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Laser fluorescence and mass spectrometric measurements of vibrational relaxation of N2+(v) with He, Ne, Ar, Kr, and Xe
ELSEVIER
International Journal of Mass Spectrometry and Ion Processes 149/150 (1995) 469-486
Spactrometry andlo”Processes
Laser fluorescence and mass spectrometric measurements of vibrational relaxation of N:(v) with He, Ne, Ar, Kr, and Xe* Shuji Kate’, JILA, National Institute of Standa&
Veronica
M. Bierbaum,
Stephen
R. Leone*
and Technology and University of Colorado, Department University of Colorado, Boulder, CO 80309-0440, USA
of Chemistry
and Biochemistry,
Received 18 April 1995; accepted 28 June 1995
Abstract
The vibrational relaxation of N:(v) is studied at thermal energies for the rare gas collision partners, He, Ne, Ar, Kr and Xe. The selected ion flow tube-laser-induced fluorescence technique is combined with conventional mass spectrometry to measure accurately the extremely small rate constants for vibrational relaxation with these rare gas atoms. Measured rate constants for Ni(v = 1) are 9.8(f0.7) x lo-l6 cm3 molecule-t s-i for He, 3.6(fO.S) x lo-l4 for Ne, cl.2 x lo-” for Ar, <2 x 1O--‘2for Kr, and 1.6(f0.2) x lo-l3 for Xe. For Ne, laser fluorescence is used to probe the individual levels, N:(v = l-4). The small deactivation probabilities, ranging from 1.7 x 10m6for He to 1.6 x 10S4 for Xe, are discussed in terms of two types of relaxation mechanisms. The correlation between the rare gas polarizability and the relaxation rate constant strongly suggests the importance of attractive forces in the vibrational relaxation. A direct impulsive mechanism may be operative for the vibrational relaxation of N:(v) with He. Keywords: Laser fluorescence; Rare gas atoms; Rate constants; SIFT; Vibrational
1. Introduction
Vibrational relaxation processes of molecular ions by collisions with neutral molecules and atoms are important processes, in part because the relaxation competes with concurrent chemical reactions that are often vibrationally state specific. For example, consider the vibrational relaxation (Eq. (1)) and the * Dedicated to Professor David Smith FRS on the occasion of his 60th birthday. * Corresponding author. ’Present address: Toyota Physical and Chemical Research Institute, 41-1 Yokomichi, Nagakute, Nagakute-cho, Aichi 480- 11, Japan.
relaxation
charge transfer process as shown in Eq. (2), both of which are dependent on vibrational level, v: N;(v) + M ----N;(v’ ‘~~(4 N;(v) + M ----+N2+M+ kcT(V)
< v) + M
(1) (2)
As a specific example of interest here, the formation and loss of N;(v) is important in the chemistry of the Earth’s upper atmosphere, ultimately determining the density of ions at various altitudes rll. The vibrational relaxation of neutral species has been widely studied and has been given a firm theoretical basis (Landau-Teller,
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Schwartz-Slawsky-Herzfeld (SSH), and dipole-dipole theories) [2]. In contrast, much less is known about ion vibrational relaxation, due in part to the experimental difficulty in generating, selecting, and detecting vibrationally excited molecular ions. The selected ion flow tube (SIFT) technique, developed by Smith and Adams [3,4], has provided new access to the physics and chemistry of vibrationally excited ions. Among other methods for ion/molecule studies, the SIFT technique is especially suited for the study of reaction and relaxation of vibrationally excited ions at thermal energies. Vibrationally excited ions, which are usually generated by electron impact, are extracted and mass-selected before collisional deactivation can occur with the neutral precursors. The ions are then injected into a flow tube where collisions with He buffer gas thermalize the ions rotationally and translationally, but the vibrational excitation is preserved. Neutral reactants are added downstream to initiate chemical reactions. Vibrational relaxation has been studied by measuring the vibrationally excited states by exothermic charge transfer with the monitor ion technique [5-71. The relaxation rates of NC(v) [5,6,8-lo], O,‘(v) [7] and NO+ (w) [11,12] with a variety of collision partners have been studied in this manner and a detailed review is found in Ref. [ 131. Some striking differences between ion/ neutral and neutral/neutral relaxation processes have been revealed. The vibrational relaxation of ions is usually much more efficient than that of neutrals, and the ion results show a dependence upon collision energy and reduced mass that is opposite to that of neutral relaxation. To account for this behavior, a model was proposed in which ion relaxation occurs via vibrational predissociation of ion-molecule transient complexes that are stabilized by strong attractive forces due to the charge-induced dipole interaction. Indeed, a positive correlation is found between
polarizability and relaxation efficiency for neutral collision partners [7,13]. Nevertheless, studies of ion vibrational relaxation remain scarce and many discrepancies and questions are unresolved. The relatively slow relaxation of ions with rare gases exemplifies this point. The relaxation with rare gas atoms is considered to be one of the simplest systems to study; there is no rovibrational structure in rare gas atoms and hence relaxation should occur solely by vibration-totranslation (V-T) energy transfer. There are no hydrogen-bonding interactions and there is little anisotropy of the intermolecular potential energy surface; both factors could enhance vibrational relaxation in complex ways. Here the factors that can affect the relaxation process are the masses and polarizabilities of the rare gas atoms. In spite of the apparent simplicity of these systems, some of the previous results are puzzling. For example, results suggest that the vibrational relaxation of N,f(v = 1) with Ne is surprisingly efficient compared to that of Oz(u = 1) with Ne; the reported rate constant for the relaxation of Nz(v = 1) (4.5x lo-l2 cm3 molecule-’ s-l) [9] is more than two orders of magnitude greater than that of O,‘(u = 1) (
S. Kato et al./International Journal of Mass Spectrometry and Ion Processes 149/150 (1995) 469-486
411
LIF signal
4
Blowerpump
Fig. 1. Schematic
of the SIFT-LIF
with laser-induced fluorescence (LIF) detection for optical monitoring of ion vibrational states [14]. This permits complementary optical and mass spectrometric (MS) measurements (with the monitor ion method) to extract the rates. The vibrational population distributions can be accurately determined with the SIFT-LIF. This is not always possible with the conventional monitor-ion technique which utilizes fortuitous coincidences of the thermochemistry between excited ions and monitor molecules. In previous work, the SIFT-LIF technique has been used to study the kinetics and dynamics for isotopitally labeled “N;(TJ = 0, 1, 2) +I4 N2 resonant charge transfer reactions [ 15,161, as well as the vibrational specificity and relaxation for the reactions of N;(v) with Ar and O2 [17], CO and NO [18], and H2 [19]. In the present study, we combine the SIFT-LIF and conventional mass spectrometric (MS)
instrument.
methods to provide a powerful approach for measuring the relatively slow relaxation rates of N;(U) with rare gas atoms. Rate constants are extracted for Nl(v = 1) relaxation with each of the rare gases and additional information is obtained for N,f (v = l-4) in the specific case of Ne. On the basis of the rate constants obtained, we discuss the mechanism of ion vibrational relaxation and examine the applicability of the vibrational predissociation model and other alternatives.
