J . Phys. Chem. 1990, 94. 5200-5202
5200
R -
Figure 4. Dependence of the barrier-crossing frequency, Y , of an weakly adiabatic electron-transfer reaction (for model 11) on the solute-solvent size ratio, R. The calculated values of Y are plotted against R for two different values of the translational parameter, p’. The values of the barrier frequency, the dielectricconstant, and the reduced density of the solvent are the same as in Figure 3. The values of the longitudinal relaxation time and the Debye relaxation time are the same as in Figure I.
than that for a strongly adiabatic reaction. Also, the reactive friction is less for the former than for the latter. Figures 3 and 4 show the results of our calculations for model 11. In Figure 3, the dependence of v on p’is shown for a weakly adiabatic reaction. The results of this figure are rather similar to those of Figure 1 except that here the dependence on p’is much stronger. This is because the reacting system is modeled as a point dipole, so the reaction coordinate does not contain any contribution from the zero wavevector pr~cesses.’~ The intermediate wavevector processes are more important in this model and hence the stronger dependence on p’than observed for model I. The dependence of Y on the solutesolvent size ratio, R , is shown in Figure 4. It shows that, for zero translational contribution (p’ = 0), the rate of electron transfer increases with increases in the value of R. However, for a sizable translational contribution @’>0.5), the
rate of electron transfer decreases with increasing R. The reason for the above behavior is as follows. As we increase the value of R, the reaction coordinate receives a greater contribution from the small wavevector processes. These small wavevector processes occur at a faster rate than the large wavevector processes when the translational contribution is absent. Thus, in the absence of translation, the rate of electron transfer increases with increase in R . However, in the presence of a sizable translational contribution, the intermediate wavevector processes occur at a faster rate than the small wavevector processes. So in the presence of finite translation, the rate of electron transfer decreases as the value of the reactant-solvent size ratio, R , is increased. We have also calculated the rates predicted by the transitionstate theory for both models. For the weakly adiabatic case, the Grote-Hynes formula12gives a rate that is typically 0.8-0.9times the transition-state-theory value. For a strongly adiabatic reaction, the friction effects are more important and we get kcH = (0.50.6)kTST.Note that these numbers are in good agreement with the computer simulation results of Zichi et al.’ It is interesting to note that, in this one-dimensional model, kTSThas a dependence on p’that enters through wR. This explains the weak p’dependence of the ratio kCH/kTST. The dramatic effect of the translational diffusion on the rate of an electron-transfer reaction has a simple physical origin. At small length scales, the collective orientational relaxation of a dense dipolar liquid is slow in the absence of translational contribution.’3a However, the translational modes are especially effective at small length scales. These two effects combine to give rise to the marked dependence of the rate constant on p’ In conclusion, we have considered here two somewhat different models of outer-sphere adiabatic electron-transfer reactions and have shown that, for both models, the translational modes of the dipolar solvent can significantly enhance the rate of the reaction which is demonstrated here for the first time. Moreover, these dynamic effects are found to be significantly dependent on the adiabaticity of the reaction. Acknowledgment. This work was supported in part by NSF, USA (G.R.F.), CSIR, INDIA (A.C.), and INSA, INDIA (B.B.). B.B. is a Homi Bhabha Fellow for 1989-1991.
Electron Impact Mass Spectrometry of Cholesterol in Supersonic Molecular Beams Aviv Amirav Sackler Faculty of Exact Sciences, School of Chemistry, Tel- Aviu University, Ramat Auiv 69978, Israel (Received: March 1, 1990)
The effect of vibrational supercooling on the electron impact mass spectrometry of cholesterol was studied in supersonic molecular beams. An extensive mass spectral simplification was observed at 20 eV electron energy. The parent undissociated molecular ion becomes the dominant peak even at 70 eV electron energy but the conventional complex fragmentation pattern is retained in spite of the large vibrational cooling. Some of the unique aspects of electron impact mass spectrometry in supersonic molecular beams are mentioned.
Since the pioneering demonstration of Smalley et al.,’ supersonic molecular beams (SMB) revolutionized the research of optical spectroscopy and intramolecular dynamics. The extreme molecular vibrational-rotational cooling considerably simplifies laser-induced fluorescence spectra of large polyatomic molecules, ( 1 ) Smalley, R. E.; Ramakrishna, B. L.; Levy, D. H.; Wharton, L. J . Chem. Phys. 1974, 61. 4363.
