is supported by a comparison with quantum yields. Using eq 12, the quantum yield of hydrated electron at 310 nm excitation and ps 200 ps time delay, given in ref 4, Φe200 - (310 nm) ) 0.018, and aq the probability for geminate recombination η(310 nm) ) 0.55, given in ref 12, we can estimate the maximum quantum yield of hydrated electron at 310 nm to be Φemax -(310 nm) ) 0.04, aq much lower than our measured value Φemax -(282 nm) ) 0.11. aq As a result, the possible contribution of products of the dissociation channel ((x) state) relative to that of ionization one (e-) should be stronger by a factor of ≈3.3 for excitation at 310 nm as compared to 282 nm. By the help of numerical simulations, we have investigated the effect of the pump pulse intensity, probe pulse duration, and excitation wavelength on the relative contribution of the ultrafast blue-absorbing component to the induced absorption kinetics according to three different hypotheses discussed above. First, we have varied the pump pulse intensity in the range from I0 ) 1 × 1015 W/m2 to I0 ) 5 × 1015 W/m2 and probe pulse duration in the 200-500 fs range. It was demonstrated that the calculated signal form did not change on variation of either pump pulse intensity or probe pulse duration in all three cases (data not shown). After that we have changed in our numerical calculations the quantum yield of hydrated electron (4% instead of 11%) and immediately reproduced the strong absorption maximum near zero delay in induced absorption kinetics in the cases (b) and (c) discussed above (Figure 8b,c) whereas the calculations according to the scheme (a) do not reveal any maximum (Figure 8a). Therefore, the additional ultrafast blueabsorbing component in the induced absorption kinetics cannot be assigned as H2O+ ion neither at 310 nm excitation (Etotal ) 8.0 eV) nor at 282 nm excitation (Etotal ) 8.8 eV). This means that at given experimental conditions no direct photoionization
Primary Photochemical Processes in Water
J. Phys. Chem., Vol. 100, No. 42, 1996 16799 of a fast blue-absorbing component, the second one which assigns this intermediate to the (x) state seems to be most probable. Conclusions Femtosecond laser studies of the excitation and relaxation processes in pure neat water have been carried out with excitation at 282 nm via two-photon absorption. We have determined the two-photon absorption coefficient for pure liquid water at 282 nm, β ) (1.9 ( 0.5) × 10-12 m/W, and the quantum yield of the hydrated electron at λ ) 282 nm, Φ(eaq-) ) 0.11 ( 0.03. The measured dynamics of the electron solvation and geminate recombination for excitation at 282 nm (E2hν ) 8.8 eV) are compared with the results obtained by other groups using excitation wavelengths of 310 and 248 nm (total excitation energy ∼8.0 and 10 eV, respectively). The numerical simulations performed strongly suggest that the energy threshold for H2O+ ion formation is above 8.8 eV. Acknowledgment. The authors indebted to Profs. A. Bernas, C. Ferradini, J.-P. Jay-Gerin, and L. Lindqvist for fruitful discussions. Appendix
Figure 8. Results of numerical simulations of the primary processes in a 1 mm water sample under 310 nm femtosecond excitation (I0 ) 2 × 1015 W/m2) and 450 nm probing (tpump ) tprobe ) 200 fs, Φemax - ) aq 0.04) considering three different hypotheses for the origin of the fast component: (a) H2O*(1) state; (b) H2O*(2) state; (c) TPA with β(282nm+450nm) ) 2 × 10-14 m/W. The thick line represents the calculated transient absorption. The other curves respectively denote the contributions of eaq- (thin line), of ewet- (dashed), and of the ultrafast blue-absorbing component (dotted).
or autoionization of liquid water takes place (see discussion in ref 23). This conclusion agrees with the results of ref 37, where the bandgap energy value for liquid water was estimated to lie above 8.9 eV. Let us return to the mechanism (c) (Figure 8c). The numerical simulations performed revealed the rise of the signal near zero delay when changing the excitation wavelength from 282 to 310 nm. We will compare our results with experimental data presented in Figure 2 of ref 13. At time delay t > 1 ps the main blue-absorbing species in induced absorption kinetics should be the hydrated electron with molar extinction coefficient values differing in 1.7 times at the wavelengths 410 and 460 nm (see ref 4). As the TPA peak amplitude is proportional to two-photon absorption coefficient β, then for equal pump pulse intensity values in the cases of 410 and 460 nm values we should obtain TPA peak amplitudes differing in 1.2 times. (According to ref 4 the decrease of total excitation energy by 0.3 eV leads to a β fall in 1.2 times in the region of 9 eV total energy value and to an even smaller fall for 7 eV total energy.) Consequently, the equality between TPA peak amplitudes (we recall that Figure 2 from ref 13 represents the induced absorbance in arbitrary units) means 1.2 times (or less) difference in pump pulse intensities in the cases of 410 and 460 nm probing. As the signal amplitude of the long-lived component in Figure 2 of ref 13 (eaq-) is proportional to the square of the pump pulse intensity, this gives with respect to the different molar extinction coefficients for eaq- at 410 and 460 nm a factor of 2.4 (or less) difference between the signal amplitudes for probing at 460 and 410 nm. The experiment (Figure 2 of ref 13), on the other hand, reveals a factor of 3.2 difference. Therefore, mechanism (c) alone cannot fit the experimental data of ref 13. Thus, from the three different hypotheses describing the origin
The numerical calculations were performed, taking into account the decrease of pump pulse intensity during the propagation through the sample due to two-photon absorption in water and single-photon absorption of generated photoproducts. When calculating the absorption for the weak probe pulse, the difference in group velocity between pump and probe pulses was also considered. According to ref 1, the two-photon absorption process can be described mathematically by the following equation:
)
(
∂ 1 ∂ I (z,t) ) -β(ωpu,ωpu) Ipu2(z,t) + ∂z Vpu ∂t pu
(13)
where Vpu is the group velocity of pump pulse with frequency ωpu and intensity Tpu and β(ωpu,ωpu) is the TPA coefficient of pump radiation. It is assumed that the pump pulse is propagated along the z direction, and there is no depletion of the ground state of water molecules during its propagation. Changing the reference frame by the transformation t′ ) t - z/Vpu, z′ ) z to the one, propagating with the group velocity of the pump pulse, and remembering that different intermediates formed in the course of TPA process (high-lying excited states of water molecules, primary photoproducts) are also absorbing, the equation for the propagation of the pump pulse can be written in the form
∂
Ipu(z′,t′) ) -∑σij(ωpu){ni(z′,t′) - nj(z′,t′)}Ipu(z′,t′) -
∂z′
i
