J . Phys. Chem. 1985, 89, 4617-4621
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with a value of 8.4 f 0.5 eV obtained from an electron impact mass spectrometric investigation.', From this present study and recent studies on Ti, TiO,' and V,,, the reason for the discrepancy is clear. In ref 12, the current of VO' (Ivo+) was studied as a function of incident electron energy and, in order to estimate the first ionization potential of VO, Zvo+ is extrapolated back to zero to give the appearance potential of VO+ from VO. However, in the incident electron kinetic energy range 10.0-20.0 eV it is likely that the cross section for the second one-electron ionization of VO is much greater than the cross section for the first one-electron ionization, as indicated in the present work. It is not surprising therefore that the linear extrapolation method used in ref 12 erroneously yields a value which is very close to the second IP of VO even though the measurements were calibrated by use of atomic vanadium. In the only previous spectroscopic study on V0',Is two new electronic transitions of VO' have been observed in emission (IZ'-IZ+ and IA-IA). In both cases the lower electronic states are thought to be perturbed by the A3A state and it seems fairly
4617
clear that both the A3A and lower IA state arise from the electronic configuration . . . 8 ~ ~ 3 ~ ~ 1 For 6 ~ the 9 a lower ~ . ' A state, values of AG,,,of 960 cm-l and re of 1.601 A were obtained from rotational analysis of the observed spectrum. The corresponding values obtained in this work for the VO' X3Z- state are 1050 f 40 cm-l and 1.54 f 0.01 A. Clearly further work is needed to accurately establish the position of the excited singlet states of VO+ observed in ref 18 relative to the VO' 3Z- ground state and it is hoped that this present study will stimulate both theoretical and experimental interest in this problem.
Acknowledgment. We thank the C.E.G.B. and S.E.R.C. (U.K.) for financial assistance, the S.E.R.C. for the award of a studentship to B.W.J.G. and a C.A.S.E. studentship (with C.E.G.B.) to M.P.H. Dr. A. Paul and Mr. A. M. Ellis are also acknowledged for assistance in the final stages of this work. Professor E. J. Baerends and Dr. J. Snijders are also thanked for valuable discussions and making copies of their HFS programs available. Registry No. VO, 12035-98-2.
Dynamics of CS(A'n) Formation in the Dissociation of CS2 Konrad T. Wu Department of Chemistry, State University of New York, College at Old Westbury, Old Westbury, New York 11568 (Received: May 6, 1985) CS(AIII) product energy distributions are analyzed from the fluorescence observed in an Ar(3P2,0)+ CS2 afterglow and compared with results from photodissociationat various wavelengths. The formation mechanism of CS(A) in the dissociation of CS2 originates from predissociation of the Rydberg state converging into the ground state of CS2+below the ionization limit, via a very steep repulsive potential curve. Energy disposal into translation of the fragments in this bound-continuum region is consistent with the result predicted from the simple impulsive model. Vibrational energy distributions of CS(A) fragment are found to be influenced principally by the Franck-Condon effects; such distributions fit well with the results from golden rule calculations.
Introduction Photofragment dynamics of polyatomic molecules has received considerable interest in recent years.'" New technological advances in the development of powerful light sources and sophisticated detection systems have improved our understanding of the dissociation processes under investigation. Detailed dynamical information can now be obtained from such measurements as final-state distributions (translational and internal), product angular distribution, dissociation lifetime, polarized fluorescence, etc. As a result of rapidly increasing disclosure of the microscopic details of photofragmentation, many theoretical models have been developed for interpreting the experimentally observed dynamical effects. It is believed that accurate theoretical description of the photofragment dynamics may soon become possible for simple polyatomic m o l e c ~ l e s . ~ - ~ Analysis of the vibrational and rotational structures in the fluorescence emission of electronically excited fragments provides a simple way of probing the dynamics of excited-state photofragmentation; the amount of such information available is com(1) (2) (3) (4)
Simons, J. P. J . Phys. Chem. 1984,88, 1287. Leone, S. R. Adu. Chem. Phys. 1982, 50, 255. Bersohn, R. J . Phys. Chem. 1984, 88, 5145. Shapiro, M.; Bersohn, R. Annu. Reu. Phys. Chem. 1982, 33, 409. (5) Greene, C. H.; Zare, R. N. Annu. Rev. Phys. Chem. 1982, 33, 119. (6) Freed, K. F.; Band, Y. B. "Excited States"; Lim, E. C., Ed.; Academic Press: New York, 1977; Vol. 3, p 109. (7) Morse, M. D.; Freed, K. F. J . Chem. Phys. 1981, 74, 4395. (8) Band, Y.B.; Freed, K. F.; Kouri, D. J. J . Chem. Phys. 1981, 74,4380. (9) Morse, M. D.; Freed, K. F.; Band, Y. B. J. Chem. Phys. 1979, 70, 3604, 3620.
