Gas-phase collision dynamics by means of pulse-radiolysis methods

0146-5724/89 $3.00+ 0.00 Copyright © 1989 Pergamon Press plc

Radiat. Phys. Chem. Vol. 34, No. 4, pp. 675-685, 1989 Int. J. Radiat. Appl. lnstrum., Part C Printed in Great Britain. All rights reserved

GAS-PHASE COLLISION D Y N A M I C S BY MEANS OF PULSE-RADIOLYSIS METHODS YOSHIHIKOHATANO Department of Chemistry, Tokyo Institute of Technology, Meguro-ku, Tokyo 152, Japan Abstract--After a brief survey of recent advances in gas-phase collision dynamics studies using pulse radiolysis methods, the following two topics in our research programs are presented with emphasis on the superior advantages of the pulse radiolysis methods over the various methods of gas-phase collision dynamics, such as beam methods, swarm methods and flow methods. One of the topics is electron attachment to van der Waals molecules. The attachment rates of thermal electrons to 02 and other molecules in dense gases have been measured in wide ranges of both gas temperatures and pressures, from which experimental evidence has been obtained for electron attachment to van der Waals molecules. The results have been compared with theories and discussed in terms of the effect of van der Waals interaction on the electron attachment resonance. The obtained conclusions have been related with investigations of electron attachment, solvation and localization in the condensed phase. The other is Penning ionization and its related processes. The rate constants for the de-excitation of He(2tP), He(23S), Ne(aP0), Ne(3pi), Ne(3P2), Ar(~P~), Ar(3p0, by atoms and molecules have been measured in the temperature range from 100 to 300 K, thus obtaining the collisional energy dependence of the de-excitation cross sections. The results are compared in detail with theories classified according to the excited rare gas atoms in the metastable and resonance states.

I. I N T R O D U C T I O N

Pulse radiolysis is of great importance in the understanding of gas-phase reactions (Hatano, 1984). The results obtained are also useful for understanding condensed phase reactions. The objectives of pulseradiolysis studies in the gas phase are divided into two parts. One is to understand the fundamental processes, in particular early processes, in radiolysis. The other is to make an important contribution, as one of the powerful experimental methods, to gasphase collision dynamics studies. Recent advances in the latter studies are surveyed in this paper; those in the former studies are not included here. The abovementioned objectives are however, closely related with one another in terms of the following interface relationships. New information obtained from the latter studies is useful for understanding the fundamental processes in radiolysis, while that from the former studies is an important source of new ideas and information in collision dynamics studies. Advances in pulse radiolysis studies in the gas phase have been summarized in several review papers. In a comprehensive review by Sauer (1976), a review presented by Firestone and Dorfman in 1971 was referred as the first review on gas-phase pulseradiolysis. Experimental techniques and obtained results were summarized by the present author (Hatano, 1978) with emphasis on an important contribution of pulse radiolysis to gas phase reaction dynamics studies. Examples were chosen by Sauer (1982) from the literature prior to 1981 to show the types of species which were investigated in the gas phase using the pulse radiolysis technique. Experimental data obtained from gas-phase pulse radiolysis RPC M/4---Q

675

together with those from ordinary steady-state radiolysis have been recently reviewed by Armstrong (1987). Advances in gas-phase pulse-radiolysis studies since 1981 have also been briefly reviewed very recently by Jonah et al. (1987) with emphasis on an important contribution of this technique to free radical reaction studies. An important contribution of pulse radiolysis to collision dynamics studies, such as electron attachment and Penning collision studies has also been reviewed recently (Hatano, 1983, 1986; Hatano and Shimanori, 1981). In this paper, to begin with, a very brief survey is given of recent advances in such studies reported in the 1980's, classified according to the detection technique of transient species in pulse radiolysis. Secondly, examples are chosen from our recent investigations with special emphasis on the important contributions of pulse radiolysis methods to gasphase collision dynamics; one is electron attachment, the other is Penning ionization and related processes. The detection techniques and corresponding reaction processes together with major references published mainly in the 1980's are given below. (A) Optical emission and absorption spectroscopy (1) De-excitation of excited rare gas atoms such as Penning ionization and related processes (see the following section). (2) Formation and reaction of rare gas excimers and exciplexes (Cooper et al., 1983, 1984; Doba and Arai, 1981; Kasama et al., 1982; Loeb et al., 1981; Manzahares and Firestone, 1982, 1983; Tanaka et al., 1985). (3) Reaction of atoms and free radicals (see references cited in Jonah et al., 1987).

676

Yosrnmto HATANO

(4) Electron-ion or ion-ion recombination (Cooper et al., 1984; Sauer and Mulac, 1972). (5) Ion-molecule reaction (Dreyer and Perner, 1971). (6) Reaction of excited aromatic molecules (Ueno et al., 1978). (7) Electron thermalization (Cooper et al., 1982). (11) DC-conductivity measurements

(1) Electron mobility (Freeman, 1981; Huang and Freeman, 1981; Nakamura et al., 1983; Nishikawa and Holroyd, 1980, 1982; Shinsaka et al., 1989; Wada and Freeman, 1981). (2) Electron detachment (Hansen et al., 1983). (3) Electron attachment (see the following section). (4) Electron-ion or ion-ion recombination (Nakamura et al., 1983; Sennhauser et al., 1980; Shinsaka et al., 1989). (C) Microwave-conductivity measurements

(1) Electron attachment (see the following section). (2) Electron-ion or ion-ion recombination (Warman et al., 1979). (3) Electron thermalization (Scales et al., 1987; Shizgal and Hatano, 1989; Suzuki and Hatano, 1986a, b; Warman and deHaas, 1975, 1988; Warman and Sauer, 1975). (4) Penning ionization (Hatano et al., 1982). (D) Mass spectroscopy

(1) Ion-molecule reaction (Fessenden and Bansal, 1970; Matsuoka et al., 1981, 1983).

