9413
J. Phys. Chem. 1993,97, 9413-9419
Ion Recombination Rates in Rare Gas Cation-Halide Anion Systems. 3. XeBr* and XeI* Stephen P. Mezyk,**+Ronald Cooper, and John Sherwellt Department of Chemistry, University of Melbourne, Parkville, Victoria 3052, Australia Received: May 17, I993
The techniques of electron pulse radiolysis and emission spectroscopy have been used to determine the ionic recombination rate constants, Xe2+ XXe 5 XeX* 2Xe in the formation of the XeBr* and XeI* exciplexes. These values show the typical pressure dependence of an increase to a maximum value of a -3 X 1015 M-l s-' (a 4 X 10-6 cm3 s-l) before the onset of diffusion controlled reaction. The comparison of the XeZ+/Br data to the predictions of the Langevin-Harper diffusion controlled and Bates termolecular theories show that the experimental values are far larger and peak at much lower pressures than calculated, indicating that an additional mode of recombination is occurring. This is attributed to the electrostatic tidal pathway, observed previously in Xe*+/Cl- and Kr2+/Cl- recombination. In contrast the Xe2+/1- measured peak is in excellent agreement with the Bates prediction and at high pressures has rate constants even larger in magnitude than the Langevin-Harper diffusion controlled values. The application and extension of these theories to this system are discussed.
+ +
-
Introduction The pulsed electron irradiation of mixtures of rare (R) and halogen source (AX) gases has shown that under suitable experimental conditions, the general mechanism for exciplex formation 2 - 7
-
production of initial species R
R*, R+, e-(s)
(1)
hot electron thermalization (M = R or AX)
+
(2)
'-(th)
thermal electron capture
+
e-(th) AX
-
X- + A
(3)
exciplex formation from rare gas excited states R* A X - RX* + A
+
cation dimerization R+
+ 2R
-
-
R:
(4)
+R
three body ionic recombination
R2++ Xexciplex emission
+M
RX*
+ products
(6)
+
The comparison of this data to the predictions of the Bates8 termolecular (low/medium pressures) and the Langevin-Harperg910 diffusion controlled (high pressure) theories gave mixed results. For all systems, the agreement between experiment and the Bates theory was minimal; the experimental rate constants were much larger and peaked at much lower pressures than calculated. For SFg recombination, this discrepancy was attributed to large fractions of ionic recombination proceeding by two body,8,*1-13mutual neutralizationtype mechanisms,involving an F- ion transfer. R:
+ -F-.SF,
-
RF*
+ other products
This reaction could not be invoked for the C1- systems as mutual neutralization does not produce the fluorescent exciplex. At higher gas pressures, the experimental data for the SF6recombination systems were seen to converge to the predicted Langevin-Harper limit, indicating that the recombining ions always formed the fluorescent exciplex upon their diffusing together. In contrast, the high pressure rate constant data for C1-recombination was seen to be parallel to, but far lower (- 5CL 70%) than the predicted diffusion controlled limit. This implied that diffusion controlled recombination occurred at these pressures, but with less than unit charge neutralizationfrom the initial encounter complex. Further theoretical work on the Xe2+/Cl- system by Bates and Morgan14 showed that the standard three body recombination was aided by the two body process
+ +
RX* - R X hv (7) The observed emission lifetimes of the exciplexes are all short (-1O-e s) and hence the delayed emission kinetics (ps) are characteristic of the ionic recombinationreaction (6). In several previous studies5-7 we have used this situation to measure the rate constants for the three body recombination reactions for Xe2+/SF6- (via XeF*), Kr2+/SF,5- (KrF*), Xe2+/C1- (XeCl*), and Krz+/Cl- (KrCl*). These studies have been conducted over a large pressure range and showed typical pressure profiles, consisting of an increase to a maximum value of Q (2-3) X 1015 M-1 s-1 (a (4-5) X 10-6 cm3 s-1) before the onset of diffusion controlled reaction.