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parably much less than for photodissociation processes leading to the ground-state fragments. Even for simple triatomic molecules, limited information is a ~ a i l a b l e . ' - ~ J ~ *It' is thus highly desirable to expand the data base for these molecules, which will be useful for further development of dynamical models. Analogous to the photodissociative excitation process of triatomic molecules, other fragmentation methods such as electron-12 and particle-impactI3-l5dissociative excitation provide complementary dynamical information. We have recently demonstrated13 that the vibrational energy distribution of SO(A) produced from the argon-metastable impact dissociation of SO, is comparable to that resulting from the photodissociation process. The formation mechanism of SO(A) via predissociation of SO, is identical with the photofragment dynami~s.'~It is interesting to extend this kind of study in order to obtain a better understanding of the dynamics of triatomic molecular fragmentation. Since a great deal of dynamical information is available concerning the photodissociative excitation of CS2 for the formation of CS(A'II),1'~12,'6~'7 it would be reasonable to investigate the excited-state fragmentation of
'
(10) Lahmani, F.; Lardeux, C.; Solgadi, D. J . Chem. Phys. 1982, 77, 275. (11) Ashfold, M. N. R.; Quinton, A. M.; Simons, J. P. J . Chem. SOC., Furuduy Trans. 2 1980, 76, 905 and references therein. (12) See, e.g.: Ajello, J. M.; Srivastava, S. K. J . Chem. Phys. 1981, 75, 4454. (13) Wu, K. T. Chem. Phys. 1984, 87, 109. (14) Ozaki, Y.; Kondow, T.; Kuchitsu, K. Chem. Phys. 1983, 77, 223. (15) Snyder, H. L.; Smith, B. T.; Parra, T. P.; Martin, R. M. Chem. Phys. 1982, 65, 397. (16) Lee, L. C.; Judge, D. L. J . Chem. Phys. 1975, 63, 2782. (17) Okabe, H. J . Chem. Phys. 1972, 56, 4381.
0 1985 American Chemical Society
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The Journal of Physical Chemistry, Vol. 89, No. 21, 1985 CS(A'n-X'T)
TABLE I: Relative Vibrational Population of CS(A'II) Produced from the Ar('Pn.2) CS, Process
+
d-X 4,O I
d-X 4,l I
d-X 3,l 0 ' 1,'' d-X 7 0 2,3 I 12 3,24,3 /';, 272 ,j3,34,4 O J j l ! \ 3 5z9 corresponding to energies at or above the dissociation limit. It has also been found in the photodissociation work that the CS(A) fluorescence quantum efficiency is a decreasing function of incident photon energy16 and that below the wavelength corresponding to the ionization potential of CS2 fluorescence efficiencies become quite small17 while the CS(A X) fluorescence persists with similar vibrational This indicates X) fluorescence originates from the boundthat the CS(A continuum overlap below the ionization limit and that the additional energy beyond this region is no longer efficient for promoting the vibrational excitation in the dissociation channel. The fact that relative vibrational populations of CS(A) obtained from various high energy excitation sources (Ar* or hv) are comparable suggests that about the same amount of internal energy is deposited into the product fragments from different excitation processes and that the additional energy is distributed into the translational motion. In the predissociation of triatomic molecules, the fragment vibrational energy distribution depends primarily on the relative magnitude of the Franck-Condon overlap for dissociation to various vibrational states of the fragment. Generally, such a vibrational distribution is highly sensitive to the vibronic composition of the predissociating state. Geometric changes in the diatomic fragment associated with the b o u n d a n t i m u m transition may thus play a significant roles6 Therefore, it is reasonable to discuss the present vibrational energy distributions of the CS(A) fragment in terms of Franck-Condon effect^.^^,^' Since the
+
-
-
~~
(27) Tanaka, Y.; Jursa, A. S.; LeBlanc, F. J. J . Chem. Phys. 1960, 32, 1205. (28) Fotakis, C.; Zevgolis, D.; Efthimiopoulos, T.; Patsilinakou, E. Chem. Phys. Lett. 1984, 110, 13. (29) Doering, J . P.; McDiarmid, R.J . Phys. Chem. 1983, 87, 1822. (30) Moore, D. S.;Bomse, D. S.; Valentini, J. J. J. Chem. Phys. 1983, 79, 1745.
