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Photoinduced evaporation of benzene cluster ions
3 February 1995
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 233 (1995) 36-40
Photoinduced evaporation of benzene cluster ions Yasuhiro Nakai, Kazuhiko Ohashi, Nobuyuki Nishi * Department of Chemistry, Faculty of Science, Kyushu University,Hakozaki 6-10-1, Fukuoka 812, Japan Received 7 November 1994
Abstract
Photofragmentation of benzene cluster ions, (C6H6) + with n = 5-8, is studied in a wide photon energy range of 0.5-3.0 eV. Apparent evaporation energies for n = 5-8 are determined to be 0.55-0.52 eV. These are approximately 0.2 eV larger than the binding energies for one neutral monomer to the cluster ions. The average translational energies of 50-75 meV for ejected neutral monomers are obtained in the photon energy range of 1.1-2.0 eV. The remainders of nearly 0.2 eV cannot be explained only in terms of the translational energies of the photofragments. This result indicates that a part of the imparted energy is partitioned into photofragments as internal energies.
1. Introduction
Electronic structures [ 1-6], intermolecular binding forces [ 7 - 9 ] , and dissociation dynamics [1,10] of ( C 6 H 6 ) n+ have been widely studied in the past five years. In particular, localizability or mobility of the positive charge in the clusters with n >i 3 is of interest in connection with the charge mobility in liquid or crystals of aromatic molecules. In our previous work, we presented a series of spectroscopic studies of (C6H6) + with n = 2 - 6 in the wavelength range of 4 0 0 1400 nm, including the electronic spectra for n ~<6 in the visible [ 2,6 ] and near-infrared (IR) region [ 3-6 ]. Although a slight shift of the peak positions is noticed, the spectral features for n = 3 - 6 are essentially similar to those of (C6 H6)~-. This spectral similarity suggests that (C6 H6) f is the chromophore in the larger clusters and the positive charge is localized on the dimer core subunit. Following the electronic excitation of ( C 6 H 6 ) + over the visible and near-IR region, the possible decay * Corresponding author. 0009-2614/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved
SSDI0009-2614(94)01417-5
pathway of the clusters is only the cleavage of intermolecular bonds leading to ejection of neutral monomers. The photofragmentation behavior of ( C 6 H 6 ) + is of particular interest in relation to those of van der Waals cluster ions of atoms and small molecules: (CO2) + [11], (CO2) ~- [12], and Ar + [13]. For these van der Waals cluster ions, the average number of ejected neutral monomers is found to depend linearly on photon energy [ 11-13]. The energy partitioning in the photofragmentation of cluster ions is of importance for elucidating the photofragmentation mechanisms. In this work we present a set of the experimental data on the photofragmentation of ( C 6 H 6 ) + with n = 5-8 over a wide photon energy range of 0.5-3.0 eV. Apparent evaporation energies for n = 5-8 are obtained from the plot of the average number of ejected neutral monomers against photon energy. Average translational energies of neutral fragments are determined from the arrival-time distributions in the photon energy range of 1.1-2.0 eV. On the basis of these data, we show that the photofragmentation of (C6H6) + proceeds via sequential evaporation of neutral monomers and the
37
Y. Nakai et al. / Chemical Physics Letters 233 (1995) 36--40
SIZE OF FRAGMENT IONS 1
2
3
4
5
I
I
I
I
I
(C6H6)+
]
L
0.77
t
eV
[
with the fundamental o f the Y A G laser. The ionic photofragments were mass-analyzed with a reflection mass spectrometer [ 10]. The neutral photofragments were detected by a dual microchannel plate located behind the ion reflector.
1.20 eV ,, t
>.
-
f .....
3. R e s u l t s a n d d i s c u s s i o n rT,
.
.
.
.
.
.
.
.
/ 7
•
1.81 eV I
3.1. Size distribution o f ionic products
,
N
2.03 eV
30 '
40' 5'o go 70' FLIGHT TIME / /.ts Fig. 1. Difference TOF mass spectra of the ionic photofragments from (C6H6)~- in the photon energy range of 0.77-2.82 eV. The negative peaks found at n = 5 positions are due to the depletion of the metastable ion signal induced by the ionization laser. process can be regarded as unimolecular decay o f hot (C6H6) + .