0022-3654/90/2094-5200$02.50/0
eliminates sequence congestion, and provides clear information on the initial and final ro-vibronic quantum states2 On the other hand, vibrational temperature effects on electron impact induced ion fragmentation are well-known and documented in electron (2) (a) Amirav, A.; Even, U.; Jortner, J. Chem. Phys. 1980,51, 31. (b) Amirav, A.; Even, U.; Jortner, J. J . Chem. Phys. 1981, 75, 3770. (e) Levy, D.H.;Wharton. L.; Smalley, R. E. Arc. Chem. Res. 1977. 10, 134.
0 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 13, 1990
Letters
5201
K
no
HO CHOLESTEROL
CnOL EST€ ROL
2 7 n46° PH2z 800 TORR
C27H460
7OeV-E I
L
M a 386
w 50
150
k 250
350
450
MASS(AMU)
II I
50
I
150
I
250
i . 1
i
350 MASS ( A M U 1
I
450
Figure 1. Vibrational temperature effects on the electron impact mass spectra of cholesterol in a hydrogen-seeded supersonic molecular beam. The electron energy is 20 eV and the hydrogen backing pressures behind the nozzle are indicated.
impact mass spectrometry (EI-MS).j As the electron impact ionization (El) process is vertical, the thermal molecular vibrational energy is added to that produced by the E1 process. These combined ion vibrational energies lead to the extensive mass spectral ion fragmentation observed. Recently we demonstrated4 the vibrational cooling effect in S M B on the EI-MS of 1bromopentane and 3-bromopentane and discussed the many advantages of EI-MS in SMB (EI-SMB-MS). Most notable are the possible elimination of mass spectral background of the thermal vacuum chamber residual gases, increased structural and isomeric information, simplified and faster atmospheric sample introduction, and possible tail-free coupling to a gas c h r o m a t ~ g r a p h . ~It. ~was found that the vibrational cooling in S M B resulted in a relative increase of the parent undissociated molecular ion by more than 2 orders of magnitude as compared to its relative abundance in the conventional 250 O C EI-MS. However, aside from the molecular ions, the fragmentation pattern exhibited was relatively unaffected by the vibrational cooling of the bromopentanes which are relatively small polyatomic molecules (12 atoms). It was anticipated that the vibrational temperature effects would be enhanced considerably in larger polyatomic molecules. Cholesterol is a typical large polyatomic molecule, being a prototype steroid whose mass spectra were extensively studied.6 Cholesterol has 74 atoms and thus its average internal vibrational energy at 250 O C (523 K) is over 9 eV! This value is more than the usual vibrational energy given to the molecule in 70-eV E1 ionization process. In Figure 1 we show the vibrational cooling effect in S M B on the El-MS of cholesterol. A sample of cho(3) (a) Danon, A.; Amirav, A.; Silberstein, J.; Salman, y.;Levine, R. D. J . Phys. Chem. 1989,93,49. (b) Chupka, W. A. J. Chem. Phys. 1971,54, 1936. (c) Genuit, W.; Nibering, N. M. M. Int. J . Mass Spectrom Ion Processes 1986, 73, 61. (d) Lifshitz. C.; Tiernan, T. 0.J . Chem. Phys. 1973, 59, 6143. (e) Lifshitz, C.; Weiss, M. Chem. Phys. Lett. 1972, I S , 266. (4) Amirav, A.; Danon, A. Inf. J . Mass Spectrom Ion Processes 1990, 97, 107. ( 5 ) Amirav, A.; Danon, D. "Mass Spectrometer Method and Apparatus for Analyzing Materials"; Israel Patent Application No. 90970/2, July, 1989. (6) Budzikiewicz, H.; Djerassi, C.; Williams, D. H. Mass Spectrometry of Organic Compounds; Holden-Day: San Francisco, 1967.
Figure 2. Electron energy effects on the electron impact mass spectra of vibrationally cold cholesterol in a hydrogen-seeded supersonic molecular beam. The hydrogen backing pressure behind the nozzle is 800 Torr and the electron energies are 70 eV for the upper mass spectrum and 20 eV for the lower mass spectrum.