fV1
f
V'
fV'
fV,
'V'
-
Figure 2. Observed (- * -) and calculated (- 0 - -) golden rule CS(A'II) product state vibrational distributions for the dissociation of CS, at various excitation energies. Distributions are normalized to unity. Value of the internuclear separation for the initial oscillator used in the golden rule calculations is 1.482 A.
intermediate Rydberg states prior to predissociation of CSz are formed by promoting an electron from the nonbonding molecular 0 r b i t a 1 , ~little ~ ~ change ~~ in equilibrium geometry should be expected under this condition, and the linear configuration should thus be preserved. The unexcited vibrational level of the intermediate state will, therefore, be preferentially populated during the excitation process. The simple golden rule model3' for the dissociation of triatomic molecules may be suitable for the discussion of the Franck-Condon-like effects in the present case because this model does not allow vibrational excitation in the intermediate molecule. The vibrational distributions of the excited CS(A) fragment from the dissociation of CSz were therefore evaluated on the basis of the simple golden rule model and compared with the experimental results. When the diatomic fragment is suddenly generated by a transition to a repulsive potential curve, the properties of the diatomic oscillator are immediately changed to their final values. According to Berry's golden rule,31relative transition probabilities, Wt+ for the formation of final product states can be calculated directly by a first-order treatment. In the sudden limit, matrix elements in the golden rule equation become Franck-Condon factors for initial and final oscillator states, so that
where P(E) is a density-of-final-state function which is equivalent to eq 4 in the present case. The results calculated from such a golden rule model are compared with the experimental values as shown in Figure 2. The internuclear separation (R') of the initial "dressed" oscillator giving the best fit to experimental data is 1.482 A for each case. From this comparison, it is clear that the vibrational energy disposal is a consequence of Franck-Condon-like effects. The experimental vibrational distributions are broader than simple golden rule model predictions, which implies that the dissociation of CSz leading to the CS(A) fragment occurs in the short-range region of the final repulsive potential that falls steeply as the fragments ~ e p a r a t e . ~The . ~ fact that the rotational distribution of the CS(A) fragment is broad in the photodissociation of the CSZ1'seems to support the notion that the repulsive potential curve is very steep in the Franck-Condon region of the transition which scans a wide range of translational energy.9 These observations may be helpful for the theoretical understanding9 of the excited-state fragmentation of CS2. In order to understand the dissociation dynamics of CSzin more detail, information on the energy disposal into different energy modes is required. Since the rotational structures of the CS(A X) emission could not be resolved in the present study, the rotational energy partitioning could not be obtained. However,
-
(31) Berry, M. J. Chem. Phys. Lett. 1974, 29, 329. (32) Hubin-Franskin, M. J.; Delwiche, J.; Poulin, A,; Leclerc, B.; Roy, P.; Roy, D.J . Chem. Phys. 1983, 78, 1200.