2. Experimental 2.1. SIFT-LIF
apparatus
The SIFT-LIF instrument has been used extensively for measuring kinetics and dynamics of gaseous ion/molecule reactions that are relatively fast. The details of the
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Table 1 Ion injection potentials and measured vibrational population distributions of Nap Ion injection potential (eV)
47
25
Nl vibrational distribution v=o
zJ=l
v=2
v=3
?J=4
lJ=5
0.46 0.52
0.23 0.35
0.15 0.08
0.12 0.05
0.04 (
(
a Ref. [20].
instrument and the principle of operation are described elsewhere [14]. In the present study, additional gas inlets are attached to the instrument in order to measure the extremely slow vibrational relaxation with rare gas atoms by virtue of complementary LIF and mass spectrometry measurements. Fig. 1 schematically illustrates the flow tube section equipped with a SIFT ion source, a laser beam port and an LIF detection port that are perpendicular to each other, a downstream mass filter, and four gas inlets (Mi -M4). The inlets Mi, M2, M3 and M4 are located 4,46, 70 and 111 cm, respectively, from the SIFT injection orifice. Vibrationally excited Nt ions are produced by electron impact on approx. 2.7 Pa (20 mTorr) of NZ. The Nt ions are extracted, mass selected, and injected into the flow tube, where they are entrained in He carrier gas at a pressure of 0.6 Torr (80 Pa). The He carrier gas is supplied through two concentric annular venturi inlets around the injection orifice. The average velocity of He is estimated as 105 m s-l in the laminar flow region. The injection potential (Einj) of Nl ions is typically 47 eV (laboratory). The ions acquire further vibrational excitation in the injection process but they are rotationally and translationally thermalized by collisions with He. For LIF detection of N2f(X, U) in a specific vibrational level, a corresponding B2 C$ + X2 C,’ vibronic transition is excited by radiation from an excimer-pumped dye laser operated at a typical repetition rate of 100 Hz. The fluorescence emission is acquired with gated photon-counting detection. An
improvement in LIF detection sensitivity enabled us to detect N:(U) ions in higher vibrational states than previously reported; the Nl vibrational levels are found to be populated UP to 21 = 3 and w = 4 at Einj = 25 and Einj = 47 eV, respectively (Table 1) [20]. Rare gas relaxers are added through the Mi inlet. Laser-induced fluorescence is used to monitor the change in N;(U) density at the LIF detection point, which is located between Mi and M2, about 11 cm downstream of the injection orifice. The proximity of the laser detection to the injection orifice facilitates LIF detection with good signal-to-noise (typically 2-10 photons s-i at a laser repetition rate of 100 Hz); the total N;(U) density is estimated as approx. 1 x lo5 cme3. Since the He flow is turbulent rather than laminar between Mi and M2, absolute determinations of rate constants by this method would be difficult. Instead we use the Nl(v = 1) + Ar charge transfer as a reference reaction; this system has proven to be an excellent reaction for calibrating other reaction rate constants [14,17]. Relaxant rare gases are added through the M2 inlet for the mass spectrometric measurements. This inlet is sufficiently downstream from the SIFT injector that a laminar flow of He is expected to be established at M2. Absolute measurement of the rate constants is thus feasible. Argon, which is used as a vibrational monitor reactant to react selectively with Nl(v > 0), is then added through the M4 inlet, which is immediately before the sampling orifice of the downstream mass filter. The flow tube section between M2 and M4 is
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the reaction distance in the mass spectrometric measurements. We estimate the average transit time of Nz between M2 and M4 to be about 3.9 ms, taking into account the radial distributions of both the He flow velocity and the ion density [14]. 2.2. Purity of the reactant gases The purity of the reactant gases is critical in measuring the extremely small rate constants for N;(u) vibrational relaxation with rare gases. Trace amounts of impurities (e.g. about 0.001% of N2 or Hz0 in He) can efficiently quench vibrationally excited N:(v) by chemical reaction. To remove such impurities, the He carrier gas (nominally 99.995%) is passed through a trap packed with molecular sieves and cooled to liquid nitrogen temperature. Neon (>99.999%), argon (>99.996%), krypton (>99.997%) and xenon (>99.999%) are used without further purification; the N;(V) vibrational relaxation is expected to be faster with these reactants than with He and the gas purity is less critical. However, other possible impurity sources such as contamination from gas lines must be considered. The effects of impurities from all sources can also be canceled out by an experimental procedure that is described below.
3. Measurement relaxation
methods for vibrational
The details of the kinetics used in the determinations are given in the Appendix. Here the basic features of the measurements are briefly described. 3.1. LIF measurement relaxation
for Ne, Ar and Kr
Vibrational relaxation rates of N;(v) with Ne, Ar, and Kr are measured with LIF. The
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relaxation with Ar can be assessed only by the LIF method; argon is used as the vibrational monitor reagent for Nt(v > 0) with conventional mass spectrometric methods, and no other atoms or molecules are available for detecting vibrational relaxation with Ar itself. The relaxation with Kr is also measured only with LIF; accurate values for k, are difficult to extract from analysis of conventional MS kinetic plots because the charge transfer with Kr is much faster thank, and the charge transfer rate is strongly dependent on vibrational excitation [lo]. Relaxation of N:(v) with Ne was measured by both LIF and MS methods. The dye laser is tuned to a specific band head position of N:(v) and signals are collected for a given flow rate of a rare gas reactant. A full kinetic decay is obtained by changing the flow rate and observing the change in signal intensity. Up to 30 mTorr of a reactant is added through the Mt inlet. All the vibrational levels up to v= 4 are monitored for relaxation by Ne. Only the increase in 21= 0 is monitored for Nap relaxation by Ar, since the charge transfer of Nz(v > 0) is extremely fast with Ar and vibrational relaxation amongst higher levels is difficult to observe [17]. For Kr, we conducted two independent measurements for vibrational relaxation. In one measurement, we altered the vibrational population distribution by changing Einj (47 and 25 eV) and observed the ‘u = 1 decay. The population ratio of ‘u > 1 to u= 1 changes considerably with Einj, and the measurement of the 21= 1 kinetics should be a sensitive test for vibrational relaxation from 21> 1 to u= 1. In another measurement, a small amount of Ar (l-3 mTorr) is premixed with the He carrier gas and added through the venturi inlet; this removes all Nt(v > 0) by charge transfer before relaxation or reaction with Kr. The vibrational relaxation from ZI> 0 to ZI= 0 is elucidated from the r.~= 0 kinetics measured with and without Ar addi47 eV. tion at Ei*j