II. ELECTRON ATTACHMENTPROCESSES Pulse radiolysis, as combined mainly with microwave conductivity techniques, has been applied to thermal electron attachment studies. The molecules studied are 02, N20, NO, NO2, SF6, alkyl halides, and perfluorocarbons. Alkyl halides, fluorocarbons and N20 were studied in the early 1970's (Bansal and Fessenden, 1972, 1973; Fessenden and Bansal, 1970; Warman et al., 1972), while 02, N20 and other simple molecules have been extensively studied recently with special emphasis on the important contribution of a pulse radioysis method to electron attachment studies, in particular, to the studies on electron attachment to van der Waals molecules (Hatano, 1986; Hatano and Shimamori, 1981; Kokaku et al., 1979, 1980; Shimamori and Fessenden, 1978a, b, 1979a, b, 1981; Shimamori and Hatano, 1976a, b, 1977; Shimamori and Hotta, 1983, 1984, 1986a, b, c, 1989; Toriumi and Hatano, 1983, 1984, 1985). In the following one may find a unique standpoint of the microwave technique combined with the pulse radiolysis method in electron attachment experiments. In the study of electron attachment

mechanisms, ordinary swarm techniques may have some essential limitations in the experiment as it is almost unavoidable to use only a few environmental buffer gases for which the swarm parameters, electron energy distributions etc., are well known. Therefore, in cases where the attachment mechanism is strongly dependent on the particular nature of the environmental gases, the technique may not give enough information to adequately evaluate the mechanism in detail. Usual beam techniques are evidently not suitable for the study of environmental effects on the attachment mechanism. On the other hand, the microwave technique has been used as an alternative means for such studies with the main advantage of the technique being that it allows us to observe the behavior of thermal electrons, thus excluding any factor dependent on the electron-energy distribution. For usual swarm and beam techniques it has been difficult to study electron collision processes at very low energies such as thermal, whereas such studies are obviously of great importance in understanding of not only a two-body problem such as electron interaction with molecules, but also various phenomena in ionized gases. The microwave technique combined with the pulse radiolysis method has shown recently a distinct advantage in studying thermal electron attachment to molecules. By employing the pulse radiolysis method it is possible to perform time-resolved observation of decaying electrons with a very fast response in a very wide range of pressure of an environmental gas which is chosen with virtually no limitation. Thus, the mechanism of low-energy electron attachment to molecules has been discussed primarily in terms of the interaction of electrons with molecules. Recent studies of thermal electron attachment to 02, N20 and other molecules have revealed that the electron attachment to pre-existing van der Waals (vdW) molecules or neutral clusters plays a significant role in the overall mechanism. A significant development in such studies has been started in electron attachment studies using experimental techniques which were originated from radiation chemistry; one is the microwave technique combined with pulse radiolysis (see references cited in Hatano, 1986; Hatano and Shimamori, 1981), the other is the competition kinetics of steady-state 7-radiolysis (Nagra and Armstrong, 1976, 1977, 1978). Such studies have made an important contribution to advances in electron attachment studies, as summarized at the last part of this section, and have triggered a very recent development in beam experiments of electron-van der Waals molecule collisions (Mark, 1988; Mark et al., 1985; Stamatovic, 1988). Evidently the existence of electron attachment to vdW molecules compels us to more or less reinterpret various experimental data obtained previously. Furthermore, since such processes must be more important in dense gases or in the condensed phase, the studies of those processes will provide

12! i.o

677

Gas-phase collision dynamics

5/

02XaX~

i

an electron lifetime c0 which is related to [02] and [M] as: l 1 0[o21 =

+

(5)