2. E x p e r i m e n t a l
The apparatus used in this work has been described previously [10,14]. Briefly, (C6H6) + clusters were produced by resonance enhanced 2-photon ionization (RE2PI) o f neutral benzene clusters generated in a supersonic molecular beam [ 15 ]. The cluster ions were size-selectively excited with the second laser radiation (h v = 0.5-3.0 eV) either in the acceleration region or field-free region o f a time-of-flight ( T O F ) mass spectrometer. A dye laser (Lumonics HD-300) pumped with a XeC1 excimer laser (Lumonics EX-600) was used for the excitation at 2.4-3.0 eV. The photon energy range of 1.4-2.4 eV was covered with a dye laser (Spectra-Physics PDL-3) pumped with a Nd: Y A G laser (Spectra-Physics GCR- 18S). A Raman shifter (Spectra-Physics RS- 1 ) converted the dye-laser output into the photon energies of 0.9-1.7 eV. An infrared wavelength extension system (Spectra-Physics W E X - 2 D ) generated the light of 0.5-0.8 eV through difference frequency mixing of the dye-laser output
Fig. 1 displays a series of difference T O F mass spectra of the ionic photofragments from (C6H6) + at photon energies of 0.77-2.82 eV. Each of the mass spectra is obtained by subtracting the mass spectrum measured with the excitation laser switched off. W e confirm that the photofragments are predominantly produced by one-photon absorption [ 14]. With increasing h v from 0.77 to 1.75 eV, the product distribution shifts toward smaller cluster size. Further increase in h v does not change the product distribution; (C6H6) ~- is the dominant photofragment over the photon energy range of 1.75-2.82 eV. This is explained by a large binding energy of (C6H6)~-. This behavior is similarly observed for the benzene cluster ions with n >/5. Size distribution of ionic photofragments can be characterized with the average number of ejected neutral monomers (Nav)- Fig. 2 shows plots of the Nay n=6
i
Z rrl
6
n=7
................................
i
0.0
i
1.0
~
i
2.0
,
i
•
i
•
i
......
i
3.0
0.0
1.0
2.0
3.0
PHOTON ENERGY hv / eV Fig. 2. Average number of ejected neutral monomers (Nay) against photon energy. The lines drawn through the data points in the linearly increasing data region are the results of least-squares fittings. The reciprocals of the slopes are displayed in the boxes. The horizontal lines indicate the loss of n - 2 monomers from the parent ions.
38
Y. Nakai et al. / Chemical Physics Letters 233 (1995) 36--40
values as functions of h v. Nay displays linear dependence on h v for lower photon energies and almost levels off after the number reaches n - 2. This behavior is entirely different from that found in some covalentbonded cluster ions [ 16-20], where the product distribution is almost independent of photon energy.
1.2-
0.8-
Neutral . ,~":x- hv = 1.17 eV Iragmel/. ""~.
0.40.0I
i
3. 2. Apparent evaporation energy |.2-
Parent ion
,1'I
Solid lines for n >/5 drawn through the data points in Fig. 2 are the results of least-squares fittings. The reciprocals of the slopes for n = 5-8 are displayed in the boxes. These values can be regarded as apparent evaporation energies per one neutral molecule, the average energy required for removing one neutral molecule from the clusters. The monomer binding energy, + ( C 6 H 6 ) n _ I - C 6 H 6 , was determined to be 0.34 and --0.3 eV for n = 3 and 4, respectively, by means of high-pressure mass spectrometry [8]. The binding energies for n = 3-5 were determined to be 0.27-0.11 eV [ 7 ] and the values of 0.37-0.34 eV were presented as upper limits to the binding energies for n = 7 - 1 5 [9]. Although there exist discrepancies among these data, we can safely regard the binding energy of 0.34 eV for n = 3 [ 8 ] as an upper bound for the monomer binding energies for n >/4. The evaporation energies obtained in this work are, therefore, larger than the binding energies by approximately 0.2 eV.