=
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3.2. Mass spectrometric Ne and Xe relaxation
measurement
for He,
Relaxation of vibrationally excited N:(U) by collisions with neutral gases has been measured by observing the decay of Nt(v > 0), which is determined by the monitor ion method, i.e. the titration reaction with Ar. Because of the inefficient relaxation with rare gas atoms, however, the decay of N,f(v > 0) can be significantly accelerated by chemical reactions with impurities in the rare gas reactant. The measured relaxation rate constant can be overestimated. To circumvent this problem we also measured the increase of N2f (U = 0), according to the experimental sequence described below. First, we add a rare gas relaxer (M) through the M2 inlet (up to 30 mTorr, <5% of the He carrier gas) while the M4 inlet is closed. The amount of total Nt(v = O-4) ions, [Nt (total)], is measured with the MS as a function of [Ml. The [Nz (total)] is normalized by at zero M flow, giving a ratio [Nz(total)]* labeled y21. The value of yzI consists of two components: impurity reactions and the ion mobility change upon addition of M. Next, [Nt ( II = 0)] is similarly measured as a function of [Ml, while the M4 inlet is open and sufficient Ar is added to remove all N,f(v > 0) [13]. We have confirmed that this titration end point is unchanged under various experimental conditions ([Ml < 30 mTorr). The [Nz (7~= 0)] is normalized by [N~(u = 0)]* at zero M flow, giving a ratio labeled y43. The value of yd3 consists of three components: impurity reactions, the ion mobility change, and vibrational relaxation from upper levels (predominantly from u = 1 in the limit of small fractional relaxation if Av = -1 collisions dominate). We can extract the component for vibrational relaxation by dividing y43 by y21, thereby canceling out the effects of impurity reactions and the change in ion mobility (see Appendix). There are some approximations and
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limitations in this approach. First, relaxation of more than one vibrational quantum per collision (e.g. AU = -2) is not included in the formulation. This is reasonable since the relaxation is very inefficient for the rare gas collisions studied. Second, stepwise relaxation from ‘u > 1 eventually leading to v = 0 is neglected. This contributes little to the measurements if the extent of relaxation is small, as will be shown later. It follows from these approximations that the rate constant measured is predominantly for u = 1 to v = 0 relaxation (k,,io). Third, it is assumed that the diffusion rate constant for N;(v), which is proportional to the mobility of N:(v), is not a steep function of vibrational excitation. This is again reasonable because mobility is usually only a weak function of ion vibrational excitation within the same electronic state [21]. Finally, rate constants for the reactions of N;(v) with impurities are assumed to be independent of v. There is, however, a category of impurities for which the reaction rate constants with N;(U) are not constant with v and hence the impurity effects cannot be eliminated. The above experimental sequence cancels out the effects of many typical impurities such as H20 and hydrocarbons, which react with N2f without vibrational rapidly specificity. This is not the case for Ar [5,6,17] or Kr [lo] impurities, which have marked vibrational specificity for reaction with N2f (v). Another category of impurities includes N2 [15,16], O2 [17], CO and NO [18], which react with Ni (v) by both charge transfer and relaxation, thereby altering vibrational populations in favor of v = 0. Therefore, we confirm experimentally that there are negligible O2 and NO impurities in the rare gas samples used; we detect no 0; or NO+ ion products upon reaction of N;(v) with added gases. There was also no contamination from Ar or Kr in the other rare gases. Therefore k,,io can still be overestimated because of possible contamination by N2 or CO.
S. Kato et al.lInternational Journal of Mass Spectrometry and Ion Processes 1491150 (1995) 469-486 Table 2 Rate constants
for N:(v)
vibrational
relaxation
He This workb (SIFT-LIF) Previous (SIFTSIFDT) Previous (TICR)’
9.8(f0.7)
with rare gasesa
Ne x 10-16
3.6(+0.5)
x lo-l4
Ar
Kr
Xe
<1.2 x lo-”
<2 x lo-‘*
1.6(+0.2)
S(‘l) x lo-‘Sc
4.5 x lo-‘*d
_
5(_:5,) x lo-‘*e
-
2.2(&3)
5.5(f5)
_
l.lO(f0.85)
1.45(+0.7)
x lo-‘*
415
x lo-‘*
x 10-l’
x lo-l3
x lo-”
ak,,lo in units of cm3 molecule-’ s-' b Errors reported represent one standard
deviation in fitting the data. ’ Ref. [8], error bar estimated from the scatter in the data of Fig. 5 in Ref. [S]. d Ref. [9], error bar specified as 130%. ’ Drift tube data at _&,, = 0.05 eV (Ref. [lo]). ’ Tandem ion cyclotron resonance (Ref. [24]).
A second mode of measurement is also used for the relaxation with He, which is extremely slow. Argon is added through each of the M2, M, or M4 inlets to remove Nl(v > 0) by charge transfer, thereby establishing the N,f(v = 0) population at each inlet position.
“4r---l
The experimental and analytical procedures are given in Ref. [14]. The measured VJ= 0 population is then plotted as a function of relaxation time (corresponding to the ion transit time), and any increase in this value can be attributed to vibrational relaxation from upper levels (predominantly from ZJ= 1). This method is equivalent to measuring the vibrational relaxation of Nl(v = 1) at a much higher He pressure of 600 mTorr, and hence is more sensitive.
5x1 o-l5
1.2 + Z
4. Results
G Z 1 .O
0.8
1
0
I
1
2’
3
4
I 5
He flow rate I 1O*’molecule s-’ Fig. 2. N: mass counts normalized with respect to the counts for zero He flow ([Nz]*). The triangles and circles represent Ni(tota1) and N$(w = 0), respectively, and the associated lines are yz’ (long-dash line) and yq3 (solid line), which are fit to the corresponding data points. Note that y2’ is only slightly below y43 and hence almost indistinguishable. A simulation using a relation, kq,vv- l = k,,,,, is also shown by the short-dash line, where k,,,, for He is taken as 5 x lo-l5 cm3 molecule-’ s-’ [8]; this value represents an upper limit to the true k,,lo.
