J . Phys. Chem. 1989, 93, 8187-8193
8187
Ion Recombination Rates in Rare Gas Cation-Halide Anion Systems: XeF* Stephen P. Mezyk,*Vt Ronald Cooper, and John Sherwellf Department of Physical Chemistry, University of Melbourne, Parkville. Victoria 3052, Australia (Received: February 21, 1989: In Final Form: June 5, 1989)
The techniques of pulse radiolysis and emission spectroscopy have been used to experimentally determine ionic recombination coefficientsover a large pressure range in xenon/SF6 gas mixtures. Prior to the onset of diffusion-controlledrates, a maximum rate constant of 2.5 X 1015M-l s-l was observed for the recombination of Xe dimer cations and SF6 anions. The values have been compared with current theoretical models: the Bates termolecular recombination theory at low/medium gas pressures, and the Langevin-Harper diffusion-controlled ionic recombination theory at high gas pressures. Excellent agreement was obtained between theory and experiment at high gas pressures, but the experimentalvalues were constantly higher than predicted by the Bates termolecular theory at lower gas pressures. The discrepancy is attributed to two-body enhanced neutralization reactions significantly assisting ionic recombination.
Introduction Gaseous ion-ion recombination has been the subject of theoretical interest for many and has culminated in the general termolecular theory of Bates3 in the low and medium gas pressure ranges, and the diffusion-controlled Langevin-Harper the0ry~9~ at high gas pressures. However, there is little experimental data available for the testing and verification of these theories, especially for the three-body effect of the Bates model. To date this effect has only been investigated in two studies, for recombining SF5,6+(SF6),/SF6-(SF6),6 and' NH4+(NH3),/C1-(NH,),7 ions. The bulk pressure dependences of these ionic recombination rate constants have been shown to agree with the Bates model;3 however, because the size of the recombining ions was not unique or accurately known ( n and m were believed to be in the range 1-6, with the distribution of ionic species present also being estimated), the validation of this model was indeterminate. The pulse radiolysis work on rare gas-halogen source gas mixtures has shown that there are two processes leading to rare gas-halogen atom exciplex f ~ r m a t i o n : ~ - direct '~ reaction of electronically excited rare gas atoms with the halide source molecule and ionic recombination. From these investigations, it has been determined that the pulsed electron irradiation of a rare gas, R, produces three types of entity; a range of electronically excited states, R*, positive ions, R+, and free energetic secondary electrons, e-(s). By the addition of a trace amount of a halidecontaining gas, AX, whose concentration is small enough that direct excitation by the electron beam is negligible, exciplex (RX*) formation has been found to occur by the following mechanism: R
---
+ + +
e-(s)
R*, R+, e-(s)
+M
e-(th)
e-(th) AX R*
AX RX* A
+ +
-
(1)
hot electron thermalization (M = R or AX) ( 2 )
AX-/X-
thermal electron capture
(3)
direct reaction of rare gas excited states (4)
+
R+ 2R R2+ R R2+ AX-/X- (+ M) RX* products
-
initiation
+ + +
-
cation dimerization
(5)
three-body ionic recombination (6)
RX* R X hv excimer fluorescence (7) Under suitable experimental conditions, temporal separation of the two formation processes has been achieved.14 As the recombining ionic species are well characterized, the measurement *Author to whom correspondence should be addressed. 'Present address: Radiation Laboratory, University of Notre Dame, Notre Dame, IN 46556. *Present address: Radian Corporation, P.O. Box 201088, Austin, TX 78721.
of the pressure dependence of the recombination rate constants, a,for reaction 6 is a valid test of the Bates model. The gas system chosen for this study was Xe/SF6. The XeF* exciplex produced in this gas mixture was formed solely by ionic recombination; there was no detectable emission from the reaction of xenon electronically excited states with SF6, reaction 4, in agreement with a previous determinati~n.'~The absence of this reaction greatly simplified the data analysis. The emission from the 2Z+1,2 2Z+l transition in the XeF* molecule was found to extend from 326 to 360 nm with a peak at 351 nm. Broad structured peaks were observed at the lower wavelengths, in good agreement with the vibrational fine structure results of Brau and Ewing.I6 All measurements done for this system were at the peak wavelength unless otherwise specified.