use of the relationship Wt2 = W 2 - W 2 [21 ], where We and Wv are the widths at 22% of the maximum of the TOF profiles for neutral fragments and the parent ion, respectively. Following the treatment similar to that reported by Wei et al. [ 22 ], we can relate the width Wt with the velocity v of ejected neutral molecules in the center-of-mass frame:
3.3. Average translational energy of neutral fragments
2Lv Wt= V~ '
Fig. 3 displays typical TOF profiles of the parent 1.17 eV. The profile of the neutral fragments is obviously broader than that of the parent ion due to the translational energy released during the fragmentation processes. The TOF profiles of neutral fragments from the clusters with n = 5-8 are independent of the angle between the polarization vector of the excitation laser and the ion beam direction. Each of the TOF profiles of neutral fragments and the parent ions is well reproduced by a single Gauss function, indicating that the velocity of neutral fragments has the Bolzmann distribution. The average translational energy of neutral fragments is measured from the broadening width of the TOF profiles resulting from the translational energy release. The broadening width Wt can be obtained by
where L is the drift length of neutral fragments and Vo the velocity of the parent ion in the laboratory frame. We obtain the average translational energy Cavper neutral molecule from the following equation:
(C6H6) ~- and the neutral fragments with h v =
0.80.4. 0.038'.50 39100 FLIGHT TIME / ~ts
39.50
Fig. 3. Top: TOF profile of the neutral fragments from (C6H6)~-, following photoexcitation with h v= 1.17 eV. Bottom: TOF profile of the parent ion. The broadening of the top profile arises from the translational energy released into the neutral fragments.
(1)
1my 2 _ l m ~ W t V 2 ~ 2
'~av='2
--2
!~ 2L ] '
(2)
where m is the mass of a benzene molecule. The width of We=618 ns and Wp= 184 ns from Fig. 3 gives the broadening width of Wt = 590 ns. With the length of L = 0 . 8 4 m and Vo= 3.21 × 104 m/s the average translational energy of 53 meV is obtained for the excitation of (C6H6) ~- with hu= 1.17 eV. The 6av values for n = 5-8 in the photon energy range of 1.2-2.0 eV are displayed in Fig. 4.
Y. Nakai et al. / Chemical Physics Letters 233 (1995) 36--40
n=8
n=6 A
oa
A
i zc•<"d ~ 5 r~ z
n=7 80 1ool 60 4o 2o 0 . 112
n=5
116 210 116 210 112 PHOTON ENERGY ha/ / eV Fig. 4. Average translational energy ear for n = 5-8 plotted against photon energy. The ear values show slight increase with increasing incident photon energies.
3.4. Mechanism offragmentation From the linear dependence of Nay on h v in Fig. 2, we can see that the fragmentation of (C6H6) + proceeds through sequential loss of neutral monomers rather than direct ejection of neutral clusters [ 24 ]. The velocity distribution of neutral fragments is found to obey the Boltzmann distribution. This behavior is often seen in unimolecular decay of vibrationally hot clusters. Nagata and Kondow [ 23 ] observed direct dissociation of the ionic core in their photodissociation study of Ar + with 3 ~
evaporative mechanisms. 3.5. Energy partitioning in photoinduced evaporation From the average translational energies of neutral fragments, we can estimate the total translational energy released in the whole fragmentation process.
39
For this purpose, we need to know the amount of the translational energy carried by ionic fragments. In principle, the translational energies of ionic photofragments can be determined directly with a reflectron mass spectrometer. However, the experiment is quite difficult for the benzene system because the translational energy release is very small. The amount of translational energy carried by ionic fragments can be estimated by considering the following processes: [ ( C 6 H 6 ) + ] *--) [ (C6H6)+_ 1] * -b C6H6 ,
(3a)
[ (C6H6)+_ i ] *---) [ (C6H6)n+_2] * + C6H6 ,
(3b)
[ (C6H6)~-+ 1] *---~ [ ( C 6 H 6 ) f ] * --FC6H6 ,
(3c)