The rate constants kq,10 measured in the present work for the relaxation of vibrationally excited N:(v) by collisions with rare gas atoms are listed in Table 2, together with previous values. In all cases, the measurements are made in a regime where the extent of vibrational relaxation is small (< lo%), as described in the Appendix. 4.1. Nf(v)+He Fig. 2 shows the results of the first mode of MS measurements for relaxation of N:(v) with He. Both Ni(tota1) and Nl(v = 0) increase with the amount of He added. This
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indicates that the increase of Nt, due to decreased diffusive loss, labeled D, is greater than the decrease of Ni by reactions with impurities, labeled I (i.e. c&D,0 > ki, see Appendix). There is a negligible difference between Nz(tota1) and N,f(v = 0), which strongly suggests that the vibrational relaxation is extremely inefficient with He. The short broken line in Fig. 2 is a simulation using the previously reported value of s-l assumk q,10 = 5 x lo-i5 cm3 molecule-’ ing only AU = -1 processes and that all kq,uv_ 1 are equal to k,,lo. This value represents an upper limit to the true k,,lo. By fitting y2i and y43 to the data points, the rate constant for the vibrational relaxation from ZI= 1 to 21= 0 (kq,lO) is estimated to be 6 x lo-l6 cm3 molecule-’ s-’ although the error bars exceed the measurement (f120%, one standard deviation). In another set of measurements when He was used without purification, yd3 was slightly larger than ~21;
0.55
0.54
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a trace amount of Ar impurity was found in the non-purified He. The results from the second method of MS measurement are shown in Fig. 3. The VJ= 0 population gradually increases with reaction time. The value for kq,10 is determined to be 9.8 x lo-l6 cm3 molecule-’ s-l , which is in good accord with the first mode of measurement. In Fig. 3, we also numerically simulate the exact yield of N2f(~ = 0) taking all vibrational levels (V 5 4) into account. We assume that relaxation occurs only via Au = -1 processes and that all relaxation rate constants (kq,aa_l) are equal to k,,lo, which is taken as the previously reported value of 5 x 10-15. The simulation suggests that the value by Kriegel et al. is an overestimation by more than a factor of five. The effects of impurities are not canceled out in this method. Thus the value of k,, 1o is an upper limit, but because of the sensitivity of the second method, we prefer this value. Our value is considerably smaller than that reported by Kriegel et al. (5 x 10-15) [8] but is in accord with the observation by Smith and Adams (<10-15) [6]. 4.2. Nf (v)+Ne
0.53
c
0 E
S
0.52 0.51
,
a 0.50 B 0.49 w w 0.46
I
#’
t
0.45 I_ 0
1
2
3
4
5
Reactl0.r time I msec Fig. 3. Ni (TV= 0) population as a function of the reaction time in the He flow tube. The v = 0 population is measured using the Ar monitor reaction, in which Ar is added through different neutral inlets along the tube. The solid line is the fit to the data points giving k,,,,, = 9.8 x lo-r6 cm3 molecule-’ SC’. A simulation using the same assumption and the value of k,,ro as described in Fig. 2 is shown by the broken line.
The results of the MS measurements for vibrational relaxation with Ne are shown in Fig. 4. The value of y43 is obviously larger than y21 at each Ne flow, indicating that vibrational relaxation is more efficient with Ne than with He atoms. The value of kq,10 is determined to be 3.6 x lo-l4 cm3 molecule-’ s-l, which is more than two orders of magnitude smaller than that reported by Dobler et al. (4.5 x 10-12). We numerically simulated the exact yield of N,f(v = 0) using the same assumption as in Figs. 2 and 3 but with kq,10 set equal to 3.6 x 10-14. There is only a negligible difference between the predicted exact N,f(v = 0) and y43 when all kq,vv-l are assumed to be equal to k,,lo. If the vibrational relaxation is assumed to be more efficient for
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the higher levels, according to the relation kq,vv- I = v - k,,lo, the difference becomes slightly greater but is still negligibly small. A greater deactivation efficiency for higher vibrational levels has been observed for many neutral/neutral systems [2] as well as for a few ion/neutral systems [7,22]. In any case, the effect of stepwise relaxation is negligible when vibrational relaxation is not extensive. This supports the approximation used in deriving y43, that the relaxation is described by a two-level system (v = 1 -+ v = 0) under our experimental conditions. Also shown in Fig. 4 are the simulation results for
I
I
I
I~
a
I
I
I
I
I
1
I
I
I
I
I
1.2 1.0 0.8 0.6
2.0
2 0.61 1.2,
1.6 L +hl 3 N
1.4
+-,A
1.4
]
El 1.2 I I
I
i.a o.80
I
I
I
I
I
1
2
3
4
5
Ne Flow rate / 1020 molecule 8.’ I
I
I
I
1
2
3
4
Ne flow
rate'/102' molecules 8.’
Fig. 4. Nt mass counts normalized with respect to the counts for zero Ne flow ([Nil*). The triangles and circles represent Ni(tota1) and Ni(v = 0), respectively, and the associated lines are ~2, (long-dash double dot line) and y4s (solid line), which are fit to the corresponding data points. The dash-dot line is the simulation of the N$ (V = 0) yield assuming a relation, kq,vv _ 1 = k q,lO, where k,,lo is taken as 3.6 x lo-l4 cm3 molecule-’ SC’ from these measurements for Ne relaxation. Notice that it is very close to y43. Similar simulations using different values of k q,LOare also shown by the short-dash lines with k,,,,, given in cm3 molecule-’ SC’.
Fig. 5. LIF kinetics plots for N:(w) + Ne relaxation: (a) v = 4; (b)v = 3; (c) u = 2; (d) w = 1; (e) u = 0. The solid lines and the long-dash lines are simulations assuming relations, kq,““_, = kq,Lo and kq,uv-l = v.k,,,o, respectively, where k,,,. for Ne relaxation is taken as 4.5 x lo-” cm3 molecule-’ s-’ [9]. The short-dash line is shown to guide the eye (no change in mobility, no relaxation).
Nz(v = 0) using the same assumptions as in Figs. 2 and 3 and larger values of k,,lo, demonstrating the considerable discrepancy between the previously reported value (see Table 2) and our current value.
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Mass
Spectrometry
We also observe that MS signals of the Ar+ charge transfer products, which is a measure of N2f(~ > 0), increase with the amount of Ne added. This indicates that the signal increase due to mobility effects predominates over the loss due to vibrational relaxation (and/or reactions with impurities), supporting the above observation that the vibrational relaxation rate with Ne is quite small. The extremely slow relaxation with Ne found in the MS measurements is also confirmed by independent LIF measurements (Fig. 5). The LIF signals for individual vibrational levels of N;(w) are found to be unchanged or to increase slightly, especially for u = 3, with the addition of Ne (Fig. 5). It is unlikely that these small differences in behavior of various vibrational levels are caused by the turbulent flow in the LIF region, which should affect all levels similarly. Although there are several factors which may contribute to the observed behavior, quantitative discussion of these small differences is not appropriate or fruitful. The data clearly indicate, however, that the decrease of ‘u = 1, 2, 3, 4 and the concomitant increase of u = 0, which would be predicted by a simulation using the kq,iO of Dobler et al. [9] and assuming a stepwise relaxation scheme with the values of kq,,,_l set equal to kq,10 (see Fig. 5), are not observed experimentally. Another simulation using the previous value of k4,10and assuming a more efficient relaxation for higher vibrational levels, i.e. kq,vv_ 1 = v - k,,lo, also cannot reproduce the LIF results. Since the LIF measurements reveal no evidence for the appearance of Nl(v = 5) upon addition of Ne up to 30 mTorr, no collisional up-pumping processes are occurring. This is reasonable in view of the thermal collision energies attained in the SIFT-LIF instrument. Therefore, the best explanation for the LIF results is that the vibrational relaxation is extremely slow with Ne and the mobility effect dominates the LIF kinetics, in conformity with the MS results.