when [02] '~ [M], where k u ( = k , k4/k2) is the overall three body rate constant. Based on equation (5), \ k ....... l .......... ,__-zl Shimamori and Hatano (1977) determined the value of k, = 4.8 x 10 - u cm3/s and the value ofkM for each I X X I ,'=5/ stabilization partner, which is listed in Table 1 with the value obtained by other workers. The autoioniza~. 0 v=O ........... v_'-3 tion lifetime of O~-*, i.e. the value of 1/k2, was also estimated to be ~ 10-t0 sec which was comparable to the predictions of some theoretical treatments 01~V t ..... ~l ~ ) / (Herzenberg, 1969; Koike, 1973, 1975; Koike and Watanabe, 1973; Parlant and Fiquet-Fayard, 1976) (see Table 2). Some inconsistencies existed between the results 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 obtained by Shimamori and Hatano (1977) and other INTERNUCLEAR SEPARATION(A) data. Christophorou and coworkers investigated elecFig. 1. Potential-energy curves for O2 and O~ (Hatano, tron attachment in O2-C2H4, O2-C2H6 and O2-N 2 1986; Hatano and Shimamori, 1981). mixtures at very high gas pressures ( < 3 0 a t m ) (Christophorou, 1972, 1976, 1978; Goans and Christophorou, 1974; McCorkle et al., 1972), and insight as to the effect of the density on reactions involving electrons or generally on the electron- observed that the attachment rate in 02-(22 H 4 system showed a saturation at very high pressures, but the molecule interaction processes (Smirnov, 1984). Since oxygen is probably the most extensively rates in O2-C2H 6 and O2-N 2 mixtures continued to studied molecule in both experimental and theoretical increase steeply with increasing pressures of C2H 6 investigations of low-energy electron attachment, the and N 2, respectively. They reported the value of k 1 experimental results and detailed discussion are much larger than that obtained by Shimamori and Hatano (1977) and correspondingly a considerably presented in this paper particularly for O2. The only accepted mechanism has been the overall shorter lifetime of O~-* (see Table 2). Such inconsistwo-step three-body mechanism which was originally tencies have been demonstrated more clearly and suggested by Bloch and Bradbury (1935) and was analyzed by the recent work of Kokaku and colater modified by Herzenberg (1969) to make it workers (1979, 1980). Kokaku and coworkers in the consistent with modern experimental data. The joint research between Tokyo and Notre Dame have mechanism for O2-M mixture, where M is a molecule studied, using the microwave technique combined with the pulse radiolysis method, O2-CO2 and several other than 02, is expressed as follows: O2-hydrocarbon systems at pressures from less than kl e- + 02 , Of* (1) 100Torr to 1000Torr and found that the BB mechanism can account for the data in the low k2 pressure range but fails to explain the results at higher Of* ' 02 + e(2) pressures. The data for O2-C2H 4 mixtures are shown in Fig. 2 as an example, where the high density part k3 0~-* + 02 , Of + 02 (3) of the data agrees well with the data obtained by Goans and Christophorou (1974), using a swarm k,, 0~-* + M ,0~- + M (4) technique. This research has clarified a significant discrepancy between the values of kl and Ilk 2 The vibrational characteristics of the negative ion obtained by the pulse radiolysis-microwave technique 0 2 * are established from electron-impact and and those obtained by the swarm technique. Thus it scattering experiments and the electron affinity of 02 has become obvious that a consistent interpretation is 0.44eV. For convenience, the potential energy in terms of only the BB mechanism is not possible in diagrams for O2(X3Z~ ) and O~-(X2/-/g) are shown in a wide range of the pressures of M and additional Fig. 1. It can be seen that the lowest resonance mechanism must be considered to explain the involves the vibrational levels, 02 (v = 0 ) and high-pressure data. One of the strong candidates for O~-(v'=4), at low electron energies and the such a mechanism is electron attachment to vdW molecules as was indicated by Kokaku and coresonance energy is about 0.08 eV. Since all electron decays for O2-M mixtures in the workers (1979, 1980). above-mentioned experimental conditions show g,q pseudo-first order behavior, each decay curve gives O:+M , '(02"M); (6) ..........

r

.

.

.

.

"-'=-8-/

::7

678

YOSHIHIKO HATANO

Table 1. Three-body attachment rate constants, ku for the reaction, e + 02 + M--*Q~ + M, at room temperature (Hatano, 1986; Hatano and Shimamori, 1981) M kM(10 3°cm6/s) References M kM(lO-3Ocm6/s) References He Ne Ar Kr Xe H2 D~ N2

0.033 0.03 0.07 0.023 0.05 0.05 0.085 0.48 0.14 0.06 0.085 0.09 0.1 0.11 0.15 0.26 0.10

02

1.7 2.0 2.1

Young et al. (1963) Pack and Phelps (1966) van Lind et al. (1960); Nelson and Davis (1971); Parlant and Fiquet-Fayard (1976) Crompton et al. (1979) Shimamori and Fessenden (1978a); Shimamori and Hatano (1976a); Warman et al. (1971)

2.15 2.2

2.3

CH4 C2H4

Shimamori and Hatano (1977) Chanin et al. (1962) van Lind et al. (1960) Shimamori and Hatano (1977) Shimamori and Hatano (1977) Shimamori and Hatano (1977) Shimamori and Hatano (1977) Shimamori and Hatano (1976a) Shimamori and Hatano (1976a) Chanin et al. (1962) Shimamori and Hatano (1976b) Shimamori and Fessenden (1981) Crompton et al. (1979) Hegerberg and Crompton 0983); van Lind et al. (1960) Goans and Christophorou (1974); Hackam and Lennon (1965); McCorkle and Christophorou (1972) Young et al. (1963) Toriumi and Hatano (1985)

n-C6HI4

1.3 1.5 1.7 0.9 3.2 3.3 4.2 4.5 5 7.9 7 8.0 8.1

Kokaku et al. (1980) Christophorou (1980) Shimamori and Hatano (1977) Toriumi and Hatano (1983) Kokaku et al. (1980) Shimamori and Hatano (1977) Shimamori and Fessenden (1981) Kokaku et al. (1980) Shimamori and Hatano (1977) Shimamori and Hatano (1977) Kokaku et al. (1979) Shimamori and Hatano (1977) Shimamori and Hatano (1977)

C6 H 6

8.5

Shimamori and Hatano (1977)