where the asterisk denotes the cluster with sufficient internal energy for the next evaporation. The ejection of the monomers continues until the internal energy of the cluster becomes low enough to retain the most weakly bounded molecule. The sequential process terminates in the final ionic product of cluster size k. We assume that all ejected neutral monomers have the same velocity v on average. The laws of momentum and energy conservation for each sequential process of Eq. (3) allow the calculation of the amount of translational energy released in each process. For instance, we consider the fragmentation of (C6H6) ~- into (C6H6)3+ + 3C6H 6 at h v = 1.17 eV. The translational energies associated with Eqs. ( 3 a ) - ( 3 c ) are 64, 66, and 71 meV, respectively. We obtain an upper limit of --- 100 meV to the average translational energy per neutral monomer for n = 6-8 in the photon energy range of 1.1-2.0 eV. The value of -- 100 meV does not coincide with the energy difference of --0.2 eV between the evaporation energy and the binding energy for n =5-8. In the photofragmentation studies of Ar + with n = 3-60, Levinger et al. deduced an evaporation energy of 90 meV per atom in their large cluster limit [ 13]. Nagata and Kondow determined the average translational energies of ejected atoms from Ar + with n = 3-24 with excitation at 532 nm. They reported a value of 47 meV at n = 19. The energy of 47 meV can be regarded as an upper limit to the average translational energy for the larger clusters. The difference between the evaporation energy of 90 meV and the translational energy of 47 meV is 43 meV, which is
40
Y. Nakai et al. / Chemical Physics Letters 233 (1995) 36-40
close to the binding energy of = 50 meV calculated for Arn with n > 20 by Hoare and Pal [ 25 ]. Thereby, one can explain the energy partitioning by considering only the translational energy. On the other hand, for (C6H6) + with n = 5 - 8 , the difference of = 0 . 2 eV between the evaporation energy and the binding energy cannot be explained only in terms of the translational energy of the photofragments. This result indicates that a part of the imparted photon energy is partitioned into the photofragments as internal energies. As we showed in the study of the bare (C6H6) ~[ 10], the time scale of the separation of the dimer core is expected to be quite long compared to that of typical direct dissociation. We expect that the intermolecular mode of the dimer core along the dissociation coordinate is effectively coupled to the van der Waals modes of the cluster. Following a rapid conversion of the electronic energy of the dimer core into the internal energy of the cluster ion, the hot (C6 H6) + relaxes through the sequential evaporation. It is of importance to examine how the imparted photon energy is distributed among the available modes and whether the intermolecular modes alone are active or the intramolecular vibrations are also responsible. Determination of the rate of fragmentation, if possible, will be useful to examine the number of active modes with the help of statistical theories for unimolecular dissociation.
4. Conclusion We have shown that an energy which is at least 0.2 eV larger than the static binding energy is required on the average for inducing the ejection of one neutral monomer from (C6H6)~+ through electronic excitation of the chromophoric dimer core. This is probably because energy flow among the available modes of the cluster is so fast that a large part of the imparted energy is effectively converted from the repulsive energy of the dimer core to the internal energy of the cluster. As a result, the photoexcited (C6H6)~+ decays through sequential evaporation of neutral monomers as a unimolecular decay of hot ( C 6 H 6 ) + .
Acknowledgement This work was supported by a Grant-in-Aid for New Program "Intelligent Molecular Systems with Controlled Functionality" [06NP0301 ] and for a Scientific Research program [04403002] from the Ministry of Education, Science and Culture of Japan.
References [ 1] J.T. Snodgrass,R.C. Dunbarand M.T. Bowers,J. Phys. Chem. 94 (1990) 3648. [2] K. Ohashi and N. Nishi,J. Chem. Phys. 95 ( 1991) 4002. 13] K. Ohashi and N. Nishi,J. Phys. Chem. 96 (1992) 2931. [4] K. Ohashi, Y. Nakai, T. Shibataand N. Nishi,Laser Chem. 14 (1994) 3. I5] T. Shibata, K. Ohashi, Y. Nakai and N. Nishi, Chem. Phys. Letters 229 (1994) 604. [6] Y. Nakai, K. Ohashi and N. Nishi, to be submitted. I7] H. Krause, B. Ernstberger and H.J. Neusser, Chem. Phys. Letters 184 ( 1991) 411. [8] K. Hiraoka, S. Fujimaki and K. Aruga, J. Chem. Phys. 95 (1991) 8413. [9] S.M. Beck and J.H. Hecht, J. Chem. Phys. 96 (1992) 1975. [ 10] K. Ohashi and N. Nishi, J. Chem. Phys. 98 (1993) 390. [ 11 ] M.L.Alexander,M.A. Johnsonand W.C. Lineberger,J. Chem. Phys. 82 (1985) 5288. [ 12] M.L. Alexander, M.A. Johnson, N.E. Levinger and W.C. Lineberger,Phys. Rev. Letters 57 (1986) 976. [ 13] N.E. Levinger,D. Ray, M.L. Alexanderand W.C. Lineberger, J. Chem. Phys. 89 (1988) 5654. [ 14] Y. Nakai, K. Ohashi and N. Nishi,J. Phys. Chem. 96 (1992) 7873. [ 15] H. Shinoharaand N. Nishi,J. Chem. Phys. 91 (1989) 6743. [ 16] L.A. Bloomfield,R.R. Freemanand W.L. Brown, Phys. Rev. Letters 54 (1985) 2256. [ 17] P.J. Brucat, L.S. Zheng, C.L. Pettiette, S. Yang and R.E. Smalley,J. Chem. Phys. 84 (1986) 3078. [ 18] M.E. Geusic, M.F. Jarrold, TJ. Mcllrath, R.R. Freeman and W.L. Brown,J. Chem. Phys. 86 (1987) 3862. [ 19] S.M. Beck and J.M. Andrews,J. Chem. Phys. 91 (1989) 4420. [201 K.F. Willey,P.Y. Cheng, T.G, Taylor,M.B. Bishop and M.A. Duncan,J. Phys. Chem. 94 (1990) 1544. [21] M.A. Baldwin, P.J. Derrick and R.P. Morgan, Org. Mass. Spectrom. 