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I1
3x1o-l2
0
1
I
1
2
I I
Kr flow rate I 102’molecule s-’ Fig. 6. LIF kinetics plots of N:(w = 1) + Kr relaxation at Nz injection potentials of 47 eV (circles) and 25 eV (triangles). Associated lines are single exponential fits to the data points at 47 eV (solid line) and 25 eV (dashhdot line), respectively. The broken lines are simulations of the kinetics at 25 eV injection with several assumed values of Ic,,~~ for Kr relaxation given in cm3 molecule-’ s-t.
4.3. N;(v)+Ar,
Kr
The vibrational relaxation of N,f(v = 1) with Ar was examined in our earlier work by observing the LIF kinetics plots for w = 0. Since Nl(v > 0) reacts rapidly with Ar, any relaxation from 21 = 1 should appear as an initial rise that is superimposed on the slow single exponential decay of u = 0. The relaxation is rather minor, and an upper limit of 1 2 x lo-” cm3 molecule-’ s-l was obtained for kq,10[17]. The vibrational relaxation of N;(V) with Kr is an intriguing and complex issue because of the competing, vibrationally state specific charge transfer reaction. The charge transfer results are described in detail in a separate paper [20]. Briefly, the N~(v = 0) kinetics in the presence of Ar (and hence in the absence of 21> 0) establishes the charge transfer rate constant for N~(v = 0). The Ni (V = 0) kinetics without Ar addition (and thus with
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2 x lo-l2 cm3 molecule-’ s-l deviate beyond the 20 limit of the experimental fit at 25 eV. Thus the upper limit for kq,21 is also determined to be 2 x lo-l2 cm3 molecule-t s-l (95% confidence limit). These upper limits for the relaxation rate constant with Kr are even smaller than the previous value of 5 x 10-12, which was obtained at a slightly elevated collision energy of 0.05 eV [lo]. 4.4. Ni (v)+Xe
0.2
I
I
I
0.4
0.6
0.8
Xe flow rate I 10m
molecule s”
Fig. 7. The ratio between the normalized mass counts for Nz(v = 0) and Nz(total) as a function of Xe flow rate. The solid line is the fit of Y (E y43/yZlr see Appendix) to the data points.
possible sources of TJ= 0 by relaxation from ZI= 1) are essentially indistinguishable. This allows us to establish an upper limit of &to, which is 5 2 x lo-l2 cm3 molecule-’ s-l. An LIF measurement on the u = 1 level for relaxation with Kr is shown in Fig. 6. Two sets of measurements were conducted for the u = 1 kinetics at Einj of 47 and 25 eV to vary the ‘u > 1 population. Since the observed decay of u = 1 should be a superposition of vibrational relaxation into u = 1 with the intrinsic decay of 21 = 1 (by charge transfer and relaxation), the apparent decay of ZI= 1 at 47 eV could be slower than that at 25 eV because of the greater population in 21> 1 at 47 eV. The measurement revealed little difference between results with the 47 and 25 eV injection energies, suggesting that relaxation into ZI= 1 (predominantly from 2, = 2) is rather slow. The kinetics plot at 25 eV injection is simulated by assuming different values for kq,21y taking the values of the other kq,vv_l to be equal to kq,21, and using the total loss rates for w > 1 determined in our separate paper [20]. The curves with kq,2, greater than
A small correction for reactive loss (up to 15%) must be made for the relaxation measurement with Xe. Our MS measurements show that the charge transfer of Nz with Xe is very slow, with a rate constant of about 1 x lo-t3 cm3 molecule-’ s-‘, in good agreement with the literature value (7 x lo-l4 at 300 K [23]). Since there is little vibrational dependence of the charge transfer reaction of N;(U) with Xe [23], y43 and yzI can be readily obtained after correcting for the reactive loss. The ratio of y43 to y21 (labeled Y, see Appendix) is shown in Fig. 7. The relaxation of N;(v) with Xe is somewhat faster than with other rare gas atoms. The value for kq,10 is found to be 1.6 x lo-l3 cm3 molecule-’ s-’ which is comparable to the charge transfei rate.
5. Discussion 5.1. Comparison
with previous ion relaxation
The vibrational relaxation rates of N;(v) with He, Ne and Xe exhibit higher efficiency for the heavier collision partners (Table 2). Since the upper limits for Ar and Kr are conservatively evaluated, it is reasonable to expect that the vibrational relaxation with Ar and Kr will follow the trend observed for He, Ne and Xe. The observed mass-dependence is similar to that of 0; (w) relaxation with rare gas atoms [7].
480 Table 3 Vibrational Rare gas
He Ne Ar Kr Xe
S. Kate et al.llnternational Journal of Mass Spectrometry and Ion Processes 149/150 (1995) 469-486
relaxation
of N:(v)
with rare gas atoms
Relaxation rate constant, /c~,‘~~ (cm3 molecule-’ s-‘)
9.8 3.6
x x x x x
lo-l6 IO-l4 lo-” 10-12 lo-l3
Langevin collision rate constant, kt (cm3 moleculeC’ 5.67 4.30 7.39 8.05 9.80
x x x x x
lo-” lo-‘0 10-10 lo-” IO-”
Deactivation probability,
Polarizability, (lo-24 cm3)
1.7 8.4 <1.6 <2.5 1.6
0.205 0.395 1.64 2.48 4.04
o/
SC’) x x x x x
10-6 1O-5 1O-2 10m3 lO-4
a This study. b <
> 3 kq,‘O/kL.