CO CO 2

18 1.31 3

C3H s n-C4Hi0 n-CsHi2 neo-CsHi2

H20

Hackam and Lennon (1965); Shimamori and Hatano (1976b) Hurst and Bortner (1959) Chanin et al. (1962) Hegerberg and Crompton (1983) Shimamori and Hatano (1977) Goans and Christophorou (1974) Bouby and Abgrall (1967) Kokaku et al. (1979) Hurst and Bortner (1959) Bouby et al. (1970) Shimamori and Hatano (1977) Stockdale et al. (1967) Stockdale et al. (1967) Toriumi and Hatano (1984)

2.6 2.8 2.2 0.34 1.5 1.7 2.0 2.3 2.5 3 3.1 3.4 1.3

C2H 6

H2S NH 3 CH3Oh C2HsOH CH3COCH 3

Bouby and Abgrall (1967) Shimamori and Fessenden (1981) Bouby and Abgrall 0967); Pack and Phelps (1966); Warman et al. (1971); Bauby et al. (1970)

3.2

Kokaku et aL (1970)

3.23 3.5

Crompton et al. (1979) Hegerberg and Crompton (1983)

14

Bouby et al. (1970); Pack and Phelps (1966); Stockdale et al. (1967)

15.2 9 10 6.8 7.5 8.8 9.6 11 18 27 35

Bouby and Abgrall (1967) Bauby et al. (1970) Bouby and Abgrall (1967) Bouby et al. (1970) Bouby and Abgrall (1967) Bouby et al. (1970) Bouby and AbgraU (1967) Shimamori and Hatano (1977) Shimamori and Hatano (1977) Bouby et al. (1970) Bouby and Abgrall (1967)

k5

e- + (02" M)

, (02" M)

*;

(7)

k6

(02 • M ) - *

,0 2 + M + e-;

(8)

the values for k 5 are much larger than the value of k ~ ( = 4 , 8 × 10 -11 cm3/s). T h i s r e s u l t s u g g e s t s t h a t in t h e c a s e o f v d W m o l e c u l e s t h e initial e l e c t r o n c a p t u r e m e c h a n i s m differs s u b s t a n t i a l l y f r o m t h e c a s e o f

k7

(02" M)

*+ M

,02

× 2M;

(9) Table 2. Lifetime o f O ~ * ( X 2 1 l ~ , v' = 4) (Hatano, 1986; Hatano and Shimamori, 1981) Lifetime (10 -12 S) References

w h e r e K e q is t h e e q u i l i b r i u m c o n s t a n t f o r v d W molecule formation. One should note here that the d e n s i t y o f v d W m o l e c u l e s is d e t e r m i n e d b y geq [O2][M], a n d t h e v a l u e o f geq c a n be e s t i m a t e d b y Stogryn and Hirschfelder's theoretical treatment ( S t o g r y n a n d H i r s c h f e l d e r , 1959). S e v e r a l e x p e r i ments have provided evidence for the existence of

Experiment

v d W m o l e c u l e s in t h e g a s p h a s e ( S m i r n o v , 1984; B l a n e y a n d E w i n g , 1976). I n t h e k i n e t i c t r e a t m e n t m a d e b y K o k a k u a n d c o w o r k e r s (1979, 1980), t h e e s t i m a t e d v a l u e s o f k5 a r e ( 2 - 2 0 ) x 1 0 - 9 c m 3 / s d e p e n d i n g o n M , w h e r e it is h i g h l y a t t r a c t i v e t h a t all

91 66

Theory

300 170 72 88

100 63 2

Herzenberg (1969) Koike and Watanabe (1973) Koike (1973, 1975) Parlant and Fiquet-Fayard (1976) Shimamori and Hatano (1977) Shimamori and Fessenden (1981) Christophorou (1972); Goans and Christophorou (1974); McCorkle et aL (1972) Toriumi and Hatano (1983) Toriumi and Hatano (1985)

Gas-phase collision dynamics

679

V'~ 2.5

5

°,"

02

,N

*,° •

~

/

1/11

o oo

4

2.0

o o o o

3

o

o

1.5

o o o o

o

B ~

8°

x

§

o o

/

¢

[CzH 4]

:~

i

i

i

2

3

g j/

(XlO 19 m o t e c u t e / c m 3) 0

isolated molecules. A recent study by Shimamori and Fessenden (1981) has verified clearly the presence of the vdW mechanism. They have measured the temperature dependence of three-body rate constants in pure 02, O 2 - N 2 , and O2-CO mixtures. The result for 02 is shown in Fig. 3. According to Herzenberg's theory (1969), the three-body rate constant, which corresponds to the experimentally obtained ku, can be expressed as: h 2 "~3/2

where h, rn and k have their usual meanings, kL the Langevin's rate constant, ~ the stabilization efficiency, T the absolute temperature, and E 0 the resonance energy. Equation (10) predicts a simple decrease in the rate constant with reduced temperature. The expected curve for 02 calculated from equation (10) assuming ¢ to be unity is drawn in Fig. 3. Since an extra contribution which increases with lowered temperature is evident, electron attachment to the vdW molecule (02)2 has been proposed to account for this. Similarly the importance of electron attachment to (02" N2) and (02' CO) has also been demonstrated. Since the temperature dependence of k5 is given by: 2

2rth2

V

¢f 11 //

0,5

i

1

ks=-~~Fst-~)

//1 X t 3 / 2

exp(-E,/kT);

(11)

where E, and F5 are, respectively, the energy and the width for the resonance attachment process (7), both pressure and temperature dependent experiments (Toriumi and Hatano, 1983, 1984, 1985) have given important rate parameters for the BB mechanism such as the rate constant for the initial electron attachment to O2(k~), the lifetime z of O2"; i.e. the

I

1.0

o

Fig. 2. Dependence o n C 2 H 4 density of the effective twobody rate constant of thermal electron attachment in Oz~22H4 mixtures at room temperature. The dashed curve represents the expected contribution from the BB mechanism (Kokaku et al., 1979).

