J. Phys. Chem. 1989, 93, 8031-8037
8031
sion-controlled ion recombination kinetics in low-permittivity media. This finding should facilitate the investigation of kinetics in the radiation chemistry of low-mobility alkanes as the IRT simulation can be realized much more rapidly than the full random flight simulations, which are at present the only realistic alternative. The surprising success of the independent pairs approximation under these conditions merits further investigation but also suggests the possibility of an analytic or numerical theory which, being based on the same approximation, should be equally successful. Such a description is part of our current research, and we hope to be able to describe it in a future publication. Acknowledgment. The authors thank Dr. A. Mozumder for suggesting the study of nonrandom configurations. The research described was in part funded by S.E.R.C., U.K.A.E.A. Harwell, and the Office of Basic Energy Sciences of the Department of Energy. This is Document No. NDRL-3177 from the Notre Dame Radiation Laboratory.
the diffusion approximation by performing classical simulations of electron random flights with a large mean free path. For ion-ion recombination and electron-ion recombination in low-permittivity solvents, the mean free path is low and the diffusion approximation is probably valid. The second approximation is the implicit assumption that there is a linear response to interparticle forces. Ion mobility is field-dependent and hence so is the relative diffusion coefficient. The effect has been discussed by Mozumder,& Baird:' and Rice4*but is not usually considered to be important in geminate recombination and generally Subject to these limitations, however, we have shown that the IRT simulation is a remarkably successful description of diffu(46) Mozumder, A. J. Chem. Phys. 1976, 65, 3798. (47) Baird, J. K.; Anderson, V. E.; Rice, S. A. J . Chem. Phys. 1977,67, 3842. (48) Rice, S. A. Diffusion-LimitedReactions; Elsevier: Amsterdam, 1985.
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Temperature Dependence of Termolecular Association Reactions N,+ 4- 2N, N4+ 4- N, and 0,' 4- 20, 0,' 4- 0, Occurring in Free Jet Expansions below 20 K L. K. Randeniya, X. K. Zeng, R. S. Smith, and M. A. Smith* Department of Chemistry, University of Arizona, Tucson, Arizona 85721 (Received: March 30, 1989; In Final Form: June 19, 1989)
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A new experimental technique that combines supersonic expansions and laser ionization mass spectrometry has been used to measure the termolecular association rate coefficients, k3, for the gas-phase reactions Nz+ + 2Nz N4++ N2 and 02+ + 202 04++ O2below 20 K. The continuity of the proposed inverse temperature law of k3 = CT" was observed down to 4 K for both reactions. Statistical analysis of our results along with the higher temperature data obtained by other authors respectively. The results of phase gives the values of 1.92 0.15 and 1.86 0.1 5 for n for the reactions of N2+and 02+, space calculations are presented for these reactions and excellent agreement between theory and experiment is obtained.
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Introduction Except in those instances where cluster ions are generated by the ionization of neutral clusters or via surface bombardment/ sputtering techniques, they are produced via a series of association reactions. The dynamics of ion-molecule association at the low temperatures and pressures that prevail in the interstellar medium has become an interesting astrophysical problem.I4 The radiative association reaction, which is thought to be fast at low temperatures, has been invoked by many authors to explain the abundance of a variety of molecules that have been observed in the interstellar medium. The measurement of rate coefficients of the related termolecular association process at low pressures and temperatures is expected to contribute to the advancement of these models. The study of the rates of ternary association reactions is particularly interesting since at low pressures the third-order rate coefficient follows an inverse temperature dependence given by
Inaccuracies can occur whenever the temperature range of measurements is fairly small or the measurements are not made in the low pressure limit where k3 is independent of the pressure of the third body. We have developed a technique that enables the measurement of ternary association rates for reactions occurring in the core of a supersonic expansion. This technique is unique since it extends the low-temperature limit to approximately 4 K. The method also permits the study of these reactions in the low-pressure limit which is otherwise obtained with difficulty by more conventional techniques. In this paper we report the study of the following reactions:
+
N2+ 2N2
N4+
+ N2
(2)
02+ + 2 0 2 04++ O2 (3) The above reactions have been the subject of much of the research work done to date on ternary association reactions. Both reaction rates have been studied down to about 20 K, yet for reaction 3 only lower limits to the rate coefficients have been obtained at temperatures below 70 K.8-" Extensive theoretical work has been done on the temperature dependence of the ternary association rate coefficients and has been largely successful in explaining the observed behavior for a wide range of association However, since low-
where C and n are constants for a given reaction. The value of n for a variety of such reactions has been found to vary from 0.4 to about 6 with n increasing with the complexity of the rea~tants.~' A fair amount of controversy surrounds the range of experimental values reported for n for many association reactions. ( 1 ) Williams, D. A. Astrophys. Lett. 1972, 10, 17. (2) Black, .I.H.; Dalgarno, A. Astrophys. Lett. 1984, 15, 79. (3) Herbst, E.; Klemperer, W. Astrophys. J. 1973, 185, 505. (4) Herbst, E.; Leung, C. M. Astrophys. J . 1986, 310, 378.