In general, the values of N:(v) relaxation are smaller than those previously reported (Table 2). It is not surprising that the values obtained with tandem ion cyclotron resonance (TICR) are greater than ours, possibly because of higher collision energies in the ICR cell (Elab M 0.5eV) [24]. The discrepancy between previous SIFT/SIFDT studies and the present values is most likely due to impurity effects, which are eliminated in the present study. Indeed, difficulties regarding the vibrational relaxation of N:(U) and O,‘(v) with Ne are resolved. Our results indicate that N:(v) vibrational relaxation is comparable to that for O,‘(v) in collisions with He, Ne and Ar. The reported rate constants for O,‘(v) relaxation are <2 x 10-15,
attractive interaction becomes manifest at lower temperatures. On the other hand, our thermal value of kq for N;(U) with He is consistent with the zero-field extrapolation of their higher drift-field data. In an attempt to explain the deviation observed at lower temperatures (300-500 K), Zenevich et al. carried out refined classical path calculations [25] using a variety of analytical fits to the existing ab initio potential energy surface for the Nl/He interaction [26]. In spite of their elaborate calculations, it was not possible to obtain satisfactory agreement between theory and experiment at lower temperatures. The calculations suggested that the rate constants for N2f(w)/He relaxation at 300 K should be in the range of lo-l6 cm3 molecule-’ s-i, which is far smaller than the earlier experimental value (5 x 10-15). Our value of 9.8 x 10-16, which may still be an upper limit, is closer to the theoretical prediction. It is likely that the previous experimental value suffered from impurity effects, which might be particularly evident at lower temperatures. It is thus likely that the mechanism for N;(v) relaxation with He near room temperature is a more direct interaction. Mechanisms invoking the formation of an ion-neutral complex, e.g. cluster formation as suggested by Zenevich et al. [25], do not seem to contribute significantly. The ab initio potential well depth is very small (about 0.017 eV [26]), so that Nl/He
S. Kato et al./International Journal of Mass Spectrometry and Ion Processes 149jl.50 (1995) 469-486
clusters are not expected to be important at 300 K. A similar EC, dependence is also obtained for the N;(v) relaxation with Kr, when our value for k, at thermal energies is combined with those measured at higher energies [lo]. The value of k, shows a simple, positive E Cm dependence over the collision energy range, 0.039-0.4 eV. Thus, relaxation catalyzed by long-lived complexes or clusters may not be dominant at these energies. Nevertheless, the typically more rapid rate constants for relaxation of vibrationally excited ions compared to neutrals does suggest some role of the ion-induced dipole attractive interaction. 5.2. Comparison with Nz(v) relaxation For comparison with vibrational relaxation of neutral N2(u), we list in Table 3 the N:(U) deactivation probability per collision with rare gas atoms, <
>(- kq,lO/kL), where kL is the Langevin collision rate constant. The deactivation probabilities range from lop6 (He) to 1O-4 (Xe), which are far smaller than typically observed for ion vibrational relaxation with diatomic and polyatomic neutral molecules (lo’- 10e3) [13]. Instead, the Nap relaxation with rare gas atoms may be analogous to neutral N*(w) relaxation. There are two measurements reported for the vibrational relaxation of neutral N2(w) with He near 300 K: a relaxation time of 6.9 x 10e3 (atm s) at 295 K [27] and of 5.1 x rate constant a relaxation lo-‘s cm3 molecule-’ s-l at 291 K [28]. We convert these values into
> by using N2/He collision frequencies calculated from Lennard-Jones potential parameters and collision integrals [29,30]. The values of <
> are calculated as 1.7 x lo-* and 1.5 x lo-*, respectively, in fair agreement with an estimation from an empirical relationship for V-T energy transfer probability by Millikan and
481
White [31] of 1.O x lo-‘. The deactivation probability for N;(w) with He (Table 3) is somewhat similar to these values for neutral N2(2r). This suggests that the relaxation of N;(v) with He at room temperature is a relatively direct process, in analogy to the relaxation for neutral/neutral systems that are non-polar. Indeed, the potential well depths with He are shallow, 0.017 eV [26] and 0.0015 eV [32] for N;(w) and N2(w), respectively, compared to kT at 300 K (0.026 eV). The positive kinetic energy dependence of k, as discussed in the previous section also supports the idea of a direct mechanism for the N;(w) relaxation with He at and above 300 K. This direct mechanism should be contrasted to those for ion relaxations with diatomic and polyatomic molecules that are far more efficient. The vibrational relaxation of N:(w) with the heavier rare gas atoms, however, cannot be a simple analogy to the corresponding neutral N2 (w) counterparts. The Nz (w) vibrational relaxation is found to be more efficient for heavier collision partners. This is directly opposite to the reduced-mass dependence of neutral/neutral collisional relaxations, for which relaxation is more efficient for lighter collision partners (impulsive limit) and is adequately described by the classical and quanta1 versions of Landau-Teller theory for V-T energy transfer [2]. In spite of the lack of experimental measurements near room temperature, the MilIikan-White empirical formula predicts far smaller deactivation probabilities
> for neutral N2(w) relaxation with heavier rare gas atoms, e.g. 6 x lo-l3 for Ne and 1 x lo-l4 for Ar. The positive correlation between <
>and the polarizability of rare gases (Table 3) strongly suggests that attractive forces between N:(w) and rare gas atoms, which predominate over reduced-mass effects, play a significant role in the vibrational relaxation of N;(w) with heavier rare gas atoms.
482
5.3.
S. Kate et al.lInternational Journal of Mass Sprctrometry and Ion Processes 149/150 (1995) 469-486
Models for vibrational
relaxation
The positive correlation often found between the ion deactivation efficiency and the polarizability of the neutral collision partner has led to another model for the relaxation of vibrationally excited ions: a charge-induced dipole produces a deep attractive well between an ion and a neutral. The attractive well stabilizes the ion-neutral van der Waals collision complex, which vibrationally predissociates, resulting in ion vibrational relaxation [ 131. According to this model, a correlation is anticipated between k, and the three-body association rate constant k3, such that k, = k,,k’/k,, where k,, and k, are the rate constants for vibrational predissociation and collisional stabilization, respectively, of the transient ion/molecule collision pair [ 131. In fact, k, is found to correlate positively with k3, in good conformity to the model proposed. Conversely, however, a positive correlation between k, and k3 does not necessarily assure that the ion relaxation is solely via the predissociation occurring mechanism, as was pointed out by the same author. For extremely weakly interacting ion-neutral pairs, k3 becomes too small and the lifetime of the collision pair (which is derived from the same model as 7 = k3/kLk,) is not long enough to support long-lived collision complexes. Despite the lack of experimental threebody association rate constants for Nl/rare estimate the gas pairs, we can roughly complex lifetime using k3 for 0,’ systems. The values of k3 for O,f/Kr (9.4 x 10P31 cm6 moleculeP2 s-l) O,f/Ar and (3.5 x 1o-31 cm6 moleculeP2 s-l [I 31 suggest upper limits for k3 of O,f/Ne and O$/He as about 3 x 10e31 or even smaller. These would be reasonable estimates in view of the polarizabilities for Ne and He, which are far smaller than those for Kr and Ar (Table 3). A smaller bond energy for Nl/He (0.017 eV)