where the Xe2+ vibrational and rotational modes were excited by the C1- ion passing through perihelion, leading to its dissociation and thus to the subsequent formation of the fluorescentexciplex. This behavior was termed the electrostatic tidal effect, and its inclusion into the recombination theory gavevery good agreement with the experimental data over the entire range studied. The similar experimental rate constant pressure profile observed for KrC1*,7 as well as a qualitative theoretical comparison of the major emission potential energy curves for the two species, suggested that this mechanism was also important in Kr2+/Clrecombination. In the present study, the behavior of exciplex formation from * Author to whom correspondence should be addressed. recombining dimer xenon cations and atomic anions is further t Present address: AECL Research Whiteshell Laboratories, Pinawa, investigated by the measurement of the three body recombination Manitoba, Canada ROE 1LO. t Present addres: RadianCorporation,P.O.B0~201088,Austin,TX78721. processes producing XeBr* (Xez+/Br) and XeI* (Xez+/I-).
-
N
0022-3654/93/2097-9413%04.00/0 63 1993 American Chemical Society
9414 The Journal of Physical Chemistry, Vol. 97, No. 37, 1993
Experimental Section
-
For the determination of the rate constants for the reaction
+ + Xe
Xe2+ X-
XeX*
+2
~ e
(8)
with X e X * - X e + X + hv (9) over a wide range of xenon pressures, the established pulse radiolysis facilities5Jsin this department were used. The kinetics of the recombination reaction were determined by monitoring the time dependence of the exciplex luminescence. This was measured by conventional kinetic spectroscopictechniques,based on a Febetron 706 electron beamgenerator. Thedetection system .was in two parts: dual photomultiplier tube/monochromator/ oscilloscope systems were used. One system recorded the time dependent kinetic traces, whereas the other simultaneously recorded the integrated light intensity as a function of time. This enabled the photon production from different kinetic processes to be identified and assayed. Detailsof the experimental procedure have been published in full p r e v i o ~ s l y . ~ ~ ~ Thegases used in this study, xenon (Matheson Research Grade, 99.995%), CH2Br2 (Ajax Chemicals Ltd. Laboratory Grade), and CF3I (Bristol OrganicLtd. Laboratory Grade), weresubjected to several freeze (77 K)-pumpthaw cycles prior to irradiation. 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 integrated light emission at any wavelength remained the same for up to 20 pulses, the kinetics of emission changed significantly (> 10%) after several pulses. Hence all kinetic data were recorded from the first pulse. All irradiations were done at room temperature. Data Analysis. At longer times after the initiating pulse of electrons, the formation of the exciplex is only by ion-ion recombination. Under these conditions, it has been shown that4
where I is the photon intensity observed by the detection system (related to the millivolt intensity on the oscilloscopekinetic trace by factor K), K is the proportionality constant for the light detecting efficiency of the experimental setup, a is the recombination coefficient,and [R+]o is the initial cation concentration. Thus a plot of 1 / N 2 vs t should be a straight line of slope m = a1/2/K1/2. Applying a steady-state analysis for XeX* in reactions 8 and 9, and using charge balance, gives
Thus to obtain the recombination rate constant a,the gradient of the transformed kinetic plot, m, must be multiplied by the square root of the observed emission intensity, I, (mv), at any time t , and divided by the ion concentration, n,,at this time. It was therefore necessary to resolve the observed emission into ionic and non-ionic components, and relate these exactly to the ion concentration at time t . This procedure has been described in full previously,5*6and thus only a brief outline will be given here. The emission was found to consist of several component^:^^^ X-rays, xenon dimer fluorescence, and exciplex fluorescence formed from both ionic recombination and xenon excited-state reaction. The X-ray component is small, and follows the time profile of the electron pulse (-5 ns). The xenon dimer fluorescence was typically complete within 100ns, and its intensity was proportional to the xenon pressure. The reproducibility in subtraction of this background fluorescencedetermines the upper pressure limit for rate constant measurement in these systems.