11 (1976) 440. 122] S. Wei, W.B. Tzeng and A.W. CastlemanJr., J. Chem. Phys. 92 (1989) 7143. [23] T. Nagata and T. Kondow,J. Chem. Phys. 98 (1993) 290. [24} K. Ohashi, Y. Nakai and N. Nishi,Laser Chem., in press. [25] M.R. Hoare and P. Pal, Advan.Phys. 24 (1975) 645.
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 233 (1995) 36-40
Photoinduced evaporation of benzene cluster ions Yasuhiro Nakai, Kazuhiko Ohashi, Nobuyuki Nishi * Department of Chemistry, Faculty of Science, Kyushu University,Hakozaki 6-10-1, Fukuoka 812, Japan Received 7 November 1994
Abstract
Photofragmentation of benzene cluster ions, (C6H6) + with n = 5-8, is studied in a wide photon energy range of 0.5-3.0 eV. Apparent evaporation energies for n = 5-8 are determined to be 0.55-0.52 eV. These are approximately 0.2 eV larger than the binding energies for one neutral monomer to the cluster ions. The average translational energies of 50-75 meV for ejected neutral monomers are obtained in the photon energy range of 1.1-2.0 eV. The remainders of nearly 0.2 eV cannot be explained only in terms of the translational energies of the photofragments. This result indicates that a part of the imparted energy is partitioned into photofragments as internal energies.
1. Introduction
Electronic structures [ 1-6], intermolecular binding forces [ 7 - 9 ] , and dissociation dynamics [1,10] of ( C 6 H 6 ) n+ have been widely studied in the past five years. In particular, localizability or mobility of the positive charge in the clusters with n >i 3 is of interest in connection with the charge mobility in liquid or crystals of aromatic molecules. In our previous work, we presented a series of spectroscopic studies of (C6H6) + with n = 2 - 6 in the wavelength range of 4 0 0 1400 nm, including the electronic spectra for n ~<6 in the visible [ 2,6 ] and near-infrared (IR) region [ 3-6 ]. Although a slight shift of the peak positions is noticed, the spectral features for n = 3 - 6 are essentially similar to those of (C6 H6)~-. This spectral similarity suggests that (C6 H6) f is the chromophore in the larger clusters and the positive charge is localized on the dimer core subunit. Following the electronic excitation of ( C 6 H 6 ) + over the visible and near-IR region, the possible decay * Corresponding author. 0009-2614/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved
SSDI0009-2614(94)01417-5
pathway of the clusters is only the cleavage of intermolecular bonds leading to ejection of neutral monomers. The photofragmentation behavior of ( C 6 H 6 ) + is of particular interest in relation to those of van der Waals cluster ions of atoms and small molecules: (CO2) + [11], (CO2) ~- [12], and Ar + [13]. For these van der Waals cluster ions, the average number of ejected neutral monomers is found to depend linearly on photon energy [ 11-13]. The energy partitioning in the photofragmentation of cluster ions is of importance for elucidating the photofragmentation mechanisms. In this work we present a set of the experimental data on the photofragmentation of ( C 6 H 6 ) + with n = 5-8 over a wide photon energy range of 0.5-3.0 eV. Apparent evaporation energies for n = 5-8 are obtained from the plot of the average number of ejected neutral monomers against photon energy. Average translational energies of neutral fragments are determined from the arrival-time distributions in the photon energy range of 1.1-2.0 eV. On the basis of these data, we show that the photofragmentation of (C6H6) + proceeds via sequential evaporation of neutral monomers and the
37
Y. Nakai et al. / Chemical Physics Letters 233 (1995) 36--40
SIZE OF FRAGMENT IONS 1
2
3
4
5
I
I
I
I
I
(C6H6)+
]
L
0.77
t
eV
[
with the fundamental o f the Y A G laser. The ionic photofragments were mass-analyzed with a reflection mass spectrometer [ 10]. The neutral photofragments were detected by a dual microchannel plate located behind the ion reflector.