than for Ol/He (about 0.026 eV) [33] implies a weaker interaction for Nl than for 0; with these lighter rare gas atoms. Thus the values of k3 for Ni/Ne and Nl/He would be still smaller than those for the corresponding 0; systems. Therefore we estimate the upper limit of k3 for both Nz/Ne and N2f/He as 1 x 10P3t. After correction for effective stabilization efficiencies [ 121, the lifetimes for Nz/Ne and N2f/He are estimated to be shorter than 1 ps. This lifetime supports fewer than tens of N;(U) vibrations before the complex dissociates, and hence might be too short for vibrational predissociation to occur on an approximately nanosecond time scale (this time scale is also estimated from the predissociation model [13]). If we assume that k3 for N,‘/Xe is comparable to that for Ol/Kr, the lifetime is shorter than 1 ps, again too short for vibrational predissociation. These short lifetimes are reasonable for Nj!/rare gas systems because for these atomic neutrals there is no stabilization possible by conversion of relative translational energy into neutral rotational energy [13,34]. Thus, van der Waals vibrational predissociation does not seem to be a dominant mechanism for the extremely inefficient Nz relaxation with rare gas atoms. More recently, Tanner and Maricq proposed an alternative approach for ion/neutral vibrational relaxation [35]. The attractive part of the potential energy surface increases the effective collision energy, thereby making a stronger collision at the repulsive part of the potential well [2]. From the results of their scattering calculations, they concluded that the ion vibrational relaxation occurs repulsively in the vicinity of the classical turning point of the ion/neutral interaction potential well. This led them to formulate a more direct model for vibrational relaxation (modified Landau-Teller model) that does not invoke a long-lived ion-molecule complex stabilized by attractive forces. According to their model, a strong attractive well between
S. Kate et al.lInternational Journal
of MassSpectrometry
an ion-neutral pair (E) alters the steepness, i.e. the hardness (L-l) of the repulsive wall and also increases the effective collision energy (& + E), thereby enhancing vibrational relaxation with respect to that for neutral-neutral pairs. Their equation for the probability of relaxation
> [35] is MwL2 = constant -
> for Nz(w)/He. A much deeper attractive well for Nt/He (e M 0.017 eV) will increase the steepness of the repulsion, or in other words, decrease L. From the value of L of 0.209 A for N2/He and the values of E for N2/He [32] and Nt/He [26], we find that the modified Landau-Teller theory (Eqs. (3) and (4)) reproduces > for Nz (v)/He when L is assumed to be 0.162 A at 300 K. This value of L can be compared to 0.176 A, which is calculated from Eq. (4) and the ab initio potential energy surface for a collinear collision between Nl/He [26].0 Conversely, the theoretical value of 0.176 A predicts > and k, for Nz(w)/He to be 6.0 x 10e7 and
J%
r
21.57rMo.5~L
’exp I- (EC +c)‘.’+ (EC +
E +
1
and Ion Processes 1491150 (1995) 469-486
483
3.4 x lo-l6 cm3 molecule-’ s-l respectively. The predicted value of k, may ‘be reasonable since the experimental value of 9.8 x lo-t6 is still an upper limit. Thus the vibrational relaxation of N:(v) with He might be accounted for without invoking the idea of van der Waals vibrational gredissociation. Even smaller values of L (
Tzw)~.~]
where L-1
____- _dW)
=
dR
1 E,+E
It is of interest to apply their model to N;(v) relaxation in order to examine if the relaxation can be treated within the framework of the Landau-Teller theory. First, the interaction range parameter, L, is determined to be 0.209 A by using “Method B” [2] and Eq. (4) for a collinear collision between N2 neutral and He at 300 K (E, = 0.039 eV). The potential parameters (e and ao) are taken from the ab initio calculation of Banks et al. [32]. The constant in Eq. (3) is determined from the L and <
6. Conclusions Using the SIFT-LIF technique, we have measured relaxation rate constants for N;(u) + He , Ne and Kr at thermal energies and provided the first measurement for N:(v) + Xe, along with our recent measurement for N;(w) + Ar. The observed rate constants are significantly smaller than those previously reported, primarily because impurity problems have been carefully eliminated. The rate constants for N~(z,I = l)/rare gases are found to be similar to those for O,‘(v = l)/rare gases in terms of both magnitude and mass dependence. A positive correlation is observed between the rare gas polarizability and the relaxation rate constant, strongly suggesting the importance of attractive forces in the vibrational relaxation.. However, the mechanism may be different from the vibrational predissociation of ion-neutral van der Waals complexes. The deactivation probabilities are extremely small, suggesting complex lifetimes shorter than 1 ps that may be too short for vibrational predissociation to occur. A more direct mechanism (a modified Landau-Teller model) can account for the N;(u) relaxation with He. Such a direct mechanism may also be operative for the N:(w) relaxation with heavier rare gases.
484
S. Kato et al./International Journal of Mass Spectrometry and Ion Processes 1491150 (1995) 469-486
the following
Acknowledgment The authors gratefully acknowledge the financial support of the US Air Force Office of Scientific Research.
- d[Nt(total)] dt
differential =
equations:
kD[N,f(tOtd)]
+ kf[M][Nz(total)] -
“[“:‘d”, =‘)I = k,[N;(v
(A?
= O)]
Appendix + k;[M][N,f(v = 0)] The MS measurements of N,f(total) and Ni(v = 0) upon addition of the rare gas relaxer, M, are modeled in a manner similar to that described in Ref. [14]. The Ni ion concentration in the flow tube is described as the sum of components for diffusive loss, reactive loss (with impurities in M), and vibrational relaxation (with M). The rate constant for the diffusive loss (kD) is proportional to the ion diffusion coefficient (DA) and hence to the zero-field ion mobility (&(O)) : kD
0; DA
a
(Al)
KO(o)
The value of Ko(0) is altered by the addition M according to Blanc’s law l/K,(O)
=
where
+
XM/KO,M(0)
(AZ)
the mole fraction, and are the zero-field mobilKo,H~(~) and KO,M (0) ities for pure He and M, respectively. Under our experimental conditions, xM < 0.05 and hence XHe = 1 so that Eq. (A2) is approximated as KO(“)
x
XHdKO,Hdo)
of
=
denotes
KO,He(“)(l
-
d”I)
=
kD,O(l
-
4MI)
(fw
Based on an assumption that there is negligible contribution to the relaxation of more than one vibrational quantum per collision (e.g. Au = -2), which is reasonable for the inefficient relaxation with rare gas atoms, the evolution of Nl(total) and Nl(v = 0) is given by
~,,,o~WW;(v= I>1(-46)
where k,, 1o is the rate constant for vibrational relaxation from v = 1 to v = 0. The k’,(= xlkl) is the effective rate constant for reactive loss with impurities, where x1 is the mole fraction with respect to M, and k1 the reaction rate constant of N2f with the impurities in M. The relative increase in [Nt(v = 0)] due to vibrational relaxation is a posteriori less than 10% in our measurements, and hence stepwise relaxation from v > 1 to v = 0 also contributes little to [N2f(v = O)]. This approximation is equivalent to dropping the term = 2)] from the differential -/c~,~, [M][Ni(v equation for N,f(v = 1) when determining its effect on N,f (v = 0). For completeness when considering the LIF measurements of v = 1, we use _
dP,f(v= 1>1= dt
kD[N,f(v = 1) + k;[M][N;(v
(w
where a G (KO,He(0)/KO,M(O))/[He]. The diffusion rate constant is thus given from Eqs. (Al) and (A3) as kD
-
= l)]
+ k,,,o[Ml[N;(v -
kq,21
= 1)
[Ml[N;(v= 4
(A7)
Additional terms are added if charge transfer also occurs. The yield of N,f(total) at the M4 inlet is derived from Eq. (A5) as [N,f(total)]
= [N:(total)]oe-(kD’k;[MJ)t
(A8)
time from M2 to where t is the reaction M4 (= 3.9 ms) and the subscript 0 denotes the concentration of Nt(tota1) at t = 0 (i.e. at the M2 inlet). For zero reactant flow, Eq. (A8)
S. Kato et al./International Journal of Mass Spectrometry and Ion Processes 149/150 (1995) 469-486
reduces
to
References
[N,f(total)]*
= [N2f(total)]0e-kD,ot
where the [Nt (total)],
aster:t;k denotes [M] = 0. The normalized by [Nt (total)]*, gives
(A9)
yzl = [N~(total)]/[N~(total)]* =
WO)
e(ak~,o-k;)[Mlt
The yield of Nt(v = 0) at the M4 inlet is similarly derived from Eqs. (A6) and (A7) as
(91 = [N2+(21 = ~)]~,-(~~+k;b’fl)t
]N3
=
_
[~2f(~
=
l)o]{e-(k~+k;[Ml+~~,~o[Ml)~
_ ,-(b+k;[Ml)t) +
additional
terms
(All)
The additional terms arise from stepwise relaxation of the higher levels through u = 1 to u = 0. Referring to Fig. 4, the small difference when these terms are included suggests that they can be neglected. For zero reactant flow [Nz(v = 0)]* = [Nl(v
= O)]se-
The [N2f(~ = 0)] is normalized to give y43 = [N;(v
= O)]/[N;(v
ko,ot
(A121
by [Nl (w = 0)] *
= 0)]*
= { 1 + Rio( 1 _ e-k,,lo[M]r)}e(cukD,o-k:;Wlt
where Ris(= [Nz(w = l)]e/[Nt(v = 0 the ratio of vibrational populations at t = 0 as measured by LIF (Table 1). Finally, ~43 is divided by yzl to give y = Y43/Y21 =
1 + R,,(l
485
_ e-k,,lOIMlt)
(A14)
Components for impurity reactions and mobility change cancel out in the final result of Eq. (A14).