-
Experimental Section The established pulse radiolysis facilities in the Department of Physical Chemistry at the University of Melbourne were used in this study. A schematic of the experimental setup, which has previously been described in detail,15 can be seen in Figure 1. The irradiation device used for all this work was a Field Emission Corp. Febetron 706 electron pulser. This machine emits a 3-ns (fwhm) beam of 0.24.6-MeV electrons with a peak current of 7000 A. This device was used with either type 5510 or 5515 electron beam tubes, the type 5510 tube having only one half the output dose of the 5515 tube.!' (1) See: Bates, D. R. In Case Studies in Atomic Physics; McDaniel, E. W., McDowell, M. R. C., Eds.; North Holland: Amsterdam, 1974; Vol. 4, p 57 and references therein. (2) See: Bates, D. R. In Advances in Atomic and Molecular Physics; Bates, D. R., Bederson, B., Eds.; Academic Press: New York, 1985; Vol. 20, p 1 and references therein. (3) Bates, D. R.; Mendas, I. Chem. Phys. Left. 1982, 88, 528. (4) Langevin, P. Ann. Chim. Phys. 1903, 28, 433. (5) Harper, W. R. Proc. Cambridge Philos. SOC.1932, 28, 219. (6) Schmidt, W. F.; Jungblut, H.; Hansen, D.; Tagashira, H. Proceedings of the 6th International Conference of Gas Discharges and their Applications, Heriot-Watt University, New York, 1980; pp 12-15. (7) Sennhauser, E. S.; Armstrong, D. A. J . Phys. Chem. 1980,84, 123. (8) Cooper, R.; Grieser, F.; Sauer, M. C., Jr. J. Phys. Chem. 1977, 81, 1889. (9) Maeda, M.; Nishirarumizu, T.;Miyazoe, Y. Jpn. J . Appl. Phys. 1979, 18, 439. (10) Grieser, F.; Shimamori, H. J. Phys. Chem. 1980, 84, 247. (11) Cooper, R.; Mulac, W. Chem. Phys. Lett. 1983, 99, 217. (12) Cooper, R.; Grieser, F.; Sauer, M. C., Jr. J . Phys. Chem. 1976, 80, 2138. (13) Cooper, R.; Denison, L. S.; Zeglinski, P.; Roy, C. R.; Gillis, H. J . Appl. Phys. 1983, 54, 3053. (14) Cooper, R.; Mezyk, S. P.; Armstrong, D. A. Radial. Phys. Chem. 1984, 24, 545. (15) Young, J. Ph.D. Thesis, University of Melbourne, 1987. (16) Brau, C. A.; Ewing, J. J. J . Chem. Phys. 1975, 63, 4640.
0022-3654/89/2093-8187.$01.50/00 1989 American Chemical Society
8188 The Journal of Physical Chemistry, Vol. 93, No. 25, 1989
Mezyk et ai. 200
100
..*-.*.
-
(a)
'.It
0.
... ........... ......... ( b ) 0.
01.
1500
-
1000
-
I
I
I
I
Ionic r,ecombination., emission
\
..e.*
..e' .e'
U
U
500-
Figure 1. Schematic of the experimental setup used for emission ionic recombination rate constant determinations,and ozone absorption measurements. Key: (A) Febetron 706; (B) irradiation cell; ( C ) lead wall; (D) faraday cage; (E) lens; (F) beam splitter; ( G ) monochromators; (H) photomultiplier tubes; (I) storage oscilloscopes; (J) digital voltmeter; (K) sample and hold; (L) digitization camera; (M) computer. a)
II
.*
*......11:/ I
0.00 0
200
400
600
000
TiME (ns)
cross- section
1
Figure 3. (a) Typical kinetic emission curve for 500 Torr of xenon and 0.50 Torr of SF6 at 351 nm. (b) Integrated kinetic emission curve. (c) Transformed kinetic emission curve with straight-lineanalysis beginning at time t .
J
Light emissions from the cell were monitored perpendicular to the electron beam and were focused by two lenses onto a 27.0 mm diameter half silvered beam splitter. The split beams then entered two identical Spex Minimate grating monochromators set at a band-bass of 2 nm. Accurate line up of the entire optical system was achieved by using a 0.5-mW He/Ne laser. The selected wavelengths were monitored by EM1 9783B ( H l ) and Hamamatsu R666UH (H2) photomultiplier tubes utilizing all dynodes. The resulting signals were displayed on two calibrated Tektronix 7633 storage oscilloscopes. The beam of light continuing straight through the beam splitter was used to generate a conventional kinetic trace (Figure 3a), which was recorded with 50 R termination, (11, system rise time about 5-7 ns). The other beam of light, reflected at right angles, was used to produce an integrated emission signal (12). This was achieved by terminating the photomultiplier tube output into 1 MR and 20 pF at the oscilloscope. This gave traces as shown in Figure 3b, these being the integrated form of the kinetic trace. A conventional sample and hold circuit, which sampled for 8 p s and displayed the held value on a digital voltmeter (G.E. Model GDM-8045), was placed in parallel with I2 and measured the total amount of light emitted at that wavelength. The internal resistance of this circuit was -500 MR and had no effect on the I2 trace. All oscilloscope traces were digitized and stored via a TV camera (Sony, Model 3250CE), interfaced to a Heathkit LSIl 1 computer. The resulting data was stored on a dual floppy disk system and later analyzed. The gases in this study, xenon (Matheson Research Grade (99.995%)) and SF, (Matheson Pure Grade (99.9%)), were used as received but further degassed by several freeze (77 K)pump-thaw cycles prior to usage. All gas manipulations were done in a conventional mercury-free metal/glass vacuum line. Gas cylinders and the irradiation cells were connected to the vacuum line via stainless steel or brass Cajon Ultra-torr fittings. Purified gas samples were contained in storage bulbs attached to the line itself. The filling of cells for gas mixtures containing rare gas at pressures less than 1200 Torr was done by expansion of the purified gases from their respective storage bulbs. All pressures were measured on a MKS Baratron pressure gauge, type 170M-6B. For rare gas pressures greater than 1200 Torr,
cavity
Figure 2. (a) Schematic of the irradiation emission cell used for rate constant measurement. (b) Dosimetry cell, constructed by adding external mirrors to a standard irradiation cell.