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The Journal of Physical Chemistry. Vol. 89, No. 21, 1985
If there exists a potential barrier in the exit channel, the prior distribution for a generalized RRK form should be given as34
-
2000
it . ’ L /
E,/E=0.48
where V, is the barrier height. V, must be equal to 16%of the total available energy ( E ) in order for a P‘vT) function to result i n y T = 52%. However, no threshold can be recognized in the straight line extrapolation to the available energy axis, as shown in Figure 3. In addition, there is no evidence of an activation barrier in the photodissociative excitation of CS2 from the fluorescence excitation res~1ts.l~ This disagreement suggests that the translational energy distribution of the product fragments in the dissociation of CS2 is not controlled by the statistical factor. Furthermore, the rotational band contour of the CS(A X) emission produced from photodissociation of CS2 at 130.4 nm” is not a simple Boltzmann distribution, but agrees qualitatively with the Franck-Condon model predictions for near collinear dissociation. Since a very steep repulsive potential suddenly develops between S and CS fragments upon excitation of CS,, the simple impulsive may be suitable for interpreting the energy disposal in the present case. According to this model, the available energy released after bond scission and electronic excitation of fragments is transferred instantaneously to the motion of the separating atoms (S and C in CS2). From the laws of conservation of energy and momentum, the fraction of the translational energy deposited into product fragments is expected to be
-
1
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0
1o
1
I
m
2oooo
E (cm-l)
Figure 3. Internal energy content of CS(A) as a function of available energy ( E ) . The dashed line indicates the energy corresponding to the first ionization potential of CS2.
the linear equilibrium geometry is preserved in the intermediate bound state after excitation of CS2due to the promotion of an electron from a nonbonding orbital, and the maximum rotational energy distribution in the nascent fragment of CS(A) can be predicted from the conservation of angular m o m e n t ~ m . ’ ~ For -~~ the nonvibrating molecule, the Boltzmann rotational distribution should peak at J’ = 30.4 for the CS(A) fragment, corresponding to a fraction of -8% of the total available energy in the present reaction system. Partitioning of energy into rotation at 130.4 nm was estimated from Figure 4 of ref 11 in which the band contour corresponds to J’(most probable) = 21.3. Such data at other wavelengths are estimated on the basis of the assumption that the rotational distributions shift smoothly toward higher J‘ as the photon energy increases9 while the upper limit is set at Ar* excitation energy in which the rotational distribution is constrained by angular momentum con~ervation.~ J’ = 21.7, 23.9, and 24.6 were thus used for X = 129.5, 123.6, and 121.6 nm, respectively. The results of energy partitioning at various excitation energies are summarized in Table 11. The variation of the total internal energy content of the CS(A) fragment can thus be calculated with increasing available energy. As shown in Figure 3, the CS(A) internal energy content follows a linear dependence as a function of available energy below the ionization potential of CS,; it levels off at higher energies. The slope of the straight line at low energies is -0.48 0.05, assuming a maximum uncertainty of 10%from the photodissociation data.” This indicates that -48% of the total available energy is partitioned into the internal motion and therefore 52%of the total energy should appear as the kinetic energy of the separating products during dissociation. Since the excited-state dissociation mechanism of CS2 is predissociative either after internal conversion or after intersystem crossing to the repulsive triplet state, the translational energy distribution is expected to be statistical. The prior translational energy distribution from the RRHO model is given24.25by
It predicts that the traFslationa1 energy distribution should peak a t y T = 33% and thatf’, = 43%. This result is inconsistent with the experimental estimation OfTT = 52 5%.