2/

! °',

o// ol /

0

//

,~r" 100

/z

/

/

/ i 200

i 300

Temperoture (°K)

Fig. 3. The temperature dependence of the three-body rate constant of 02 (Shimamori and Fessenden, 1981). The broken line shows the temperature dependence of the rate constant calculated from Herzenberg's theory. The solid line shows a calculated curve which involves both the contributions from the broken line and the rate constant due to electron attachment to van der Waals molecule (05)2. resonance width, and the overall three body attachment rate constants for O2~C2H6, O2-C2H2 and O2-N 2 mixtures. The values of z are again in good agreement with those obtained by theories (see Table 2). Each three body rate constant is, respectively, smaller than that obtained previously without taking into consideration of the vdW mechanism. The value of k I obtained from O2-N 2 system (Toriumi and Hatano, 1985), which is selected as a convenient system to determine the value of k I , is about 3 x 10 -11 cm3/s. This value agrees within experimental error with those obtained from O : - C : H 6 and O2--C2H4 systems (Toriumi and Hatano, 1983, 1984) and with the value, 4.8 × 10 - u cma/s, which was obtained previously by Shimamori and Hatano (1977). This value is also consistent with qualitative results of k I obtained by other groups except for the value obtained by the extremely high pressure swarm technique (Goans and Christophorou, 1974). It should be noted here that the value, 3 x 10 11cm3/s, is in good agreement with the theoretical values (Koike, 1973, 1975; Koike and Watanabe, 1973; Parlant and Fiquet-Fayard, 1976), 2.5 x 10 - l l and 2.1 x 10 -11 cma/s. The important rate parameters for the vdW mechanism, such as the rate constant for the initial electron attachment to (O2"M) where M = C2H6, C2H4 and N2, and the lifetime z of (02" M)-*, i.e. the resonance width, have been also obtained from this experiment and summarized in Table 3 (Hatano, 1986). The value of k 5 in Table 3 are again much larger than the above-mentioned k~ values. The resonance energy for e- + (02" M)--+(O2- M)-* is much smaller than that for e- + O2~O~-*, while its

680

Y O S m H I K O HATANO Table 3. Rate constant k s, resonance energy E,, resonance width F S, electron density v,f~ and cross section a , ( H a t a n o , 1986; H a t a n o a n d Shimamori, 1981) (O2"M)

E,(meV)

Fs0teV )

v,f~

a , ( A 2)

ks(10 -H cm3/s)

20 30 45

800 450 270

0.71 0.89 0.92

2500 1700 1100

3000 1100 380

88(E0)

I0(F~)

0.47

570

3(kl)

(O2-N2) (O2-C2H6) (O2"C2H4) 02

width for the former process is much larger than that for the latter process. The large enhancement in the attachment rate constant from k~ to k 5 has been discussed qualitatively as related to the decrease in the resonance energy and the increase in the resonance width. The reason for the decrease in the resonance energy has been ascribed to the fact that the resonance state is much stabilized by the polarization interaction between O~- and M. Such situation is depicted in Fig. 4 where schematic potential energy curves are shown for O2-M and O ~ - M systems (Hatano, 1986; Hatano and Shimamori, 1981). Figure 4 shows that near to the equilibrium intermolecular distance, the effective resonance energy of O~--M system is much reduced and even superimposed on the O2-M curve. The existence of a number of vibrational states in both ion complex and neutral systems may be another major factor of the large transition probabilities. When the resonance width is narrower than the energy distribution of thermal electrons, the attachment rate constant is expressed as:

ks= ]vfa dv =vrfi :a dv;

(12)

where v is electron velocity, f is a Maxwell distribution function of electrons, a is attachment cross section, the suffix r means a value at resonance energy E,. The factor v,fr in this equation means the density of electrons with velocity v, to attach to vdW molecules. The value of vrf~ is given in Table 3, which shows that v,f, increases with decreasing resonance energy. The number of electrons which can attach to

0.5 0.4 0.3 ~j 0.2 Z 0.1 b,J ..j 0 _~ -o.1 ;~ -0.2 bJ -0.3 ~-0.4 0... -0.5

o2

~...'~

O~Iv'-4l-M (v .01- M

~.6

:~=~, \ ~

>.