The irradiation cell design was as shown in Figure 2a and was constructed from brass or stainless steel. The incident electron pulse entered the irradiation cell through a 2.5 X mm thick stainless steel window, glued (Torr-Seal) or O-ring sealed to the front of the cell. The irradiation cavity within the cell was of height 42.0 mm, width 14.0 mm, and depth 55.0 mm, the total volume being 32.3 cm3. The electron window was the same size as the front cross section of the irradiation cavity. The dimensions of the irradiation cavity were such that its cross section area was less than the total area of the incident electron beam. This ensured that uniform irradiation of the gas mixture was achieved, Le., no dead space effects. The body of the cell was fitted with two O-ring sealed Suprasil windows, 2.0 mm thick and 29.0 mm diameter, centered 43.9 mm from the electron window, which allowed emitted light to be observed at right angles to the incident electron pulse. The cell was bolted directly to the front of the Febetron. (17) Field Emission Corporation Model 706 System Instruction Manual, 1969; p 1.
Ion Recombination Rates in XeF* a brass cell was modified by having a copper cold finger attached to the tap stem of the normal cell. The halide source and rare gas pressures were measured in the vacuum line and then frozen into the side arm by using liquid nitrogen. The frozen side arm was then heated and left for 1 h to achieve "thermal" equilibrium and to allow diffusion of the halide source gas throughout the rare gas. Leaving the gas mixture for longer periods (up to 3 h) had no observable effect on the obtained emission. The final gas pressure in the cell was calculated from the known ratio of volumes of the cell and the vacuum line. Experiments were conducted to see whether repetitive pulsing of the gas sample caused significant degradation. It was found in all gas mixtures that although the total amount of light being emitted at any wavelength remained the same for up to 20 pulses, the kinetics of emission changed significantly (>lo%) from the first pulse. Hence all kinetic data were recorded from the first pulse. Unless otherwise stated, all measurements for this system were done using a constant SF6 gas pressure of 0.50 Torr. All irradiations were done at room temperature.
Ozone Dosimetry The dose delivered from the Febetron tube was measured by using conventional ozone dosimetry.18 The brass irradiation cell used for emission measurements had external mirrors added, to give a four-pass absorption cell (see Figure 2b). The internal dimensions of the cell were unchanged; thus the dosimetry was performed under conditions identical with the experimental emission measurements. The gas mixture used for dose measurement was a l % SF6/02gas mixture at 800 Torr of 02,for which the G value is 6.2 molecules/100 eV.I8 This measurement was done regularly to monitor any slight variations in the electron beam tube output. The ozone concentration produced by a single pulse into 800 Torr of Oz/8 Torr of SF6 was determined from the measured absorbance change, the known extinction coefficient ( 6 = 3.18 X IO3 M-I cm-' at h = 256 nm19), and the path length in the irradiation cell (6.43 cm). From this and the G value for ozone formation, the output dose of the Febetron tube could be calculated. This value was then divided by 800 to give the dose per Torr of oxygen (the contribution of SF6 was negligible). The amount of energy deposited in Xe/SF6 gas systems was then calculated by converting the pressures of these gases into the equivalent pressure of oxygen by using molar stopping powemzo This equivalent oxygen pressure, when multiplied by the dose per Torr of oxygen, gave the dose delivered to the Xe/SF6 gas mixture. In these experiments, the gas mixtures consisted of small amounts of s F 6 and a vast exof xenon. To calculate the initial ion concentration produced, a W (average energy needed to produce an ion pair) value for xenon of 21.9 eV/ion pairZowas used. The absorbed dose was varied to suit the time resolution of the detection system. This was done by the insertion of perforated brass disks into a provided space between the cell and the mounting plate on the front of the Febetron and by lowering the charging voltage which governed the overall number and energy of the electrons. The dose per pulse was found to be reproducible to better than f10% throughout these experiments. Typically the initial ion concentration was -10-9-10-8 M (-5-50 X 10" cm-').
The Journal of Physical Chemistry, Vol. 93, No. 25, 1989 8189 Assuming that the XeF* concentration is at steady state it has been shown thatI4
where I is the photon intensity at time t observed by the detection system and K is a proportionality constant for the light-detecting efficiency of the experimental setup. Thus a plot of I/I1l2vs t should be a straight line of slope
m = a1/2/K1/2
(11)
The photon intensity at any time, t , is given by
If = Ka[Xe2+],[SF,], and from charge balance [Xe2+]t = ISF6-1, = n, i.e.