which agrees with the experimental estimation of 0.52 f 0.05 below the ionization limit. This finding indicates that the fragment translational energy is dependent on impulsive, interfragment kinematic effects. The present study on the predissociation of CS2 shows that the internal and translational energy distributions are dictated by different factors in the bound-continuum region. Since linear geometry is preserved during dissociation, the rotational energy disposal is constrained by angular momentum conservation.” The translational energy disposal is controlled by kinematic effects, while the vibrational energy distribution of the CS(A) product fragment is influenced only by Franck-Condon-like effects. For a given product vibrational energy, there is a fixed amount of energy to be divided between rotation and translation through energy conservation. The experimental evidence strongly suggests that the repulsive dissociating potential curve is very steep in the Franck-Condon region of the effective oscillator so that it scans a wide translational energy range, using the reflection principle,’ which screens up to six vibrational quanta (0’ = 0 6) of the product fragment. For low photon energies (below the ionization limit), partitioning of energy into translation is well-defined pT = 50%) because it is within the Franck-Condon range. When the available energy is high (above the ionization potential), the maximum translational energy is above the Franck-Condon range. Additional energy must be partitioned into rotation to keep the translational energy in the Franck-Condon range.’ However, the rotational energy is fixed by angular momentum conservation in the collinear dissociation of CS2. The excess energy must remain in translation, which explains why the energy partitioning into translation of the product fragments increases with the excitation energy beyond the ionization limit. In this high energy case, the limited range of rotational states is insufficient to scan the entire Franck-Condon region for dissociation, and the Franck-Condon overlap integral will then decline with increasing available energy. In fact, the CS(A X) fluorescence cross section has been found to decrease with increasing incident photon energy in the photodissociation of CS2.I6 This experimental observation seems to support the present qualitative dynamical interpretation.
(33) Simons, J. P. In ‘Gas Kinetics and Energy Transfer”; Ashmore, P. G., Donovan, R. J., Eds.; The Chemical Society: London, 1977; Chem. Soc. Spec. Period. Rep. Vol. 2, p 58.
(34) Parson, J. M.; Shobatake, K.; Lee, Y . T.; Rice, S. A. J . Chem. Phys. 1973, 59, 1402. (35) Busch, G. E.; Wilson, K. R. J . Chem. Phys. 1972, 56, 3655.
*
-
(7)
*
-
-
J . Phys. Chem. 1985, 89, 4621-4626 TABLE 11: Energy Partitionings for the Dissociation of CS2 Leading to CS(A) at Various Excitation Energies excitation wavelength. nm
4621
for a better understanding of the fragmentation dynamics of Cs2. Such information will be important for developing theoretical dissociation models.
~~~
130.4
129.5
123.6
121.6
Ar*
Y"
15"
3 3"
YTC
39 46
22" 31
30" 13 57
1Ob 8 82
fk
From ref 11.
41
15 52
Estimated from E , = C,,P,,Ed. 'f;= 100 - f'u -
fR.
Downloaded by FLORIDA STATE UNIV on September 10, 2015 | http://pubs.acs.org Publication Date: October 1, 1985 | doi: 10.1021/j100267a041
In this work, the excited-state fragmentation dynamics of a linear molecule is extracted from the fluorescence measurements. This should be considered an initial step in unravelling the dynamics of CS2 dissociation leading to the CS(A) fragment. More experimental results, especially the rotational as well as translational energy disposals at different excitation energies or the orientation dependence of dissociative fluore~cence,~~ are required
Acknowledgment. I thank Dr. Jon Hougen of National Bureau of Standards for providing me with the RKR-FCF programs and Professor Bryan Kohler for his hospitality during my visit at Wesleyan University. Acknowledgment is made to Research Corporation and the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research. Registry No. CS2, 75-15-0; CS, 2944-05-0; S-, 18496-25-8; Ar, 7440-37-1. (36) Martin, R. M. "Symposium on Gas-Phase Chemiluminescence and Chemi-ionization"; 188th National Meeting of the American Chemical Society, Philadelphia, Aug 1984; American Chemical Society: Washington, DC, 1984.