D.4 )0.2 w

i

i [ i i 5 rO2-M

%

IV °'

i i i I1 ~._.~_ -0.2 V10 \ 1.4% \~_ -0.4 I~ r^ ^1.6 \ fit. u-u 1.8% \,

Fig. 4. A model of variation of potential energies for 02 (v = 0)-M and O~-(v'= 4)-M systems as a function of intermoiecular distance (Hatano, 1986; Hatano and Shimamori, 1981).

vdW molecules increases as compared with those to isolated 02. Since the cross section of a resonance process is expressed by the Breit-Wigner formula, the energyintegrated cross section is written as follows: f a dE = 4~z2 ~-k-~F 5 = ahFs;

(13)

where k is the wave number of incident electron, Er and F 5 are assumed to be independent of energy, and a h means the effective magnitude of electron attachment cross section, which equals to the geometrical cross section corresponding to the de Broglie wave length for the incident electron. The values of ah are also listed in Table 3. At extremely low energy electron collision such as electron attachment to vdW molecules, a "small" vdW molecule is supposed to collide with "large" electron clouds, of which cross section is determined by a size of the de Broglie wave length of incident electrons. With decreasing the resonance energy, therefore, the attachment cross section should increase. It should be noted that the maximum value of empirically obtained cross section values for dissociative attachment processes at low energy are resonably explained by the de Broglie wavelength of incident electron (Christophorou, 1980; Christophorou and Stockdale, 1968). The resonance width F 5 is expressed by the Wigner's threshold rule. In the case of isolated 02 the resonance state O~-*(X2//v v ' = 4) can couple with only one electronic partial wave with an angular momentum l = 2. In the case of vdW molecules intermolecular interaction may couple with additional partial waves such as p wave and s wave with low energy. If the orbital of O~- (llg) is distorted by a third-body molecule, new attachment channels can open with lower angular momentum of electrons and the resonance width may increase. It has been necessary to make a quantitative calculation of these effects using precise wave functions of O:-M system. Very recently, Huo et al. (1984) have made such calculations on O2-N2 system and compared their result with experiments. They have been successful in explaining the large enhancement in the attachment rate constant for vdW molecules using SCF wave functions corresponding to two geometries, T-shape and linear, for (02" N2)vdW molecules. The large enhancement in the attachment rate constant has been clearly elucidated quantitatively in this theoretical calculation by the effect of additional vibrational structures of the

Gas-phase collision dynamics

012 o21

039 ~0 /,3 23

05 37e

)

4

034

31

@11

19

• 18

ews L~,O o 7 So 015

---4~

i

03

I

I

AE = e(He') - mM

(eV)

Fig. 5. Correlation between the deexcitation probability, P. and the energy difference, AE, between the excitation energy of He(23S) and the first ionization potentials of M (Ueno et al., 1980). The numbers in the figure refer to atoms or molecules M as follows. (1) Ar; (2) Kr; (3) Xe; (4) [-[2; (5) D2; (6) N2; (7) 02; (8) NO; (9) CO; (10) N20; (I l) CO2; (12) SO2; (13) NH3; (14) SF6; (15) CH4; (16) C2H6; (17) C2H2; (18) C2H4; (19) C3Hs; (20) C3H6; (21) CH3C-= CH; (22) cyclo-C3H6; (23) H2C=C=CH2; (24) n-C4H]0; (25) iso-C4H]0; (26) C4H8-I; (27) iso-C4Hs; (28) trans-C4Ha-2; (29) cis-C4Hg-2; (30) H2C = C H - - C H = C H 2 ; (31) C2H5C -= CH; (32) nco6C5HI2; (33) cyclo-C6H12; (34) C6H6; (35) n-CTHz6; (36) CH3C1; (37) CH2C12; (38) CHC13; (39) CC14; (40) C2H5C1; (41) CC12F2; (42) CH3OH; (43) C2HsOH; (44) H20; (45) D20. vdW molecule on the attachment process, the symmetry breaking which allows the molecule to attach a p wave electron, and the lowering o f resonance energy due to a deeper O~--N2 potential in comparison with O2-N2 potential as shown schematically in Fig. 4. Very recently an interesting approach (Shimamori and Hotta, 1983, 1984) to this problem, the use of ]802 instead of 1602, has further substantiated the electron attachment to vdW molecules. F o r the BB mechanism, the isotope effect may be expected to appear as a change in the rates of initial attachment and autoionization channels, which are caused by a decrease of the resonance energy for 1sO2 in comparison with 1602 . As mentioned in the beginning of this section, electron swarm data were reported (Christophorou, 1972, 1976, 1978; Goans and Christophorou, 1974; McCorkle et al., 1972) in O2-C2H6, O2--C2H 4 and O2-N2 systems up to about 102]molecules/cm 3 (3 × 104 Torr) and simply elucidated only by the BB mechanism. An attempt (Kokaku et al., 1979; Toriumi and Hatano, 1983, 1984) has been made, therefore, to elucidate the high-pressure swarm data by the combination of the BB mechanism and the vdW mechanism. The electron swarm data are well explained up to about 4 x 102omolccules/cm 3 by the combination of both mechanisms. It is obvious that the contribution from the vdW molecule is dominant in these density ranges. The large deviations in the