(8) Van Koppen, P. A. M.; Jarrold, M. F.; Bowers, M. T.; Bass, L. M.; Jennings, K. R. J . Chem. Phys. 1984, 81, 288. (9) Bohringer, H.; Arnold, F. J. Chem. Phys. 1982, 77, 5534. (10) Bohringer, H.; Arnold, F.; Smith, D.; Adams, N. G. Int. J . Mass. Spectrom. Ion Phys. 1983, 52, 25. ( 1 1) Rowe, B. R.; Dupeyrat, G.; Marquette, J. B.; Gaucherel, P. J . Chem. Phys. 1984, 80, 4915. (12) Bates, D. R. J. Phys. B 1979, 12, 4135.
(5) Castleman, A. W., Jr.; Keesee, R. G. Chem. Reu. 1986, 86, 589. (6) Adams, N. G.; Smith, D. In Reactions of Small Transient Species; Fontijn, A., Clyne, M. A. A., Eds.; Academic Press: London, 1983; p 31 1. (7) Liu,S.; Jarrold, M. F.; Bowers, M. T. J. Am. Chem. Soc. 1985, 89, 3127.
0022-3654/89/2093-8031$01.50/0
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0 1989 American Chemical Societv
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8032 The Journal of Physical Chemistry, Vol. 93, No. 24, 1989
temperature measurements were not available at the time these theories were developed, not much attention has been paid to the limits of these theories a t temperatures approaching 0 K. Nevertheless, these theories suggest that the inverse temperature dependence given in eq 1 for the low pressure limit of the rate coefficient should apply. The first experimental test of this concept was a study of reactions 2 and 3 by Rowe and co-workers using the CRESU technique (an acronym for the French translation of reaction kinetics in uniform supersonic flow)." The CRESU method employs a modified wind tunnel for the study of ionmolecule rate coefficients at very low temperatures. The results confirmed that the inverse temperature law holds down to 20 K for reaction 2 despite evidence from drift tube studies that suggested strong deviation^.^^'^ A maximum value for the rate coefficient around 60 K was suggested for reaction 3 from the low-temperature drift tube studies. To the contrary, Rowe and co-workers found no evidence for the existence of any maximum value. The rate coefficients obtained for reaction 3 by the CRESU technique, however, were not conclusive at the lowest temperatures (only the lower limits to the rate coefficients were reported for temperatures below 70 K). A recent study by our group has suggested that the third-order clustering reaction of NO+ with NO shows the inverse temperature dependence down to about 4 K.25 In this paper the results of a study of reactions 1 and 2 at temperatures below 30 K are presented. The observed rates of association are discussed within the framework of statistical reaction theory with particular emphasis upon the verification of inverse temperature rate laws at extremely low collision energies. Before this analysis is presented, a brief description of our experimental technique will be reviewed.
Randeniya et al.
i
Figure 1. Schematic of the free jet flow reaction zone: NZ, translatable pulsed nozzle assembly; LF, laser focus; RP, pulsed ion repeller plate; MS, ion focusing optics and translatable TOF mass spectrometer.
produced in low u levels (u = 1, 2), vibrational relaxation of the ions is expected to be much faster than for nitrogen since the charge transfer to produce 02+( u = 0) and O2 ( u = 1) is exothermic. Thus, 02+ions are completely vibrationally relaxed before significant clustering occurs. The rate coefficients are determined by monitoring the temporal mass composition of a reactant ion packet produced in the core of the supersonic expansion. This ion packet is sampled by a mass spectrometer which translates parallel to the expansion flow axis. A schematic of the experimental apparatus is shown in Figure 1. A free jet of 200-250-ps duration is obtained by expanding Experimental Section neutral reactant gas through flat nozzles with diameters of 0.03 A discussion of our experimental technique has been presented and 0.05 cm. The stagnation pressure was varied from 0.45 to elsewhere and is the topic of a detailed paper f o r t h c ~ m i n g . ~ ~ - ~2.2 ~ atm. Nozzle throat limited flow was confirmed for all exOnly a brief discussion pertaining to specific details of the present periments reported here. The stagnation temperature was experiment will be given in this paper. The reactant ions are maintained at 298 K. The effective third body density for the produced in a free jet expansion of N2 and O2by resonance-enassociation process is varied by varying the distance between the hanced multiphoton ionization (REMPI). The N2+ ions are nozzle and the ionization region. After the ion packet has traveled obtained by a 2 + 2 photon resonance excitation through the a distance z with the jet under field-free conditions, the ions are a1I'Iq(u = 2 or 3) state^.