lesterol was heated to 180 O C in front of the nozzle which was differentially heated to 250 O C . ' The hydrogen-seeded beam was skimmed and collimated through a differential pumping chamber and entered axially into a quadrupole mass spectrometer (VGSXP-600). The collimated molecular beam entered the ionizer and left it through the ion extractor without scattering from its walls. The ion energy consisted of 4 eV due to electrostatic acceleration and the molecular kinetic energy which was proportional to the fragment mass. The kinetic energy contribution was about 20 eV for the molecular ion at 800 Torr and only a few electronvolts at 30 Torr of hydrogen backing pressure. The lower mass spectrum shown in Figure 1 is very similar to that obtained in our conventional magnetic sector MS or that found in the literature. There is some reduction in the relative mass transfer at high masses which is compensated by the slight cooling at P(H,) = 30 Torr. Upon the increase of the hydrogen backing pressure to 110 Torr, the vibrational cooling is enhanced and the middle trace already demonstrates a 25-fold relative increase in the molecular ion abundance. Similar vibrational temperature effects were observed for the steroid 3a-hydroxyandrost- 17-ene by lowering the ion source temperature,* at the price of a considerably reduced molecular vapor pressure. Above 400 Torr of hydrogen backing pressure, the spectrum is almost totally dominated by the molecular undissociated ions and the upper trace demonstrates it in the 20-eV EI-SMB-MS of the vibrationally cold cholesterol. To the best of our knowledge this is the most dramatic vibrational temperature effect demonstrated in EI-MS. In Figure 2 we compare the EI-SMB-MS of cholesterol at 20 eV electron energy shown at the bottom to the one obtained by using 70 eV electron energy (upper trace). Actually the 70-eV El-MS in supersonic molecular beam exhibits as many fragments as the thermal 70-eV El-MS, with the main difference being in the molecular parent ion which is now the strongest peak in the mass spectrum. As the molecular peaks are very high, the true isotopic constituents (shown in the insert) are revealed and elemental information is exhibited. This information is unavailable in chemical ionization (CI) that gives quasi-molecular peaks. In addition, as the thermal vibrational energy in SMB is negligible, the electron energy is the only experimental parameter that governs
(7) Danon, A,; Amirav, A. Rev. Sci. Instrum. 1987, 58, 1724. (8) Budzikiewicz, H. In Biochemical Applications of Mass Spectrometry; Waller, G.R., Ed.; Wiley-Interscience: New York, 1972; p 251.
5202
J . Phys. Chem. 1990, 94, 5202-5205 of 20-eV E l of vibrational warm molecules. The 70-eV EISMB-MS of cholesterol reflects the fact that the vibrational energy given by the electron promotes a different fragmentation pattern than thermal vibrational energy. Possible reasons for that are different vibrational energy distribution functions, nonstatistical electronic predissociation, or the role of double charge ionization which leads to a different fragmentation that is dominated by the nature of the ions' Coulombic explosion.I0 It is further anticipated that these considerable effects of the vibrational cooling in SMB on EI-MS are universal and will dominate the nature and information content of EI-MS of large polyatomic molecules. EI-SMB-MS can also be supplemented by the coupling of surface ionization in hyperthermal supersonic molecular beams" to form a new and powerful mass spectrometric approach.
the degree of fragmentation which can be fully controlled and help in structural identification. The two normalized traces shown in Figure 2 were obtained with the same electron multiplier gain, as the reduced ionization cross section at 20 eV electron energy was fully compensated by the reduced degree of parent ion fragmentation. We also note that the spectrum obtained with 70 eV electron energy for the vibrationally cold cholesterol (Figure 2) is very similar to a superposition of the 20-eV thermal spectrum plus the 20-eV EI-SMB-MS. Actually the 70-eV EI-MS of the vibrationally cold cholesterol resembles very much the conventional thermal 70-eV El-MS except for a 2 order of magnitude enhancement in the molecular peak whereas all other peaks were almost unchanged. If we consider statistical theories such as the QET,9 it is anticipated that the total intramolecular vibration energy will dictate the fragmentation pattern regardless of its origin. We expect therefore that the 70-eV E1 spectrum of cold molecules will resemble the one shown in Figure 1 middle trace
Acknowledgment. The enlightening discussions and help of Mr. A. Danon and Dr. M. de Vries are greatly appreciated. This work was supported by the United States-Israel Binational Science Foundation, Grant No. 86-00054, and by a grant from the United States Army.
(9) (a) Frost, W. Theory of Unimolecular Reactions; Academic Press: New York, 1973; and ref 3c. (b) Rosenstock, H . M.; Wallenstein, M. B.; Warhaftig, A. L.; Eyring. H. Proc. Natl. Acad. Sci. U.S.A. 1952, 38, 667. (c) Lifshitz, C. Ado. Mass. Spectrom. 1989, 11, 713. (d) Rebentrost, F.; Kompa, K. L.; Ben-Shaul, A. Chem. Phys. Lett. 1981, 77, 394. (e) Silberstein, J.; Ohmichi, N.; Levine, R. D. J . Phys. Chem. 1985, 89, 5606
Eland, J. H. D. Arc. Chem. Res. 1989, 22, 381. ( 1 1 ) (a) Danon, A.; Amirav, A. J. Phys. Chem. 1989, 93, 5549. (b) Danon. A ; Amirav. A. I n t . J. Mass Spectrom. Ion Processes 1990. 96. 139. ( 10)
Collective Tilt Behavior in Dense, Substrate-Supported Monolayers of Long-chain Molecules: A Molecular Dynamics Study James P. Bareman and Michael L. Klein* Department of Chemistry and Laboratory f o r Research on the Structure of Matter, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323 (Receiued: March 13, 1990)
Molecular dynamics calculations have been used to investigate collective molecular tilt as a function of area per chain at room temperature in substrate-supported monolayers of long-chain molecules. At the highest densities the chains align approximately normal to the substrate and show a continuous increase in the collective tilt as the molecular area is increased, a finding in agreement with recent experimental results on Langmuir monolayers.'J An intermolecular potential which represents the methylene group as a single interaction site ("united atoms") is compared with a potential in which all atoms are included explicitly. Commonly used parameters for the united atom potential underestimate the effective diameter of the chains.