Mezyk et al. The exciplex fluorescence formed by the reaction of excited xenon atoms with AX (reaction 4) wasagain complete typically within 100 ns. It was more intense at low xenon pressures. The ionic recombination formed exciplex fluorescencehad the slowest rate of production, being observed for many hundreds of nanoseconds. Its intensity was also dependent on total gas pressure; being comparable to the excited-state formed fluorescence intensity at low gas pressures, but accounting for nearly 100% of the exciplex fluorescence at high xenon pressures. The presence of the non-ionic recombination derived emissions at short times causes the initial part of the transformed kinetic curve to be nonlinear. Thus the gradient analysis to give m,by linear least squares fitting, was done only on the limiting portion, and the time, to, at which the analysis began, noted. It has been shown previously6 that at time to onward, there was only ion recombination formed fluorescence occurring. The square root of the millivolt intensity on the kinetic trace, PI2, at that time was simply determined from the digitized oscilloscope trace. The ion concentration at to, n,, was determined using the integrated light intensity traces. The exciplex fluorescence was isolated by subtraction of the X-ray and dimer xenon fluorescence intensities. This was done using the technique described previously6 involving the irradiation of the gas mixture a second time to measure the total intensity at a wavelength just outside the exciplex emission band. A separate irradiation of only the rare gas correlated the emission intensity at this wavelength to the intensity at the wavelength at which the kinetic measurement was made. The resolution of the remaining yield into neutral reaction and ionic recombinationfluorescencecould not be determined directly from the experimental measurements for these systems. The fractionalyield for each process was thus calculated using a general quenching mechanism with known/measured rate constants.6This procedure, and the values used, are given for each exciplex in the following section. The initial ion concentration was obtained by routine ozone dosimetry16together with the Wvaluel' for xenon and appropriate stopping powers. The calculated fraction of the intensity due to ionic recombination was equated to this value, and this allowed the ion concentration, n,,and emission intensity, I,,at time to, to be directly linked. Thus the slope, m, of the transformed kinetic plot could be directly converted into the rate constant a. Results and Discussion To measure the ionic recombination rate constants, it was essential toensure that theionicrecombination process was indeed the rate limiting step in the exciplex formation mechanism. This was achieved by using the following experimental conditions. The hot electrons, e-(*),were thermalized by both gases in the mixture, and this process was typically complete within the duration of the electron beam pulse (-5 ns). The thermalized electrons, e-(th),were then rapidly captured by the halide source molecules, (CH2Br2, k = (5.60 0.84) X 1013 M-l s-*,l* and CF31, k = (1.16 f 0.07) X 1014M-* s-l 19) to form the atomic anion. Fast ionic dimerization of the xenon cation via
*
Xe'
+ 2Xe
-
+
Xe2+ 2Xe
k = 7.3 X 10" M-'s-l
2o
was achieved by using high rare gas pressures, or at lower gas pressures, by observing the recombination on microsecond time scales. The lower ionization potentials of the halide source molecules, CH2Br2, 10.8 eV,21 and CF31, 10.4 eV,22than that ofXe2+, 11.10 eV,23allowed the charge-transfer reaction Xe,'
+ AX
-
2Xe + (AX)'
Ion Recombination Rates in R-AX Systems
-
The Journal of Physical Chemistry, Vol. 97, No. 37, 1993 9415
to occur in competition with the recombination reaction
+ +
120
,
+
Xe,+ X- Xe XeX* 2 ~ e This problem was minimized by using a very small pressure of the halide source gas, typically 0.10 Torr, and keeping the ion concentrations as high as possible, usually greater than 5 X 10-8 M. This maximized the rate of the ion recombination reaction, relative to the charge-transfer reaction. Xe2+/Br Ionic Recombination. The XeBr* emission spectrum's for the 2 2 1 / 2 + 2 2 1 / 2 + transition covers the range 266336 nm, with an intense peak centered at 282 nm and a secondary maxima at 326 nm. All kinetic measurements were done at the primary maxima of 282 nm. For this species the xenon dimer fluorescence and X-ray intensities were subtracted from the integrated measurements using a background wavelength of 338 nm. Although temporal separation of the excited-state reaction and ionic recombination formed XeBr* fluorescence has been reusing pulsed electron irradiated Xe/CF3Br gas mixtures, such separation was not achieved in this study. Hence the yields of the two contributions were calculated, as for XeC1* and KrC1* 6,7 previously. The procedure was as follows. At a constant xenon pressure of 80 Torr, the total exciplex fluorescenceyield, YT,as a function of CH2Br2pressure over the range 0.02-1 .O Torr, was determined. This was done by measuring the integrated intensity under the entire exciplex fluorescence spectrum at 2.0-nm intervals. The inverse plot of these yields (Figure 1) shows a limiting linear slope at higher CH2Br2 pressures (10.6 Torr). It has previously been demonstrated that at these higher pressures, the charge-transfer reaction