Substituting for K'l2 in eq I1 gives
Data Analysis For ionic recombination as the only XeF* formation process, the reactions are formation of exciplex: a Xe,+ + SF6- (+ M) XeF* + other products decay of exciplex: XeF* Xe + F + hv k2
So, to obtain a, the gradient of the transformed kinetic plot, m, must be multiplied by the square root of the kinetic emission intensity at any time t , I f , and divided by the ion concentration, n,, at this time. Figure 3a shows the kinetic emission curve from 500 Torr of xenon and 0.50 Torr of SF6 a t 351 nm. This curve consists of several parts: (a) X-rays, (b) dimer rare gas fluorescence, and (c) ionic recombination formed exciplex fluorescence. The X-ray signal followed the time profile of the electron pulse ( - 5 ns), and was typically only a few percent of the signal. The first peak of this emission was also observed in irradiated xenon, at all wavelengths across and outside the XeF* emission spectrum, and was thus assigned to the broad dimer xenon, Xe2*, (1.3Eu+ ]Eg+) fluorescence. Its decay was typically complete within 200 ns, but its intensity varied greatly with xenon pressure. At low pressures (e100 Torr), its intensity was low, lo00 Torr) it accounted for more than 60%. This background fluorescence determined the upper pressure limit of the measurements done in this study; when the fluorescence due to the background rare gas dimer was greater than 90% of the total, its subtraction from the integrated curve (see later) gave large errors and very poor reproducibility. The upper limit for subtraction corresponded to a xenon pressure of approximately 1500 Torr. The second peak was emission due to ion-ion recombination reactions. The transformed curve of Figure 3a, according to eq 11, is seen in Figure 3c. As expected, the initial part of the transformed curve is not straight, and thus its analysis, by linear least-squares fitting, was done only on the limiting linear portion, and the time, t , at which the analysis began, noted. The ion concentration at this time was obtained from the integrated intensity from the I2 measurement at this time (Figure 3b), since ionic recombination is the only reaction occurring from time t onwards. The fraction, J of fluorescence left at time t corresponds to the fraction of ions that have not yet recombined. This fraction can be calculated by total intensity - intensity at t f=( total intensity
(18) Willis, C.; Boyd, A. W.; Young, M. J.; Armstrong, D. A. Can. J . Chem. 1970.48, 1505. (19) DeMore, W.B.; Raper, 0.J. Phys. Chem. 1964,68, 412. (20)Prosser, R. Ph.D. Thesis, University of Melbourne, 1973.
where the total intensity is the value from the sample and hold circuit. Knowingf and the initial ion concentration (from dosimetry and stopping powers) gives the ion concentration at this time.
--
-
1
8190 The Journal of Physical Chemistry, Vol. 93, No. 25, 1989
Mezyk et al.
This formula is only correct when the entire integrated signal is due to ionic recombination fluorescence. To subtract the X-ray and background xenon dimer fluorescence in this measurement, the gas mixture was irradiated a second time, with I1 measuring the total integrated emission at a wavelength outside the XeF* emission spectrum (362 nm). The I2 measurement was identical with that of the first irradiation, and the total integrated signal (sample and hold value) again recorded. Correlation of the signals between the two oscilloscopes was achieved by separately irradiating and calibrating the two detection systems to give a constant ratio of the combined integrated signal of the X-ray and xenon dimer emission for the two wavelengths used, Le., 362 and 351 nm. Using the total integrated signals as a normalization for any pulse to pulse variation, the second pulse I1 integrated value gave a background correction for the first pulse I2 integrated value.
Results and Discussion To measure the ionic recombination rate constants it was essential to ensure that reaction 6 was the rate-limiting step in the reaction mechanism. To optimize for this reaction, and to eliminate or diminish other competing reactions, the following experimental conditions were used. The hot electrons, e-(s), were thermalized by both xenon and SF6. Under typical conditions of this study, thermalization was complete within the duration of the electron beam pulse (-5 ns). The thermal electrons, e-(th),were then rapidly captured by SF6 ( k = (1.37 f 0.04) X I O l 4 M-' s-' 21) to form the molecular anion SF(, which was stable over the time domain of these experiments22 (0.5-2.0 ps). Fast ionic dimerization of the rare gas cation, Rt, was ensured by using high bulk rare gas pressures. The removal of the dimer and/or the monomer cation by charge transfer to SF6 was impossible, as the ionization potential of SF6 (15.4 eVZ3)is higher than that of xenon (12.15 eV24). The fluorescence lifetime of XeF* is short (- 15 ns25)and thus the ionic recombination reaction controls the observed rate of decay of emission when the initial ion concentrations are very low. Under these conditions, the recombination coefficients were obtained as a function of xenon pressure, over the range 18-1600 Torr, and are shown in Figure 4a. These values are seen to continuously increase with increasing xenon pressure, to a maximum value of -2.5 X 1015 M-l s-l at -500 Torr, and then to decrease with higher xenon pressures. These values exhibit the characteristic recombination coefficient pressure profile seen in the two previous studies of ionic recombination in this pressure ranges6,' In these investigations, the ionic recombination mechanism at low pressures was believed to be two body; i.e. Xe2+ + SF6-
-
XeF*
-
A
I
30
30
c
'.I
aLH %ATES DcEXP.
I
I
I
100
300
1000
Pressure X e (torr)
I 3000
b)
0
z
3-
I
I
I
I
I
30
100
300
1000
3000
Pressure X c (torr)
Figure 4. Xenon pressure dependence of the experimental XeF* ionic recombination rate constants (aExp), in comparison with the calculated and Langevin-Harper (aLH) values for the Bates termolecular (aBATES)
-
+
following reactions: (a) Xezt SFC + Xe XeF* products.