1.20 eV ,, t
>.
-
f .....
3. R e s u l t s a n d d i s c u s s i o n rT,
.
.
.
.
.
.
.
.
/ 7
•
1.81 eV I
3.1. Size distribution o f ionic products
,
N
2.03 eV
30 '
40' 5'o go 70' FLIGHT TIME / /.ts Fig. 1. Difference TOF mass spectra of the ionic photofragments from (C6H6)~- in the photon energy range of 0.77-2.82 eV. The negative peaks found at n = 5 positions are due to the depletion of the metastable ion signal induced by the ionization laser. process can be regarded as unimolecular decay o f hot (C6H6) + .
2. E x p e r i m e n t a l
The apparatus used in this work has been described previously [10,14]. Briefly, (C6H6) + clusters were produced by resonance enhanced 2-photon ionization (RE2PI) o f neutral benzene clusters generated in a supersonic molecular beam [ 15 ]. The cluster ions were size-selectively excited with the second laser radiation (h v = 0.5-3.0 eV) either in the acceleration region or field-free region o f a time-of-flight ( T O F ) mass spectrometer. A dye laser (Lumonics HD-300) pumped with a XeC1 excimer laser (Lumonics EX-600) was used for the excitation at 2.4-3.0 eV. The photon energy range of 1.4-2.4 eV was covered with a dye laser (Spectra-Physics PDL-3) pumped with a Nd: Y A G laser (Spectra-Physics GCR- 18S). A Raman shifter (Spectra-Physics RS- 1 ) converted the dye-laser output into the photon energies of 0.9-1.7 eV. An infrared wavelength extension system (Spectra-Physics W E X - 2 D ) generated the light of 0.5-0.8 eV through difference frequency mixing of the dye-laser output
Fig. 1 displays a series of difference T O F mass spectra of the ionic photofragments from (C6H6) + at photon energies of 0.77-2.82 eV. Each of the mass spectra is obtained by subtracting the mass spectrum measured with the excitation laser switched off. W e confirm that the photofragments are predominantly produced by one-photon absorption [ 14]. With increasing h v from 0.77 to 1.75 eV, the product distribution shifts toward smaller cluster size. Further increase in h v does not change the product distribution; (C6H6) ~- is the dominant photofragment over the photon energy range of 1.75-2.82 eV. This is explained by a large binding energy of (C6H6)~-. This behavior is similarly observed for the benzene cluster ions with n >/5. Size distribution of ionic photofragments can be characterized with the average number of ejected neutral monomers (Nav)- Fig. 2 shows plots of the Nay n=6
i
Z rrl
6
n=7
................................
i
0.0
i
1.0
~
i
2.0
,
i
•
i
•
i
......
i
3.0
0.0
1.0
2.0
3.0
PHOTON ENERGY hv / eV Fig. 2. Average number of ejected neutral monomers (Nay) against photon energy. The lines drawn through the data points in the linearly increasing data region are the results of least-squares fittings. The reciprocals of the slopes are displayed in the boxes. The horizontal lines indicate the loss of n - 2 monomers from the parent ions.
38
Y. Nakai et al. / Chemical Physics Letters 233 (1995) 36--40
values as functions of h v. Nay displays linear dependence on h v for lower photon energies and almost levels off after the number reaches n - 2. This behavior is entirely different from that found in some covalentbonded cluster ions [ 16-20], where the product distribution is almost independent of photon energy.
1.2-
0.8-
Neutral . ,~":x- hv = 1.17 eV Iragmel/. ""~.