^**^^ In a pure N2 expansion, fast virepelled out of the beam into a time-of-flight mass analyzer by brational relaxation occurs and the association reaction will be application of a pulsed extraction field. The mass analyzer rests mainly due to the vibrational ground state of the ion. This is perpendicular to the flow axis and can translate parallel to this confirmed by the fact that we do not observe charge transfer to axis for a distance of 50 cm from the nozzle. The combination Ar atoms seeded in the beam, a reaction which is exothermic and of small mass analyzer entrance aperture and laser crossing geshould be rapid for all N2+(u > 0). At room temperature the ometry ensures that we sample only a small packet of ions lying vibrational quenching rate constant for N2+(u) + N2 is about 63% on the center streamline of flow. This experimental arrangement that of the collision rate.30 At lower temperatures this efficiency allows the use of flow theories developed for center line free jet is expected to be higher. The 02+ions are prepared through the expansion flows. The reaction time is determined by the time C311,(u = 0) ~ t a t e . ~ 'Although .~~ a small fraction of ions are needed for the ion packet to flow from the ionization region to the extraction zone. A study of the ion intensities and mass distribution as a function of the distance from the nozzle to the (13) Bates, D. R. J . Chem. Phys. 1979, 71, 2318. ionization region yields a complete reaction history of the traveling (14) Bates, D. R. J . Chem. Phys. 1980, 73, 1000. (15) Herbst, E. J . Chem. Phys. 1979, 70, 2201. ion packet as a function of reactant density. Collisional frag(16) Herbst, E. J. Chem. Phys. 1980, 72, 5284. mentation of the ion clusters during the extraction process was (17) Herbst, E. Chem. Phys. 1982,68, 323. found to be negligible at the 100 V/cm extraction fields used. (18) Bates, D. R. J . Chem. Phys. 1984,81, 298. Assuming Langevin cross sections, we calculate the probability (19) Bates, D. R. J . Chem. Phys. 1988,89, 192. (20) Bates, D. R. J . Chem. Phys. 1989, 90, 87. of an ion experiencing a capture collision during the extraction (21) Chesnavich, W. J.; Bowers, M. T. J . Chem. Phys. 1977, 66, 2306. process to be less than 2 X under the present experimental (22) Chesnavich, W. J.; Bowers, M. T. J . Am. Chem. SOC.1976,98,8301. conditions. However, at much closer sampling distances and higher (23) Bass, L. M.; Chesnavich, W. J.; Bowers, M. T. J . Am. Chem. SOC. fields the number of hard collisions goes up significantly so that 1979, 101, 5493. (24) Johnsen, R. J . Chem. Phys. 1986, 83, 3869. collisional fragmentation and charge transfer to neutrals become (25) Randeniya, L. K.; Zeng, X. K.; Smith, M. A. Chem. Phys. Left. 1988, important. At closer sampling distances compared to the sampling 147, 346. distances we have used in the present study, the products of the (26) Mazely, T. L.; Smith, M. A. J . Chem. Phys. 1988, 89, 2048. charge transfer process during the extraction process appear as (27) Hawley, M.; Mazely, T. L.; Randeniya, L. R.; Smith, R. S.; Zeng, X. K.; Smith, M. A,, submitted for publication in Int. J. Mass Spectrom. Ion an unresolved mass signal arriving at the detector soon after the Processes. parent peak. These effects have been strictly avoided in this study. (28) Bruno, A. E.; Shubert, U.; Neusser, H. J.; Schlag, E. W. Chem. Phys. In addition, identical mass distributions were observed a t fields Left. 1986, 131, 31. ranging from 60 to 160 V/cm. Above 160 V/cm, minor frag(29) Carleton, K. E.; Welge, K. H.; Leone, S . R. Chem. Phys. Lett. 1985, 115. 492 - >
~
(30) Ferguson, E. E. J . Phys. Chem. 1986,90,731, and references therein. (31) Johnson, R. D.; Long,G. R.; Hudgens, J. W. J . Chem. Phys. 1987, 87. 1977.
(32) Katsumata, S.; Sato, K.; Achiba, Y.; Kimura, K. J . Electron Spectrosc. Relat. Phenom. 1986, 41, 325.
N2++ 2Nz
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N4++ Nz and Oz++ 2 0 2
-
04+ + O2
The Journal of Physical Chemistry, Vol. 93, No. 24, 1989 8033
mentation of heavier cluster ions was observed to occur.
Results and Discussion a. Theoretical Background. All modern theories of three-body ion-molecule association model the reaction using the following simple energy transfer mechanism: A+ + B
k kb
(AB)+*
M M I
(AB)+
(4)
The first step of the reaction is the bimolecular formation of a collision complex whose lifetime is assumed sufficiently long for energy randomization to be complete. This complex can subsequently decompose to give reactants or, in the presence of an inert third body, can undergo an inelastic collision to give a stable molecular ion. The collisional rate coefficients of the complex is given by k,. The parameter is a measure of the effectiveness of the third body energy transfer step. By use of the steady-state approximation, the overall third-order rate coefficient is then given by
The low-pressure limit is Pkfk, k3 = kb
This low-pressure condition may be conveniently defined using eq 5 by the following two equivalent expressions: kb > - Pk,[Ml (7) (8) k3[M]