+ F + Xe
+
-
XeF*
+ products; (b) Xezt
Theoretical Comparison Bates and co-workers2 derived the general termolecular theory by using computer simulation techniques to determine the recombination coefficient pressure profile for the reaction 04+ + 04-+ o22 [O,J
+ o2
Having calculated the pressure dependence for this reaction, they showed that scaling parameters, X and 7,could be obtained so that rate constants for any ionic recombination reaction, X, could be obtained from the standard parameters, S, by Xcyx = ffs VNX = Ns
The scaling parameters are given by
+ other products
and the increase in rate constant at medium pressures was attributed to the increasing contribution of the three-body recombination mechanism; i.e. Xe2+ + SF6- + M
.
XeF*
+ other products
and X = X'(1
+ (01/2)/6)
where
The subsequent decrease in cy at higher gas pressures is believed due to the ionic recombination reaction becoming diffusion controlled. and (21) Crompton, R. W.; Haddad, G. N. Ausr. J . Phys. 1983, 36, 15. (22) Crompton, R. N.; Christophorou, L. G.; Huebner, R. H. Phys. Leff. 1966, 2 3 , 6 5 6 .
(23) No exact value could be found in the literature. Value taken as an average of the following appearance potentials for SFS+. 15.50 eV: Hildebrand, D. L. J. Phys. Chem. 1973,77,897. 15.29 eV: Dibelar, V.H.; Walker, J. A. J. Chem. Phys. 1966,44,4405. 15.35 eV: Frost, D. C.; McDowell, C. A.; Sandhu, J. S.; Vroom, D. A. Adv. Mass Spectrom. 1968, 4, 781. (24) Moore, C. E. Analyses of Oprical Spectru; Office of Standard Reference Data, National Bureau of Standards: Washington D C NSRDS-NBS 34. (25) Eden, J. G.; Searles, S. K. Appl. Phys. L e f f .1977, 30, 287
As = 2.54
X
IOd cm3 s-*
Bs = 4.73 cm2 V-I
Bx = K ,
s-I
+ K2 = 13.82P1/2(M,3-1/2+ M23-1/2)
with M , the mass of the positive ion, M2 the mass of the negative
The Journal of Physical Chemistry, Vol. 93, No. 25. 1989 8191
Ion Recombination Rates in XeF* ion, M 3 the mass of the neutral third body, P the polarizability of the bulk medium, MI3 the positive ion-third-body reduced mass, M23 the negative ion-third-body reduced mass, Ki the diffusion coefficient for ion i, and ai =
(MI + M2 - Mi) Mi(M1 + M2
+ M3)
The values for ai and F(a,) have been calculated for the symmetrical resonance charge transfer, hard-sphere ~ o r e , ~ , ,and ~’ polarization3 interaction over a very wide range of ai. The latter is believed to be the best interaction potential and is the one used in the calculations of this study. The Bates parameters were thus calculated for the reaction Xe2+ + SF,-
+ Xe -, XeF* + products
aLH =
The positive ion was taken as the dimer, because at most of the gas pressures used in this study (200 Torr or greater), the 66 ns at 200 Torr2*) is much half-life for dimerization (71/2 shorter than the initial half-life for ion recombination (7112 138 ns at 200 Torr). Cation dimerization at lower xenon pressures was ensured by observing the recombination on microsecond time scales. With the following parameters
-
-
mass of positive ion (Xe2+)
262.6 amu
mass of negative ion (SF,-)
146.1 amu
mass of neutral atom
131.3 amu
(Xe)
this gave = 0.1351
F(a1) = 0.3302
a2 = 0.4370
F(a2) = 0.5867
UI
MI3 = 87.533
P = 4.04
M23
= 69.153
T = 293 K
and Ax = 2.484 X 10” cm3 s-I Bx = 1.562 cm2 V-I s-I The termolecular calculations with the monomer cation, Xe+, showed no significant difference ( 1). As xenon and SF, have similar polarizabilities (4.04 A329 and 4.349 A334), one therefore expects a higher value for SF,- in xenon than the above Langevin limit. A value of 0.90 cm2 V-’ s-l was used in these calculations. This gave A, = 2.484 X 10” cm3 S-I and B, = 1.50 cm2 V-’ s-l. The final scaling parameters were X = 1.96 and 7) = 1.76. The theoretical curve, aBATES, generated by these values is shown in Figure 4a, in comparison with the experimental data. At very high bulk gas pressures, the ionic recombination reaction becomes diffusion controlled. The theory of this mechanism was developed by Langevin4and Harper5 who obtained the relationship
= 13.82/(P~)~/~
where p is mobility of the ion, P the polarizability of the bulk gas, and u the reduced ion-bulk gas mass, which gives a value of 0.78 (26) Flannery, M. R. J . Phys. E 1981, 14, 915. (27) Flannery, M. R. J . Phys. E 1980, 13, 3649. cm6 s-I: (28) Taken as an average of the following values: 1.8 X Bhattacharya, A. K. Appl. Phys. Lett. 1970, 17, 521. 3.57 X lo-” cm6 s-I: Smith, D.; Dean, A. G.; Plumb, I. C. J . Phys. B 1972, 5, 2134. 2.0 X lo-” cm6 s-I: Vitols, A. P.; Oskam, H. J. Phys. Rev. 1973, A8, 1860. (29) Miller, T. M.; Bederson, B. Adu. At. Mol. Phys. 1977, 13, 1 . (30) Helm, H. Phys. Rev. A 1976, 14, 680. (31) Ellis, H. W.; McDaniel, E. W.; Albrilton, D. L.; Viehland, L. A.; Lin, S. L.; Mason, E. A. At. Data Nucl. Data Tables 1978, 22, 179. (32) Bates, D. R.;Mendas, I. Chem. Phys. Lerr. 1982,88, 528.