PI W.A. Abdou,
D.G. Torr, P.G. Richards and M.R. Torr, J. Geophys. Res., 87 (1982) 6324; 89 (1984) 9069. to Molecular Energy Transfer, PI J.T. Yardley, Introduction Academic Press, New York, 1980. [31 N.G. Adams and D. Smith, Int. J. Mass Spectrom. Ion Phys., 21 (1976) 349. [41 D. Smith and N.G. Adams, in M.T. Bowers (Ed.), Gas Phase Ion Chemistry, Academic Press, New York, 1979, Chapter 1, Vol. 1. [51 W. Lindinger, F. Howorka, P. Lukac, S. Kuhn, H. Villinger, E. Alge and H. Ramler, Phys. Rev. A, 23 (1981) 2319. 161 D. Smith and N.G. Adams, Phys. Rev. A, 23 (1981) 2327. D.W. Fahey, F.C. FehI71 H. Bohringer, M. Durup-Ferguson, senfeld and E.E. Ferguson, J. Chem. Phys., 79 (1983) 4201. PI M. Kriegel, R. Richter, W. Lindinger, L. Barbier and E.E. Ferguson, J. Chem. Phys., 88 (1988) 213; Erratum, 91 (1989) 4426. [91 W. Dobler, F. Howorka and W. Lindinger, Plasma Chem. Plasma Processes, 2 (1982) 353. DOI W. Dobler, H. Ramler, H. Villinger, F. Howorka and W. Lindinger, Chem. Phys. Lett., 97 (1983) 553. Vll W. Dobler, W. Federer, F. Howorka, W. Lindinger, M. Durup-Ferguson and E.E. Ferguson, J. Chem. Phys., 79 (1983) 1543. v-21 W. Federer, W. Dobler, F. Howorka, W. Lindinger, M. Durup-Ferguson and E.E. Ferguson, J. Chem. Phys., 83 (1985) 1032. u31 E.E. Ferguson, J. Phys. Chem., 90 (1986) 73 1. [I41 S.Kato, M.J. Frost, V.M. Bierbaum and S.R. Leone, Rev. Sci. Instrum., 64 (1993) 2808. u51 M.J. Frost, S. Kato, V.M. Bierbaum and S.R. Leone, J. Chem. Phys., 98 (1993) 5993. I161 M.J. Frost, S. Kato, V.M. Bierbaum and S.R. Leone, J. Chem. Phys., 100 (1994) 6359. iI71 S. Kato, M.J. Frost, V.M. Bierbaum and S.R. Leone, Can. J. Chem., 72 (1994) 625. U81 M.J. Frost, S. Kato, V.M. Bierbaum and S.R. Leone, in preparation. [I91 J.A. de Gouw, L.N. Ding, M.J. Frost, S. Kato, V.M. Bierbaum and S.R. Leone, Chem. Phys. Lett., 240 (1995) 362. WI S. Kato, V.M. Bierbaum and S.R. Leone, in preparation. Pll M.J. Bastian, Ph.D. Thesis, University of Colorado, 1994. LQI T. Wyttenbach and M.T. Bowers, J. Phys. Chem., 97 (1993) 9573. E. Alge, H. Ramler ~231 H. Villinger, P. Lukac, F. Howorka, and W. Lindinger, Czech. J. Phys. B, 31 (1981) 832. u41 P.R. Kemper and M.T. Bowers, J. Chem. Phys., 81 (1984) 2634. f251 V.A. Zenevich, W. Lindinger and G.D. Billing, J. Chem. Phys., 97 (1992) 7257. WI S. Miller, J. Tennyson, B. Follmeg, P. Rosmus and H.-J. Werner, J. Chem. Phys., 89 (1988) 2178. [271 R. Frey, J. Lukasik and J. Ducuing, Chem. Phys. Lett., 14 (1972) 514.
486
S. Kato et al./International Journal of Mass Spectrometry and Ion Processes 149/150 (1995) 469-486
D.J. [28] M.M. Maricq, E.A. Gregory, C.T. Wickham-Jones, Cartwright and C.J.S.M. Simpson, Chem. Phys., 75 (1983) 347. [29] J.O. Hirschfelder, CF. Curtiss and R.B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York, 1954. [30] R.C. Reid, J.M. Prausnitz and T.K. Sherwood, The Properties of Gases and Liquids, McGraw-Hill, New York, 1977. [31] R.C. Millikan and D.R. White, J. Chem. Phys., 39 (1963) 3209.
[32] A.J. Banks, D.C. Clary and H.-J. Werner, J. Chem. Phys., 84 (1986) 3788. [33] H. BGhringer, F. Arnold, D. Smith and N.G. Adams, Int. J. Mass Spectrom. Ion Processes, 52 (1983) 25. [34] F.J. Schelling and A.W. Castleman, Jr., Chem. Phys. Lett., 111 (1984) 47. [35] J.J. Tanner and M.M. Maricq, Chem. Phys. Lett., 138 (1987) 495.