681

data from the combination of the two mechanisms at the higher densities than 4 x 102omolecules/cm 3 may indicate the electron attachment to large vdW molecules such as O2(C2H6)2, or may require to introduce additionally some collective properties of these hydrocarbon molecules to explain the density effect of electron attachment in this region. An attempt (McMahon, 1981, 1982) has been made to explain theoretically such density effects in the whole density ranges using the statistical model. Electron attachment to 05 has been investigated in supercritical hydrocarbon fluids at densities up to about 1022molecules/era3 using the pulsed electric conductivity technique (Nishikawa and Holroyd, 1983) and the reuslts have been explained in terms of the effect of the change in the electron potential energy and the polarization energy of O~- in the medium fluids. In general electron attachment to 05 is considered to be a convenient probe to explore electron dynamics in the condensed phase. A similar conclusion has been obtained also in the case of N~O (Shimamori and Fessenden, 1978a,b, 1979a,b). It may be plausible to extract from the results of 02 and N 2 0 systems some general conditions under which one can predict the existence of electron attachment to vdW molecules (Hatano, 1986; Hatano and Shimamori, 1981). The common feature to both 02 and N 2 0 is that the rate constants of electron attachment to those isolated molecules are relatively small (10-1]-10-]3cm3/s) on an absolute scale. This is due to the presence of activation energy, i.e. the resonance energy, for electron attachment (0.08 eV for O5 and 0.23 eV for N20). In contrast there is virtually no activation energy in the electron attachment to vdW molecules containing 05 or N20, thus yielding much larger rate constants for this process. The formation of vdW complexes appears to act just like it has an effect of lowering the activation energy or the resonance energy. Consequently one may expect to observe the contribution of vdW molecules only for compounds which have activation energies for electron attachment, or for the molecules of which attachment cross section for electron energies near thermal increases with increasing electron energy. One may expect generally that even in the case of molecules with negative electron affinities or with high threshold electron energies for attachment some environmental effects or the effect of the vdW molecule formation bring about the large enhancement in the cross sections or the rate constants for the lower energy electron attachment to these molecules. Based on the above discussions the reasons for this expectation are summarized as follows (Hatano, 1986; Hatano and Shimamori, 1981): (1) The lowering of the resonance energy due to a deeper ion-neutral potential in comparison with neutral-neutral potential of the vdW molecule; (2) the additional vibrational structures of the vdW molecule;

682

YosmHmO HATANO

(3) the symmetry breaking due to the vdW interaction which allows the molecule to attach electron with additional partial waves; (4) the deformation of the molecular structure or the change of the vibrational modes due to the surrounding molecules; (5) the effective vibrational relaxation of the formed negative ion with excess energies due to the presence of a built-in third body molecule in the vdW molecule. The distinct features of the electron attachment to vdW molecules as summarized above may become a substantial clue to understand the fundamental nature of electron attachment not only in dense gases but also in the condensed phase (Hatano, 1986; Hatano and Shimamori, 1981). It is also apparent that most of the electron attachment in bulk system is no longer a simple process as consisted of the interaction of electron with isolated molecules. A definitely important role of pre-existing vdW molecules formed by weak intermolecular forces must be admitted. From this point of view, interesting phenomena in ionized gases such as the attachment cooling effect (Crompton et al., 1980; Koura, 1982, 1983; McMahon and Crompton, 1983; Skullerud, 1983) and the response-time of the air-filled fastresponse ionization chamber (Boag, 1984; Fessenden, 1985) should be analyzed by taking into account the important role of vdW molecules in the electron attachment mechanism. III. DE-EXCITATION OF EXCITED RARE GAS ATOMS

De-excitation processes of excited rare gas atoms have an important role in various phenomena in ionized gases. Penning ionization by long-lived metastable atoms has been studied experimentally using W-value methods, static afterglow methods, flowing afterglow methods, beam methods, and pulse radiolysis methods (Hatano, 1983; Yencha, 1984). Comparative discussions on the methods have concluded a superior advantage of the pulse radiolysis method (Hatano, 1983), which was first demonstrated by Ueno and Hatano (1976), over the other methods in determining absolute rate constant or cross section values for this process. The de-excitation rate constants of He(23S) and Ne(3P0, 3P1, and 3P2) by various atoms and molecules were obtained at room temperature using a pulse radiolysis method (Ueno and Hatano, 1976; Ueno et al., 1980; Yokayama and Hatano, 1981; Yokayama et al., 1980). An attempt has been made to correlate the rate constant values obtained with various molecular parameters such as ionization potentials and polarizabilities. A relatively good correlation has been obtained (Ueno et al., 1980) for He(23S), as shown in Fig. 5, between the deexcitation probability P(=kM/kc) and the excess energy AE[ = E(He*) - IPM], where kM, k o E(He*), and IP M are the experimentally obtained rate constant, the

calculated gas kinetic rate constant, the excitation energy of He(23S), and the ionization potential of the target atom or molecule M, respectively. However, the reason for the correlation has not been well understood. A similar experiment has been made (Yokayama and Hatano, 1981; Yokayama et al., 1980) also for the de-excitation of Ne(3p0, 3Pl, and 3p2) by atoms and molecules. Two new features of the obtained results have been demonstrated in this experiment. One is the J-dependent de-excitation cross sections, the other is a comparison between a theory of the de-excitation of optically allowed resonant state and the experimental result of Ne(3Pt) which is partly allowed because of a weak spin-orbit coupling. A pulse radiolysis is very advantageous to obtain not only absolute de-excitation rate constants or cross sections but also their collisional energy dependence. A velocity averaged absolute cross section, aM, is obtained as a function of mean collisional energy, E, from the temperature dependence of an absolute rate constant. Recently, the temperature dependence of the rate constants for the de-excitation of He(23S) by atoms and molecules has been measured (Koizumi et al., 1986) in the temperature range from 133 to 300 K. According to the theory of Penning ionization (Niehaus, 1975, 1981, 1982), the collisional energy dependence of its cross section is given, if the interaction potential V*(R) for He(23S)-M and the autoionization rate F ( R ) / h from He(23S)-M to H e - ( M + - e -) are obtained, by the following simple equation: trrocE ~/~-1/2 or

k(T)ocT~/~;