+ p-)
4~e(p+
where p+ and p- are the positive and negative ion mobilities, respectively. By substituting the average ionic mobilities for the two ions in this expression, we obtain the diffusion-controlled limiting rate constant (aLH),again shown in Figure 4a. From this point it can be seen that the experimental data are always greater in magnitude than the calculated termolecular values, with the discrepancy being far worse at low pressures. The maximum in the experimental pressure profile is also observed at a much lower pressure than predicted by the calculations. However, the agreement with the Langevin-Harper limit at high pressures is excellent, with the experimental data appearing to converge to the calculated limit. This implies a unit efficiency of recombination between the ions, i.e., that the two ions always recombine once collisions with the bulk gas have reduced the energy of the ionic system below zero and thus formed a bound state. Unfortunately, due to experimental difficulties, no values of a at higher xenon pressures could be obtained in order to confirm this apparent convergence. The disparity between the theoretical termolecular calculations and the experimental values was so great that another calculation was performed, this time assuming F was the recombining anion. The production of this, and other anions, has been shown to result from the multiple fragmentation of S F C , ~although ~ on a much longer time scale than used in these experiments. The reaction Xe2+ + F + Xe -,XeF*
+ 2Xe
gave the values Ax = 2.828 X 10” cm3 s-I and Bx = 2.423 cm2
v-1 s-I
The mobility values of p+ = 0.60 cm2 V-I s-l (averaged), and 1.66 cm2 V-I s-I (experimentally determined32)were substituted for the Bx value. This gave X = 1.58 and 7 = 1.53. The theoretical curves generated from these values are shown with the experimental data in Figure 4b. The agreement is slightly better in the absolute magnitude of the termolecular curve with the experimental data. However, the Xe2+/F peak value is at a higher pressure than the Xe2+/SF6-value and the theoretical Langevin-Harper limit no longer matches the experimental high-pressure limit. This indicates that SF,-, not F , is the recombining anion. To try and account for the discrepancy between the experimental data and the predictions of this termolecular theory, the two following modifications were made for the Xe2+/SF{ system. (1) For two recombining ions of differing complexity, a correction may have to be made due to one of the ions taking part in symmetrical resonance charge transfer. It is possible that in the Xe2+/SF, recombination system, a symmetrical ion transfer occurs according to the reaction
p- =
Xe-Xe+
+ Xe
-,
Xe
+ Xe+-Xe
In principle, this can be treated by the same method as that used (33) Jowko, A.; Armstrong, D. A. Radial. Phys. Chem. 1982, 19, 449. (34) Hausler, H.; Kerl, K. Int. J . Thermophys. 1988, 9, 117. ( 3 5 ) Buchel’nikova, I. S. Souiet Phys.-JETP 1959, 8, 783.
8192 The Journal of Physical Chemistry, Vol. 93, No. 25, 1989
20
1
-
aEXP
30
100
1000
300
3000
Figure 5. Comparison of the XeF* experimental data with the calculated Bates termolecular and Langevin-Harper values for the reaction Xe2+ + SFC + Xe XeF* + products, with the positive ion polarizability of the bulk gas (Xe) being 1 X (aBATES ( I ) ) , 4 X (aBATES (2)), and 9 X (aBATES (3)) the polarizability of the negative ion.
-
by Bates and Mendas3 for symmetrical resonance, charge-transfer collisions, where the polarizability is modified for just one of the ion-neutral collisions. This modification was done by a multiplying factor, a, which was shown to be limited to the range 1 5 a 5 9. Figure 5 shows the predicted termolecular recombination values in comparison to the Xe2+/SF6-experimental data, with the effective polarizability of the bulk gas for the positive ion being various higher multiples than that due to the negative ion. The qualitative agreement is better as the Xe2+ polarizability effect is increased; the maximum is predicted at a lower gas pressure, and the absolute magnitudes of the theoretical values are higher than for the standard curve. However, even at the extreme of the xenon effective polarizability due to the cation, P(Xe2+),being 9 times that of the anion, P(SF6-), there is no quantitative agreement between theory and experiment. No account was taken of the possible anion symmetrical resonance charge-transfer reaction SF6-
+ SF,5
-
SF,
+ SF6-
because of the small relative pressure of this gas. (2) At high ion concentrations, the recombination coefficient may have a significant contribution from the reaction Xe2+
SF6- 4- Xe2+ (or SF6-)
-
XeF* 4- products
Le., where the third body is an ion. Bates36developed the formula 6a = 3 x
300
4s
(+)
cm3 s-1
where 6a is the increase in the recombination rate coefficient, T is the temperature (K), and n is the ion concentration (ions/cm3), to account for this contribution. For the Xe/SF6 system the maximum ion concentration used M. This gives an increase in a of 6a 1 X 1013 was -8 X M-l s-l. This is at worst a 2% correction, far less than the experimental scatter, and hence negligible. Two-Body Ionic Recombination. Ionic recombination also occurs in the absence of a bulk gas, by two-body neutralization processes with rate constant azo.This value can be estimated by extrapolating the experimental rate constants to zero xenon pressure. Figure 6b shows the plot obtained for XeF*, giving this lower limit value of azo= 4.1 X I O I 3 M-' s-I. Cor'iputer simulation experiments3742 have indicated that, for
-
( 3 6 ) Bates, D. (37) Bates, D. (38) Bates, D. 287. (39) Bates, D. (40) Bates, D. (41) Bates, D.