0.40.0I
i
3. 2. Apparent evaporation energy |.2-
Parent ion
,1'I
Solid lines for n >/5 drawn through the data points in Fig. 2 are the results of least-squares fittings. The reciprocals of the slopes for n = 5-8 are displayed in the boxes. These values can be regarded as apparent evaporation energies per one neutral molecule, the average energy required for removing one neutral molecule from the clusters. The monomer binding energy, + ( C 6 H 6 ) n _ I - C 6 H 6 , was determined to be 0.34 and --0.3 eV for n = 3 and 4, respectively, by means of high-pressure mass spectrometry [8]. The binding energies for n = 3-5 were determined to be 0.27-0.11 eV [ 7 ] and the values of 0.37-0.34 eV were presented as upper limits to the binding energies for n = 7 - 1 5 [9]. Although there exist discrepancies among these data, we can safely regard the binding energy of 0.34 eV for n = 3 [ 8 ] as an upper bound for the monomer binding energies for n >/4. The evaporation energies obtained in this work are, therefore, larger than the binding energies by approximately 0.2 eV.
use of the relationship Wt2 = W 2 - W 2 [21 ], where We and Wv are the widths at 22% of the maximum of the TOF profiles for neutral fragments and the parent ion, respectively. Following the treatment similar to that reported by Wei et al. [ 22 ], we can relate the width Wt with the velocity v of ejected neutral molecules in the center-of-mass frame:
3.3. Average translational energy of neutral fragments
2Lv Wt= V~ '
Fig. 3 displays typical TOF profiles of the parent 1.17 eV. The profile of the neutral fragments is obviously broader than that of the parent ion due to the translational energy released during the fragmentation processes. The TOF profiles of neutral fragments from the clusters with n = 5-8 are independent of the angle between the polarization vector of the excitation laser and the ion beam direction. Each of the TOF profiles of neutral fragments and the parent ions is well reproduced by a single Gauss function, indicating that the velocity of neutral fragments has the Bolzmann distribution. The average translational energy of neutral fragments is measured from the broadening width of the TOF profiles resulting from the translational energy release. The broadening width Wt can be obtained by
where L is the drift length of neutral fragments and Vo the velocity of the parent ion in the laboratory frame. We obtain the average translational energy Cavper neutral molecule from the following equation:
(C6H6) ~- and the neutral fragments with h v =
0.80.4. 0.038'.50 39100 FLIGHT TIME / ~ts
39.50
Fig. 3. Top: TOF profile of the neutral fragments from (C6H6)~-, following photoexcitation with h v= 1.17 eV. Bottom: TOF profile of the parent ion. The broadening of the top profile arises from the translational energy released into the neutral fragments.
(1)
1my 2 _ l m ~ W t V 2 ~ 2
'~av='2
--2
!~ 2L ] '
(2)
where m is the mass of a benzene molecule. The width of We=618 ns and Wp= 184 ns from Fig. 3 gives the broadening width of Wt = 590 ns. With the length of L = 0 . 8 4 m and Vo= 3.21 × 104 m/s the average translational energy of 53 meV is obtained for the excitation of (C6H6) ~- with hu= 1.17 eV. The 6av values for n = 5-8 in the photon energy range of 1.2-2.0 eV are displayed in Fig. 4.
Y. Nakai et al. / Chemical Physics Letters 233 (1995) 36--40
n=8
n=6 A
oa
A
i zc•<"d ~ 5 r~ z
n=7 80 1ool 60 4o 2o 0 . 112
n=5
116 210 116 210 112 PHOTON ENERGY ha/ / eV Fig. 4. Average translational energy ear for n = 5-8 plotted against photon energy. The ear values show slight increase with increasing incident photon energies.
3.4. Mechanism offragmentation From the linear dependence of Nay on h v in Fig. 2, we can see that the fragmentation of (C6H6) + proceeds through sequential loss of neutral monomers rather than direct ejection of neutral clusters [ 24 ]. The velocity distribution of neutral fragments is found to obey the Boltzmann distribution. This behavior is often seen in unimolecular decay of vibrationally hot clusters. Nagata and Kondow [ 23 ] observed direct dissociation of the ionic core in their photodissociation study of Ar + with 3 ~
evaporative mechanisms. 3.5. Energy partitioning in photoinduced evaporation From the average translational energies of neutral fragments, we can estimate the total translational energy released in the whole fragmentation process.