-
Xe:
+ CH,Br,
-
2Xe
+ (CH2Br2)+
and thus all the XeBr* fluorescence is formed by the direct reaction of xenon excited states with CH2Br2, Xe*
+ CH,Br,
XeBr*
+ products
and that deviation from this linearity at lower CH2Br2 pressures is due to the ionic recombination process,
+ Br-
Xe:
XeBr*
+ Xe
becoming i m p ~ r t a n t . ~ The production of exciplex fluorescence by only the excitedstate process (correspondingto the higher CH2Br2 pressure region) has been previously shown5~6to be accurately modeled by the following general mechanism:
--
+ CH,Br,
Xe*
Xe*
+ Xe
Xe*
+ CH,Br, XeBr* + Xe XeBr* + 2Xe
XeBr*
-
XeBr*
k, = 2.5 X lo', M-' s-l
XeBr*
k, = 5.4 X 10' M-' s-'
2Xe
hv
k, = 2.1 X lo6 s-l
products
products
products
-
hu
kd = 2.1 X 10" M-' s-l k, = 2.2 X lo9 M-' s-]
k, = 9.8 X 10" M-2 s-'
"
k, = 4.1 X lo7 s-l
The temporally separable Xe/CF3Br system was also successfully modeled's by this general reaction scheme. The rate constants used for reactions a-c were obtained by isolating the excited-state reaction process, by using low xenon pressures and initial ion concentrations. This allowed the direct measurement of these values, but attempts at integrating the kinetic curves under these conditions, to directly obtain the fractional yields of excited-state and ionic recombination formed exciplex fluorescence, were not reproducible.
8
l/Y, l/Y'
0.00
0.20
0.40
0.80
0.60
1.00
1.20
Pressure CH,Br, (torr) Figure 1. CHZBr2 pressure dependence of the calculated excited-state
contributionto the measuredXeBr* YTvalues, at aconstant reaction, P,
xenon pressure of 80.0 Torr.
By varying the CH2Br2 pressure, at a constant xenon pressure of 50.0 Torr, a value of k, = (2.5 f 0.1) X 10'2 M-l s-1 was obtained. This value is an "averaged" rate constant for the entire distribution of xenon electronically excited states produced upon irradiation and is much higher than that measured for the analogous KrF*, XeCl*, and KrCl* e x c i p l e x e ~ .No ~ ~ ~confirmation value could be found for this reaction in the literature. The variation of xenon pressure, at a constant CHzBr2 pressure of 0.15 Torr, gave k b = (5.43 f 0.07) X lo8 M-l s-l. This value is in excellent agreement with the value determined for XeC1* 6 of k b = 5.47 X 108 M-1 S-1. Using k, and kb, the "average" lifetime of the xenon excited states involved in reaction with CH2Br2, k,, was calculated as 480 ns, again in excellent agreement with the value of 475 ns for the Xe/CFC13 system. These identical values for k b and k, show that the same mix of electronically excited states of xenon react with both CFC13 and CH2Br2. For the reactions of XeBr*, d-g, most of the rate constants were derived from available literature data. The lifetimes of the XeBr* (B) and XeBr* (C) states have been measured as 12.5 and 138 ns, respectively,26andthe equilibrium constant between these states determined as 1 Thus the coupled radiative lifetime at 300 K is effectively -25 ns,2* corresponding to a decay rate constant of 4.1 X 107 s-1. The parameter kd7 for CH2Br2 quenching of XeBr* has been measured29 and from the calculated coupled lifetime ( T ) value, a value of kd = 2.1 X 10" M-1 s-l is obtained. The three body xenon quenching value, reaction f, has been determined as (9.8 f 3.3) X 10'0 M-2 s-1.25 The two body quenching of XeBr* by xenon could not be determined in this study. This value was obtained by assuming that the k f / k ,ratio for XeC1* (44.0 6, and XeBr* was the same. For XeBr*, this gave k, = 2.2 X lo9 M-1 s-1. From the above reaction scheme, the excited-state yield of fluorescence is given by6
-
[ R , + RRa ,+R,
la
d + R , +Rg Rf+Rg
1
where YO*is the maximum possible yield of excited state XeBr* production and Ri is the rate for the ith reaction in the scheme. The YO*value was determined by measuring P yields over the xenon pressure range 50-100 Torr, under the conditions where only excited-state formed fluorescence occurred (using CHzBrz pressures of 0.6-1.0 Torr) and then allowing for the effects of all
9416
Mezyk et al.