(14)

where tr r and k ( T ) are the total Penning ionization cross section and the corresponding rate constant, respectively, and F ( R ) and V*(R) are empirically represented as F(R) = A exp(-~R),

(15)

V*(R) = B e x p ( - fiR),

(16)

where A, B, ct, and fl are constants and R is an intermolecular distance. The slope of log-log plots of k ( T ) vs T gives the values of ct/fl (Fig. 6) (Koizumi et al., 1986). The obtained ct/fl value for each molecule M listed in Table 4 increases with decreasing the value of P, where P is a de-excitation probability per collision or 1/P is an effective collision number for energy transfer. Since/~ is not so relatively different for each M, Table 4 shows clearly that the bigger ct, i.e. the shorter range interaction between He(23S) and M, gives the smaller P, i.e. the less efficient energy transfer from He(23S) to M. This conclusion satisfies the exterior electron density model by Ohno et al. (1984). De-excitation of the resonance state of rare gas atoms has been studied less extensively than that of the metastable state because of experimental difficulties owing to the short lifetime of the resonance state. There have been reported, however,

Gas-phase collision dynamics

683 I

- 21

CO:>

o

I

I

100-

o

C2H4 ,

fi-22

•

O/

~

W-K

~..v/"-

NO

- 23

o

/

~ ~

g :~ 50-

8 0

"V 0 10

Ln T Fig. 6. Log-log plot of the de-excitation rate constants vs temperature (Koizumi et al., 1986). several theoretical formulations (Kohmoto and Watanabe, 1977; Watanabe and Katsuura, 1967) based on a long-range dipole~tipole interaction for the de-excitation cross section of radiative atoms. It is, therefore, necessary to compare the theory with the results of the resonance or the lowest radiative state atoms. It has been reported (Ukai, 1986a, 1988) recently that the collisional energy dependence of the de-excitation cross sections of He(21P), Ar(~PI), and Ar(3pl) by atoms and molecules by using a pulse radiolysis method which is very advantageous to obtain the absolute values of the de-excitation cross sections of the resonance atoms as well as the metastable states. The experimental technique is almost the same as that for the metastable states which is described in the preceding section. A comparison, as shown in Fig. 7, between the experimental results of the collisional energy dependence of the de-excitation cross section of He(2~P) by Ar and the theoretical ones calculated from the W - K theory (Watanabe and Katsuura, 1967) and the K - W theory (Kohmoto and Watanabe, 1977) makes clearly possible for the first time to compare in detail the experimental results with the theoretical ones (Ukai e t al., 1986a). Previous comparisons between experiments and theories have been made only for a value of the rate constant or the cross section, respectively, at a particular temperature of collisional energy, usually at room temperature. Table 4. The values of ct/fl and P (Koizurni et al., 1986)

N2 CO Ar Kr NO

O~ C2H 4 CO2

:
e

! .4 1.1 1.0 1.0 0.6 0.6 0.3 0.1

0.05 0.07 0.07 0.07 0.16 0.18 0.31 0.39

~ I 20 50 Cottisionat energy (rneV)

I 40

Fig. 7. Collisional energy dependence of the de-excitation cross section of He(21P) by Ar (Ukai et al., 1986a). (O) experiment; ( ) WK theory; ( - - - ) KW theory. The present experimental results can discriminate different theories and supports evidently the modified new theory, the K - W theory (Kohmoto and Watanabe, 1977), which means that the theory should take the bent trajectory into consideration. It is also the fact that very few studies have been reported on simple excitation transfer, in which Penning ionization is energetically impossible, from resonant rare gas atoms to atoms and molecules. The temperature dependence of the de-excitation rate constants of the resonance states of Ar, 1p~ and 3p~, by SF 6 and N2 has been measured in the temperature range from 133 to 300 K using a pulse radiolysis method (Ukai et al., 1988), thus obtaining the collisional energy dependence of the de-excitation cross sections. The results of the cross sections for SF6 are compared with the W - K theory and a good agreement is obtained. The results for N2 agree with predictions of the cross sections for a nonresonant case. Even in the case of the de-excitation of the resonance state, such as Ar(Ip~ ) or Ar(3pt), the cross section value and its collisional energy dependence are very similar to those for the metastable state, i.e. Ar(3p0) or Ar(3P2). This result satisfies again the W - K theory because of the fact that N2 has almost no optical absorption in the energy region corresponding to the excitation energy of Ar(Ipl) and Ar(3p~). It is concluded, therefore, that a long-range dipole-dipole interaction is important in the deexcitation processes of Ar(Ipt) and Ar(3p=) by SF6, but that a short-range interaction with curve crossing dominates in the de-excitation of Ar(~Pl ) and Ar(3Pi ) by N 2. author wishes to thank Drs K. Shinsaka, S. Takao, H. Shimamori, T. Wada, K. Ito, T. Ueno, A. Yokoyama, H. Namba, N. Kouchi, Y. Nakamura, Y. Kokaku, M. Toriumi, H. Koizumi, M.

Acknowledgements--The

684

YOSI-III-.IIKOHATANO

Ukai and E. Suzuki for their excellent collaboration. He also wishes to thank Dr W. P. Helman for giving him the results of searching the data base for recent pulse-radiolysis papers in the Radiation Chemistry Data Center, Radiation Laboratory, University of Notre Dame.

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