39
For this purpose, we need to know the amount of the translational energy carried by ionic fragments. In principle, the translational energies of ionic photofragments can be determined directly with a reflectron mass spectrometer. However, the experiment is quite difficult for the benzene system because the translational energy release is very small. The amount of translational energy carried by ionic fragments can be estimated by considering the following processes: [ ( C 6 H 6 ) + ] *--) [ (C6H6)+_ 1] * -b C6H6 ,
(3a)
[ (C6H6)+_ i ] *---) [ (C6H6)n+_2] * + C6H6 ,
(3b)
[ (C6H6)~-+ 1] *---~ [ ( C 6 H 6 ) f ] * --FC6H6 ,
(3c)
where the asterisk denotes the cluster with sufficient internal energy for the next evaporation. The ejection of the monomers continues until the internal energy of the cluster becomes low enough to retain the most weakly bounded molecule. The sequential process terminates in the final ionic product of cluster size k. We assume that all ejected neutral monomers have the same velocity v on average. The laws of momentum and energy conservation for each sequential process of Eq. (3) allow the calculation of the amount of translational energy released in each process. For instance, we consider the fragmentation of (C6H6) ~- into (C6H6)3+ + 3C6H 6 at h v = 1.17 eV. The translational energies associated with Eqs. ( 3 a ) - ( 3 c ) are 64, 66, and 71 meV, respectively. We obtain an upper limit of --- 100 meV to the average translational energy per neutral monomer for n = 6-8 in the photon energy range of 1.1-2.0 eV. The value of -- 100 meV does not coincide with the energy difference of --0.2 eV between the evaporation energy and the binding energy for n =5-8. In the photofragmentation studies of Ar + with n = 3-60, Levinger et al. deduced an evaporation energy of 90 meV per atom in their large cluster limit [ 13]. Nagata and Kondow determined the average translational energies of ejected atoms from Ar + with n = 3-24 with excitation at 532 nm. They reported a value of 47 meV at n = 19. The energy of 47 meV can be regarded as an upper limit to the average translational energy for the larger clusters. The difference between the evaporation energy of 90 meV and the translational energy of 47 meV is 43 meV, which is
40
Y. Nakai et al. / Chemical Physics Letters 233 (1995) 36-40
close to the binding energy of = 50 meV calculated for Arn with n > 20 by Hoare and Pal [ 25 ]. Thereby, one can explain the energy partitioning by considering only the translational energy. On the other hand, for (C6H6) + with n = 5 - 8 , the difference of = 0 . 2 eV between the evaporation energy and the binding energy cannot be explained only in terms of the translational energy of the photofragments. This result indicates that a part of the imparted photon energy is partitioned into the photofragments as internal energies. As we showed in the study of the bare (C6H6) ~[ 10], the time scale of the separation of the dimer core is expected to be quite long compared to that of typical direct dissociation. We expect that the intermolecular mode of the dimer core along the dissociation coordinate is effectively coupled to the van der Waals modes of the cluster. Following a rapid conversion of the electronic energy of the dimer core into the internal energy of the cluster ion, the hot (C6 H6) + relaxes through the sequential evaporation. It is of importance to examine how the imparted photon energy is distributed among the available modes and whether the intermolecular modes alone are active or the intramolecular vibrations are also responsible. Determination of the rate of fragmentation, if possible, will be useful to examine the number of active modes with the help of statistical theories for unimolecular dissociation.
4. Conclusion We have shown that an energy which is at least 0.2 eV larger than the static binding energy is required on the average for inducing the ejection of one neutral monomer from (C6H6)~+ through electronic excitation of the chromophoric dimer core. This is probably because energy flow among the available modes of the cluster is so fast that a large part of the imparted energy is effectively converted from the repulsive energy of the dimer core to the internal energy of the cluster. As a result, the photoexcited (C6H6)~+ decays through sequential evaporation of neutral monomers as a unimolecular decay of hot ( C 6 H 6 ) + .
Acknowledgement This work was supported by a Grant-in-Aid for New Program "Intelligent Molecular Systems with Controlled Functionality" [06NP0301 ] and for a Scientific Research program [04403002] from the Ministry of Education, Science and Culture of Japan.
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