The Journal of Physical Chemistry, Vol. 97, No. 37, 1993
-
reaction becoming diffusion controlled. The pressure and magnitude of the maxima in this curve (a 3 X 10'5 M-I s-I a t -250 Torr of xenon) is similar to that observed for KrCl* and XeCl* previously,6J but the pressure profile here is far less broad. Comparisonwith Theory. At low and medium pressures Bates and co-workers*have calculated the recombination rate constant pressure profile for the reaction a,
+
04+ 0,-+ 0, [O,]+ 0, +
From this, they obtained scaling parameters which allow determination of rate constants for any ionic recombination reaction. The application of their theory to the reaction lo-'
Xe,' 0
500
1000
1500
Pressure Xe (torr)
Figure 2. Xenon pressure dependence of the calculated P contribution to the XeBr* YTvalues, at a constant CH2Brz pressure of 0.10 Torr.
+ Br- + Xe
-
XeBr* +2Xe
gives the theoretical curve, C Y B A T ~shown , in contrast to the experimental data in Figure 3. This curve has been slightly modified by the inclusion of known experimental ion mobilities (p(Xe2+) = 0.60 cm2 V-l s-l , p ( B r ) = 0.98 cm2 V-' s-l 22 a t standard pressure and 295 K) in the model, as described previo~sly.6~~ From this plot, the experimental data are seen to be always greater in magnitude, and to peak at a much lower pressure, than predicted. At higher xenon pressures, the ionic recombination becomes diffusion controlled, and is describable by the Langevin-HarpergJo formula aLH= 4?re(p+
Pressure Xenon (torr)
Figure 3. Comparison of the xenon pressure dependence of the experimentalXez+/Brrecombinationrateconstants ( a m ) ,at a constant CH2Brz pressure of 0.10 Torr, with the termolecular Bates (QLBATB) and ) for the reaction Xez+ + B r + Xe Langevin-Harper ( ~ L Hvalues XeBr* + 2Xe.