c
8t# ip 0'
Pressure Xe (torr)
R. J . Phys. E 1982, 15, L755. R. Chem. Phys. Left. 1983, 95, 1. R.; Mendas, I. h o c . R. SOC.London Ser. A 1978, A359, R. Proc. R. SOC.London Ser. A 1980, A369, 327. R. J . Phys. E 1980, 13, 205. R. J . Phys. E 1981, 14, 4207.
Mezyk et al.
I
I
I
I
400
800
1200
1000
Pressure X e (torr)
Figure 6. (a) The experimental XeF* recombination rate constants plotted as the Bates calculation^^^ for enhanced oxygen mutual neutralization. (b) Calculation of a;, the two-body, zero buffer gas pressure, mutual neutralization rate constant.
mutual neutralization, two-body recombination can assist the total removal of ions up to quite high gas pressures. Mutual neutralization is a charge exchange reaction of the form A+
+ B- LE.A + B
and may be regarded as occurring through an avoided crossing between the ionic and covalent potential surfaces2 The presence of an bulk gas enhances this process by collisionally converting free ion pairs to bound ion pairs, which allows the avoided crossing to be traversed many more times. The amount by which mutual neutralization increases the rate of loss of ions is given by2 ACY= CY^ - ( ~ 3 ' where Aa is the enhancement of the rate of loss, ax is the rate coefficient for total ion loss, and a 3 0 is the rate coefficient for termolecular recombination in the absence of a mutual neutralization channel. The parameter Aa has been calculated by Bate@ using a hard-sphere core potential for ion-neutral interaction, for the reaction
+
+
04+ 04- O2
-
products
Bates' calculations at 300 K show that Aa has a maximum which is much narrower and occurs at much lower gas pressures than the maximum in the corresponding termolecular rate coefficient. For several different fractional components of enhancement, it occurs near 300 Torr in the oxygen system, when a linear plot of Aa vs pressure is made. Figure 6a shows the experimental XeF* results plotted in a similar fashion. The shape of the obtained curve and the position of the maximum agree with the enhanced mutual neutralization values of Bates' calculations3* far better than the termolecular plot (Figure 4a). The enhanced mutual neutralization process in this system would correspond to a charge neutralization process involving an F- ion transfer to the dimer rare gas cation, to produce the rare gas-halide exciplex, i.e. Xe,+--F-SF,
-
XeF*
+ other products
It can equivalently be described as a fluoride anion abstraction by the dimer cation to produce the observed exciplex. Quantitative estimates of the above process were beyond the scope of this study. However, by analysis of the pressure profiles, qualitative estimates indicate that it is a surprisingly large value; a value of approximately 0.6 was predicted. Quantitative calculations are in progress at present.43 (42) Whitten, B. L.; Morgan, W. L.; Bardsley, J. N. J . Chem. Phys. 1983, 78, 1339. (43) Bates, D. R., private communication.
J. Phys. Chem. 1989, 93, 8193-8197
with unit efficiency upon the energy of the ionic system being collisionally reduced below zero. The experimental values at lower rare gas pressures are not accurately modeled by the low/medium-pressure Bates termolecular recombination theory. The predicted rate constants are far lower than observed experimentally and the calculated maxima occur at much higher gas pressures. Previous applicable extensions of the Bates theory fail to give any significant improvement in qualitative or quantitative agreement when applied to this gas system. The experimentally determined rate coefficient pressure profiles are shown to parallel the oxygen ionic recombination system when a large fraction of mutual neutralization enhancement assists the termolecular recombination process. In the Xe/SF6 system, this process corresponds to charge neutralization by an F ion abstraction from SF6- by Xe2+,to give the fluorescent exciplex. The fractional enhancement is estimated to be large, with up to -60% of ionic recombination proceeding by this pathway. Registry No. Xe2+,14066-95-6;SFC,25031-39-4.
Other Third Bodies The effect of other third bodies, M, aiding ionic recombination via Xe2+
+ SF6- + M
-
XeF*
8193
+ products
was also investigated. It was found that there was no effect on the recombination rate constant when the SF6 gas pressure was varied from 0.01 to 5.00 Torr, at a constant xenon pressure of 20.0 Torr, or when helium (0-100 Torr) was added to a 100.0 Torr of Xe/0.50 Torr of SF6gas mixture. This indicates that both these gases are poor third bodies, relative to xenon, for recombination under these conditions.