Effect of Formamide and Other Organic Polar Solvents on the Micelle Formation of Sodlum Dodecyl Sulfate Mats Almgren,* Shanti Swarup,+ The Institute of Physical Chemistry, University of Uppsala, S-751 21 Uppsala, Sweden
and J. E. Lofroth Department of Physical Chemistry, Chalmers University of Technology and University of Goteborg, S-412 96, Goteborg, Sweden (Received: February 7 , 1985; In Final Form: May 28, 1985)
The critical micelle concentration (cmc) and the micelle aggregation number have been determined for sodium dodecyl sulfate in mixtures of water and organic polar solvents. For dimethyl sulfoxide and dimethylacetamide the logarithm of the cmc value increases linearly with the weight percent of organic liquid added up to 50-70%; it decreases linearly for formamide. The micellar size decreases in all cases. With more of the organic component and in the pure organic solvents, a break point in conductan-ncentration plots similar to the cmc is still observed, but the combined evidence from fluorescence quenching, self-diffusion determinations, and solubilizationstudies leads to the conclusion that proper micelles are not formed, but lipophilic molecules may be solubilized by inducing the formation of solute-surfactant particles.
Introduction The aggregation of amphiphilic substances in aqueous solutions to form micelles and similar structures has long been regarded as a clear manifestation of the hydrophobic effect. Such aggregation has been reported also for nonaqueous solvents, however-in some cases very exotic ones like fused salts,'-6 water at 160 O C (where it is rather nonaqueous),' and hydrazine.* It must be regarded as a false supposition, therefore, that solvent structuring and hydrogen bonding are essential prerequisites for micelle formation. This conjecture was earlier carried over to the nonaqueous sphere by Ray,9*'0who found evidence for micelle formation in some polar, hydrogen-bonding solvents, e.g. ethylene glycol, formamide, and glycol, but not in some other solvents like N,N-dimethylformamide which are equally polar but with less hydrogen bonding and supposedly with less structure. Gopal and J. R. Singh"J2 found similar behavior for other surfactants, whereas H. N. Singh et al.I3 claimed that micelles of sodium dodecyl sulfate (SDS) and cetyltrimethylammonium bromide (CTAB) were formed not only in formamide and N-methylacetamide but also in dimethyl sulfoxide and N,N-dimethylformamide. 'Present address: Department of Chemistry, The State University of New Jersey-Rutgers, P.O. Box 939, Piscataway, NJ 08854.
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While there are good reasons to expect that surfactant structures may form in solvents other than water-also in solvents without hydrogen bonds and special structure-the experimental evidence for such micelles is meager or very indirect. For the polar organic solvents the sole observation is that a break occurs in the value of some property of the solution (surface t e n s i ~ n , ~conduc,'~ tance,l1-I3 refractive index1'J2)at a certain concentration of the surfactant, the cmc. A determination of the size of the proposed micelles would be an obvious first step toward a better characterization of the microstructure in these solutions. Such a de(1) Bloom, H.; Reinsborough, V. C. Aust. J . Chem. 1967, 20, 2583. (2) Bloom, H.; Reinsborough, V. C. Aust. J . Chem. 1968, 21, 1525. (3) Bloom, H.; Reinsborough, V. C. Aust. J . Chem. 1969, 22, 519. (4) Reinsborough, V. C. Aust. J . Chem. 1970, 23, 1473. (5) Reinsborough, V. C . ; Valleau, J. P. Aust. J . Chem. 1968, 21, 2905. (6) Evans, D. F.; Yamauchi, A,; Roman, R.; Casassa, E . Z . J . Colloid Interface Sei. 1982, 88, 89. (7) Evans, D. F.; Wightman, P. J. J . Colloid InterfaceSci. 1982, 86, 515. (8) Evans, D. F.; Ninham, B. W. J . Phys. Chem. 1983, 87, 5025. (9) Ray, A. J . A m . Chem. Soc. 1969, 91, 6511. (10) Ray, A. Nature (London) 1971, 231, 313. (11) Gopal, R.; Singh, J . R. J . Phys. Chem. 1973, 71, 554. (12) Gopal, R.; Singh, J . R. Kolloid Z . Z . Pofym. 1970, 239, 699. (1 3) Singh, H. N.: Saleem, S. M.: Singh, R. P.; Birdi, K . S . J . Phys. Chem. 1980, 84, 2191.
0 1985 American Chemical Society