-+
the quenching/emission reactions via the expression
With the YO*value, the P fractions were then calculated as a function of CH2Br2 ptessure (Figure 1) and of xenon pressure (Figure 2). These are shown in contrast to the experimentally determined YTvalues. The excited-state yields, and hence the corrections to the experimental rate constants, are larger than those seen for previous systems,6J due to the large rate constant for xenon excited-state reaction with CH2Br2 and the low xenon quenching rate constants for XeBr*. As the excited-state yield corrections for XeBr* are so large, about 25% of the total fluorescenceacrossthe entire xenon pressure range, the sensitivity of the calculated P value to the rate constants used was checked. It was found that reaction a dominates and that if this measured rate constant were incorrect by a factor of 2, this would give an error in a of 15%; the same magnitude as attributed to experimental scatter. Similarly a 50% variation in k, would cause less than an 8% error in CY,and thus this assumed value is seen not to be critical. The measured Xe2+/Br recombination rate constants, as a function of xenon pressure, are shown in Figure 3. The experimental curve shows the characteristic initial increase and subsequent decrease with increasing xenon pressure, attributed first to the two and three body recombination mechanisms becoming more efficient with increasing pressure and then to the
-
+ 1.1-1
By substituting the experimental ionic mobilities into this equation, the diffusion controlled limiting rate constant, CYLH,is obtained. These values are also shown in Figure 3. The limiting high pressure slope of the experimental data is again seen to parallel the CYLHvalues and is much closer to the Langevin-Harper values than those observed for KrCl* and XeC1*.6 Theory Modifications. Several modifications to the three body Bates theory that were explored in previous investigation^^^^ have also been considered here. The termolecular values calculated by assuming that the recombining anion was CH2Br2- (mobility of this ion in xenon calculated30 as 0.60 cm2 V-1 s-1) gave far worse agreement to the experimental data; the new termolecular values are lower than for the standard calculations, and the Langevin-Harper values cross the experimental curve. The maximum rate constant pressure prediction was approximately the same as before. The contribution from symmetrical resonance charge-transfer reactions30 of the form
+ Xe
-
+ Br- + (Xe,+/Br-)
-
Xe-Xe+
+
Xe Xe+-Xe was again calculated, but even when the maximum possible effect is assumed, no significant improvement in the quantitative agreement between experiment and theory was achieved. No account was taken of possible anion symmetrical resonance chargetransfer reactions because of the low concentration of the halide gas. Also the contribution from ionic recombination with an ion as the third body31 Xe;
XeBr*
+ other products
was found to be negligible, even at the highest ion concentration used. As the three body recombination theory did not accurately model the Xez+/Br experimental data, it was concluded that two body recombination mechanisms had to be the significant contributing reaction in the total recombination. The limiting high pressure experimental values being parallel to the LangevinHarper limit suggest that the two body process described for XeCl* and KrCl*, electrostatic tidal recombination, is also
The Journal of Physical Chemistry, Vol. 97, No. 37, 1993 9417
Ion Recombination Rates in R-AX Systems occurring for this exciplex. Unfortunately the further confirmation of the presence of this mechanism, as observed for KrCl*,7 could not be done, as potential energy curves for Xe2Br* could not be found in the literature. However the far better agreement of the experimental values to the high pressure theoretical predictions, and the higher pressure of the experimental peak for Xez+/Br recombination, indicates that these recombining ions would form encounter complexes of much lower energy than in KrZ+/Cl- and Xe2+/Cl- recombination. Xe2+/I- Ionic Recombination. The ionic recombination rate constants for Xe,+
+ I- + Xe
-
XeI*
-
0.25
VI
L
'2
0.20
¶
@
0.15
2%
0.10
E .g 2 7
lo3
0.05 0.00
0.w 0.20 0.40
0.60
0.80
1.00 1.20
los6 (Pressure Xe)'/(torr)
+ 2Xe
were obtained using the same procedure as described for XeBr*. TheXeI* emission spectrum1sfor the 2Z1p++ 2 2 ~ / 2 +and 2 2 ~ / 2 + %3/2 transitions cover the ranges 239-260 and 307-328 nm with peaks at 251 and 319 nm, respectively. For this exciplex the X-ray and dimer rare gas fluorescence intensities were subtracted using background wavelengths of 262 and 330 nm, respectively. Most of the experiments performed for this exciplex were for the 221p+ 221/2+ transition (251 nm), and unless otherwise stated, the following discussion refers only to measurements done at this wavelength. The excited-state formed exciplex fluorescence contribution to the total observed fluorescence was calculated as before, as direct measurement of the yields of the two formation processes was not possible. This process was again isolated by using low initial ion concentrations at low xenon pressures. Using the standard reaction scheme, the contribution of the direct reaction formed exciplex fluorescencewas calculated using the rate constants
(a)
-
-
-
+ CFJ Xe* + Xe
Xe*
Xe*
+ CFJ XeI* + Xe
XeI*
XeI*
+ 2Xe
XeI*
k, = 5.5 X 10' M-I s-'
2Xe
products
kd = 5 X 10" M-I s-l
products
k, = 1.0 X 10'' M-I s-]
products
k f = 4.4 X 10" M-' s-l
hv
k, = 1.3 X lo7 s-'
Y'
1000
0
3000
2000
Pressure Xe (torr) Figure4. (a) Xenonpressuredependenceof thecalculated Y+ contribution to the XeI* YTvalues, at a constant CF31pressure of 0.10 Torr. (b)
Determinationof the (kf/k,) rate constant ratio from theXeI* measured YTvalues.