Conclusion The agreement between experiment and theory for ionic recombination in pulse electron irradiated Xe/SF6 gas mixtures at very high rare gas pressures is excellent. The exciplex is seen to be formed by diffusion-controlled ionic recombination processes, as described by the Langevin-Harper model, and to recombine
Stationary and Pulsed Photolysis and Pyrolysis of 1,1-Dimethylsilacyclobutane+ Th. Brix, N. L. Arthur,$ and P. Potzinger*?$ Max- Planck- Institut fur Strahlenchemie. Stiftstrasse 34-36, 0 - 4 3 3 0 Mulheim a.d. Ruhr. FRG (Received: March 2, 1989; In Final Form: June 20, 1989)
A study of the photolysis of 1,l-dimethylsilacyclobutaneat 147-214 nm shows that of the four primary processes identified
. -
the predominant mode of decomposition is to C2H4 and dimethylsilaethene. Evidence from experiments in the presence of SF6 suggests that the dimethylsilaethene is formed initially in a vibrationally excited state: Me2SiCHzCH2CH2+ hv Me2SiCH2"+ CH2 = CH2. Laser pulsed photolysis experiments at 193 nm have been carried out to measure the absorption spectrum of Me2SiCH2, its absorption cross section, and the rate constant for Me2SCH2combination: 2Me2SiCH2 (Me2SiCH2)2.The values obtained are u (240 nm, base e ) = (1.0 0.2) X cm2 and k7 = (3.3 0.8) X IO-'' cm3 s-I. The kinetics of the pyrolysis of Me2SiCH2CH2CH2have also been reexamined, yielding the following rate constant exp(-(31043 218)/7') and k-l/k71/2/(~m3/2 d2) = 10-7.0*0.3 exp(-(7850 f 3 O O ) l T ) . expressions: kl/(s-') = 1015.46*0.'3 From these results, the heat of formation, *-bond energy, and entropy, of Me2SiCH2,have been deduced: AH,8(g, 298 K) = 36 f 7 kJ mol-', B, = 157 11 kJ mol-', and SB(g,298 K) = 332 8 J mol-' K-I.
.
*
-
*
*
Introduction Silaethenes have been the subject of much interest in recent years, and a large amount of data, especially on dimethylsilaethene, Me2SiCH2,has accumulated.' Most of the data are spectroscopic and thermochemical in nature, and few quantitative kinetic data have been reported. Me2SiCH2dimerizes readily to tetramethyldisilacyclobutane, DSiCB, in pyrolysis experiments, and the combination rate constant has been measured by Guselnikov and co-workers.2 From data obtained in flow experiments, they extracted, in a rather indirect way, the value k7 = 6.6 X cm3 s-I, which they found to be independent of temperature. As has been shown by W a l ~ h , ~ this value, being so low, is incompatible with presently accepted thermochemistry and with the results of Flowers and Guselnikov4 on the pyrolysis of dimethylsilacyclobutane, SiCB. Walsh3 did not abandon this value of the rate constant, altogether, however, suggesting that it was loaded with an appreciable activation energy. This contradicts conclusions drawn from experiments carried out in this laboratory. In an investigation of the photolysis of tetrameth~lsilane,~ we concluded that both the 'In memoriam of 0.E. Polansky. *Permanent address: Chemistry Department, La Trobe University, Melbourne, Victoria 3083, Australia. 1 Permanent address: Max-Planck-Institut fur Stromungsforschung, Bunsenstrasse-10, D-4300 Gottingen, FRG.
0022-3654/89/2093-8193$01.50/0
*
combination of Me2SiCH2 and radical addition to Me2SiCH2 proceed with negligible activation energy. Carrying this result over to our studies of the Hg-sensitized photolysis of tetramethylsilane6 and he~amethyldisilane~ we obtained, in each case, a high value for the a-bond energy (190 f 20 kJ mol-') in Me2SiCH2,in agreement with theory.* If we had assumed that combination of, and addition to, Me2SiCH2involved an activation energy, we would have obtained a much higher value for the a-bond energy. In order to resolve these inconsistencies, we decided to remeasure the rate constant for Me2SiCH2 combination in a pulsed laser experiment with Me2SiCH2being generated by the long-wavelength photolysis of SiCB. It has been shown that SiCB decomposes thermally4 and p h o t ~ c h e m i c a l l y ,mainly ~ ~ ~ ~ ' ~to Me2SiCH2and C2H4. In pyrolysis (1) Raabe, G.; Michl, J. Chem. Reu. 1985, 85, 419. (2) Guselnikov, L. E.; Konobeyevsky, K. S.; Vdovin, V. M.; Nametkin, N., S. Dokl. Akad. Nauk.SSSR, 1977, 235, 1086. (3) Walsh, R. J . Phys. Chem. 1986, 90, 389. (4) Flowers, M. C.; Guselnikov, L. E. J . Chem. SOC.B. 1968, 419, 1396. (5) Bastian, E.; Potzinger, P.; Ritter, A,; Schuchmann, H.-P.; von Sonntag, C.; Weddle, G. Ber. Bunsen-Ges. Phys. Chem. 1980, 84, 56. (6) Potzinger, P.; Reimann, B.; Roy, R. S. Ber. Bunsen-Ges. Phys. Chem. 1981, 85, 1119. (7) Davidson, I. M. T.; Potzinger, P.; Reimann, B. Ber. Bunsen-Ges.Phys. Chem. 1982, 86, 13. ( 8 ) Ahlrichs, R.; Heinzmann, R. J . Am. Chem. SOC.1977, 99, 7452.
0 1989 American Chemical Society