Introduction The behavior of assemblies of amphiphilic molecules at both the air/water ( Langmuir)'s2 and air/solid (Lang~nuir-Blodgett)~.~ interfaces has been the subject of numerous investigations. Such systems serve as simple models of biological membranes and are also of interest from a more fundamental viewpoint because of their two-dimensional n a t ~ r e . The ~ combination of new, highly sensitive experimental techniques, capable of monolayer resolution. and stringent control of experimental conditions has greatly enhanced the understanding of these films.'-I7 This, in turn, has stimulated considerable theoretical In this Letter we present results of a molecular dynamics (MD) investigation of collective molecular tilt, as a function of the area per chain, in substrate-supported monolayers of long-chain molecules at densities near close-packing. Two distinct pairwise additive intermolecular potentials have been investigated, one employing a "united atom" and the other an all-atom representation of the methylene (Me) groups. Simulation Details The MD simulations were carried out in the microcanonical ensemble, with periodic boundary conditions appropriate to a 'Author to whom correspondence should be addressed.
0022-3654/90/2094-5202$02.50/0
triangular lattice. The phase behavior of Langmuir monolayers at relatively high surface densities (p-' I25 Az/chain) is strongly ( I ) Kjaer, K.; Als-Nielsen, J.; Helm, C. A,; Tippman-Krayer, P.; Mohwald, H. J . Phys. Chem. 1989, 93, 3200. (2) Lin, B.; Bohanon, T. M.; Shih, M. C.; Dutta, P., submitted for publication in Phys. Reu. Lett. ( 3 ) Roberts, G. G. Ado. Phys. 1985, 34, 475. (4) Swalen, J. D.; Allara, D. L.; Andrade, J. D.; Chandross, E. A.; Garoff, S.; Israelachvili, J.; McCarthy, T. J.; Murray, R.; Pease, R. F.; Rabolt, J. F.; Wynne, K. J.; Yu, H . Langmuir 1987, 3, 932. (5) For a recent review see: Knobler, C. M. Ado. Chem. Phys. 1990,77, 397. (6) Fischer, A.; Sackmann, E. J . Phys. (Poris) 1984, 45, 517. (7) Middleton, S . R.; Iwahashi, M.; Pallas, N. R.; Pethica, B. A. Proc. R . SOC.London, Ser. A 1984, 396, 143. Pallas, N. R.; Pethica, B. A. Langmuir 1985, I , 509. Pallas, N. R.; Pethica, B. A. J . Chem. Sor., Faraday Trans. I 1987, 83, 585. (8) Rasing, Th.; Shen, Y. R.; Kim, M. W.; Grubb, S. Phys. Reu. Lett. 1985, 55, 2903. (9) Vogei, V.; Woll, C. J . Chem. Phys. 1986, 84, 5200.
(IO) Smith, D. P. E.; Bryant, A.; Quate, C. F.; Rabe, J. P.; Gerber, Ch.; Swalen, J. D. Proc. Natl. Acad. Sci. U S A 1987, 84, 969. (1 1) Kjaer, K.; Als-Nielsen, J.; Helm, C. A.; Laxhuber, L. A.; Mbhwald, H. Phys. Reo. Lett. 1987,58, 2224. Helm, C. A,; Mohwald, H.: Kjaer, K.; Ais-Nielsen, J . Biophys. J. 1987, 5 2 , 381. ( I 2) Dutta, P.; Peng, J. B.; Lin, B.; Ketterson, J. B.; Prakash, M.; Georgopoulos, P.; Ehrlich, S. Phys. Reo. Lerr. 1987, 58, 2228. (13) Helm, C. A.; Mohwald, H.; Kjaer, K.; Als-Nielsen, J. Europhys. Lett. 1987. 4 . 697.
G 1990 American Chemical Society