100
- 1
.i-1A\ \ '
l/YT
liY'
40
k, = 2.1 X lo6 s-l
hu
' yT
60
k, = 2.4 X 10" M-' s-l
XeI*
'
24
24s32
Thevariation of the first-order rateconstant with CF31pressure, for the isolated direct reaction process, gave k, = (2.44 f 0.09) X 1011 M-1 s-1. This value is in reasonable agreement with the value of 3.7 X 10l1 M-1 s-1 24 obtained in a previous study, and of the deactivation of the Xe (3P2) state by CF31, 3.2 X 1O1IM-l s-1-33
The variation of xenon pressure at several different CF31gas pressures gave kb = (5.47 f 0.12) X 108 M-1 s-I, in very good agreement with the equivalent values determined previously for XeC1* and XeBr*. The value of k, = 2.1 X 106 s-1 was calculated from this and the k, value. The quenching rate constant, kd = 5 X 1011M-1 s-I, had been previously determined,24and the lifetime of this species measured as -80 118.24.32 No rate constants for two or three body xenon quenching of XeI* could be found in the literature. The kfvalue was determined by measuring the total exciplex yield, YT,as a function of xenon pressure at a constant CF31 pressure of 0.10 Torr. By plotting Y T -vs ~ the square of the xenon pressure (Figure 4b), a straight line of slope/intercept ratio6 of krlk, = 35 200 is obtained. From the known k, value, this gave kf = 4.4 X 1011 M-2 s-l. The rate constant for two body quenching of XeI* by
2o 0 0.00
0.20
0.40
0.60
0.60
1.00
1. 0
Pressure CF31(torr)
Figure 5. CF31pressure dependence of the calculated ' Y contribution to the measured XeI* YTvalues, at a constant xenon pressure of 80.0 Torr. Xe was calculated by assuming the kf/k, ratio was the same as for XeBr*, giving k, = 1.0 X 1010 M-1 s-l. The I" variation with CF31 pressure, at a constant xenon pressure of 100 Torr is contrasted with the measured UTvalues in Figure 5 . The variation with xenon pressure, at a constant CF31pressure of 0.10 Torr, is shown in Figure 4a. The latter plot shows that the corrections to the experimental rate constants are negligible, except at very low xenon pressures. The measured XeZ+/I- recombination rate constants, as a function of xenon pressure, are shown in Figure 6. The experimental curve again shows the increase and subsequent decrease with increasing xenon pressure, but, for this system, the peak value is at a much higher xenon pressure than that observed for XeF*,5 XeC1*,7 or XeBr* previously. For this system, some ionic recombination measurements were also performed at 3 19 nm. These results are contrasted with the 251-nm values in Figure 6. The only correction needed for the integrated measurements at 319 nm was for X-ray and dimer rare gas fluorescence,but excellent agreement was obtained with the previous measurements. Comparison with Theory. These experimental values are contrasted with the calculated Bates*termolecular recombination
The Journal of Physical Chemistry, Vol. 97, No. 37, 1993
9418 I"
, .
+
UBATES
0
2.ULH
~
r
L
H
aLH = 4 m ( p +
A u319
fA 7
a
Torr, the experimental rate constant is a = 8.00 X 1014M-l s-l. Assuming the reaction a t this pressure is diffusion controlled, then from
uEXP
.
Mezyk et al.
+ p-)
we get
+
1 0 ' ~ ~
p+ p- = 1.8 12 cm2 V-I s-l As the recombining cation is Xez+ ( p + = 0.60 cm2 V-l s-l gives
9, this
-
,
1014
, *, , , , , ,,
,
, , , , , , ,,
I
I
1000
100
10
,,,
,..I 10000
Pressure Xe (torr)
+
and the Langevin-HarpergJO diffusion controlled limit values for the reaction
+ I- + X e
-
XeI*
+2
1.212 = 13.82/(Pu) where P is the polarizability of xenon and u is the reduced mass of the reacting pair. Solving for the anion mass gives -42.7 amu, which clearly is impossible! At this time, we have no explanation for this observation. The reason for the experimental rate coefficients being greater in magnitude than the Langevin-Harper values is speculative but is believed to lie in the derivation of the formula itself. A derivation of the Langevin-Harper9Jo formula based on the examination of the inward flux of ions about a specified ion of opposite charge has been given previously by B a t e ~ . 3With ~ the definition of ro as the distance that recombination is ensured for oppositely charged ions and n(r) as the concentration of ions of opposite sign a t a distance r from the specified ion, the inward flux, F, toward this ion is given by p-=
Figure 6. Comparison of the xenon pressure dependence of the experimental Xez+/I-recombination rate constants ((YE=), at a constant CF3I pressure of 0.10 Torr, with the termolecular Bates ( ( Y B A ~ ) ,the standard ((YLH), and extended (2.(YLH) Langevin-Harper values for the reaction Xez++ I- + Xe XeI* + 2Xe. Also shown are the experimental rate constants determined at 319 nm.
Xe,+
p1.212 cm2 v-'s-~ From this, the approximate mass of the recombining anion can be calculated by30
~ e
in Figure 6. Again the substitution of the known mobilities of the recombining ions (p(Xez+) = 0.60 cm2 V-l s - ~p(I-) , ~ = 0.86 cm* V-1 s-1 22) in the model was made. For this exciplex the experimental maximum is in excellent agreement with the predicted termolecular value. The experimental rate constants are still much greater in magnitude than the termolecular predictions and, over the pressure range 5602500 Torr, are seen to be even higher than the predicted LangevinHarper values, the theoretical upper limit to the recombination rate coefficient. The error associated with the experimental data is not sufficient to explain these discrepancies. The experimental high gas pressure limiting slope is also steeper than the predicted values, not parallel as previously seen. Bates Theory Modification. The termolecular calculations, assuming the recombining anion to be CF31- (mobility of this complex anion calculated30 to be 0.56 cm2 V-l s-l) shows no significant quantitative improvement between theory and experiment. The effects of symmetrical resonance charge transfer of Xe2+ with the bulk gas, and ionic third body recombination reactions were again found to be negligible. The difference in magnitude between the experimental and termolecular calculated values is puzzling, and can only be attributed to the three body recombination mechanism being more efficient than calculated. The role of two body processes for Xez+/I-recombination could not be resolved in this study. The agreement observed for the gas pressure of the experimental and theoretical rate constant maxima suggests that they are less important than in the previously studied recombination systems.6~~ One possible explanation for this could be the existence of low energy predissociation channels, such as the two body formation of XeI* with vibrational energy above the predissociation limit to I*. Langevin-Harper Theory Modifications. The LangevinHarper values obtained from the sum of the mobilities of the two ions in the bulk gas represents the upper limit for ionic recombination rate constants. For XeI*, there are two points of interest observed experimentally in the xenon pressure range above 1000 Torr; the experimental limiting slope being far steeper than the predicted Langevin-Harper slope, and the experimental data are greater in magnitude than the Langevin-Harper values. From the experimental limiting slope, the mobilities of the recombining ions can be obtained. For a xenon pressure of 2000
where K is the sum of mobilities of the positive and negative ions (=p+ p-) and D is the diffusion coefficient corresponding to the mobility K . Under the conditions of these experiments, consisting of a weakly ionized gas and no external electric field, D is given by35
+
D = kTK/e Satisfying the boundary conditions n(r)+N
as r + O
n(ro) = 0 where N is the neutral gas density gives
and thus 4reK -F= N 1 - exp[-(Ke/Dro)]
r 2 ro
Recombination of the two ions occurs a t a separation r,, a value small compared with the characteristic length associated with the thermal motion of the ions, r,, at room temperature. The parameter r, is given by
rc = If ro > r,, but ro
eL
4 7 0 A at 293 K
