J. Phys. Chem. 1992, 96, 8858-8863
8858
for Scientific Research (No. 03650722) from the Ministry of Education, Science and Culture.
References and Notes (1) (a) Tsuchida, A.; Nakano, M.; Yoshida, M.; Yamamoto, M.; Wada, Y. Polym. Bull. 1988, 20, 297. (b) Yamamoto, M.; Tsuchida, A.; Nakano, M. MRS Int. Meeting Ada Mater. 1989,12, 243. (c) Tsuchida, A.; Nakano, M.; Yamamoto, M. In Polymers for Microelectronics; Tabata, Y., Mita, I., Nonogami, S., Horie, K., Tagawa, S., Eds.; Kodansha: Tokyo, 1990; p 541. (d) Tsuchida, A.; Sakai, W.; Miyake, M.; Yamamoto, M. J . Photopolymn. Sci. Technol. 1991, 4 , 221. (e) Tsuchida, A.; Sakai, W.; Nakano, M.; Yoshida, M.; Yamamoto, M. Chem. Phys. Lett. 1992, 188, 254. (2) Kira, A,; Imamura, M. J . Phys. Chem. 1984,88,1865, and references therein. (3) Thomas, J. K. J . Chem. Phys. 1969, 51, 770.
(4) Abell, G. C.; Funabashi, K. J . Chem. Phys. 1973, 58, 1079. (5) Yoshida, Y.; Tagawa, S.;Tabata, Y. Radiat. Phys. Chem. 1986, 28,
201. (6) Siegel, S.; Stewart, T. J . Chem. Phys. 1971, 55, 1775. (7) Cadogan, K. D.; Albrecht, A. C. J . Chem. Phys. 1965, 43, 2550. (8) Fieser, L. F.; Fieser, M. Reagents for Organic Synthesis; Wiley: New York, 1967; p 287. (9) Weinberg, N . L., Ed. Technique of Electroorganic Synthesis; Wiley: New York, 1975. (10) (a) Tsuchida, A,; Yamamoto, M.; Nishijima, Y. J . Phys. Chem. 1984, 88, 5062. (b) Tsuchida, A,; Masuda, N.; Yamamoto, M.; Nishijima, Y. Macromolecules 1986, 19, 1299. (1 1) Burrows, H. D.; Greatorex, D.; Kemp, T. J. J . Phys. Chem. 1972, 76, 20. (12) Perrin, F. C. R. Acad. Sci. Paris 1924, 178, 1978. (13) Inokuti, M.; Hirayama, F. J . Chem. Phys. 1965, 43, 1978.
Measurement of Kr,+/CI- Ionic Recombination Rate Constants in Krypton Stephen P. Mezyk,*" Ronald Cooper,and John Sherwellt Department of Chemistry, University of Melbourne, Parkville, Victoria 3052, Australia (Received: November 19, 1991; In Final Form: June 23, 1992)
The techniques of pulse radiolysis and emission spectroscopy have been used to measure ionic recombination rate constants for Kr2+/C1-ions in irradiated Kr/CFC13 gas mixtures. The measured values are seen to have the typical prasure dependence, showing an increase with pressure to a maximum value of -3 X lOI5 M-' s-I ( - 5 X lod cm3 s-') at -250 Torr, before the onset of diffusion-controlled reaction. However, the experimental values at low/medium gas pressures are seen to be far larger, and to peak at a much lower pressure, than predicted by Bates three-body recombination theory. At high gas pressures, the data are parallel to, but lower than the values predicted by Langevin-Harper diffusion-controlled reaction. This behavior is identicalto that observed in the previously studied Xq+/Cl-/Xe recombination system, and thus the discrepancies in the Kr2+/C1-/Kr system are likewise attributed to two-body electrostatic tidal action mechanisms significantly contributing to ionic recombination. Based on a qualitative investigation of the major emitting potential energy curves for both these systems, a criterion is proposed for the prediction of this additional reaction occurring in other exciplex systems.
Introduction Several recent1v2experimental studies of ionic recombination in rare gas/halogen source gas mixtures (R/AX) have reported the measured rate constants for the reaction
R2+ + X-
+ M 2 products
(M = R or AX)
in the formation of the XeF* (Xe2+/SFc/Xe), KrF* (Kr2+/ SFc/Kr) and XeCl* (Xe,+/Cl-/Xe) exciplexes. These rate constants exhibited the characteristic pressure dependence on bulk pressure seen in previous studies of ionic recombination in this pressure r a ~ ~ g increasing e ; ~ , ~ with increasing pressure to a maximum and then decreasing at higher pressures. The contrast of these values to current theoretical ionic recombination models, the Bates termolecular recombination model5 a t low and medium pressures, and the Langevin-Harper diffusion-controlled model6*'at high gas pressure, showed major discrepancies at low/medium pressures (20-1000 Torr). For all three systems the experimental ionic recombination rate constants were much larger and peaked at much lower pressures than calculated by the Bates theory. Although for SF; recombination this discrepancy was attributed to large fractions of recombination proceeding by a two-body, mutual neutralization, mechanism, involving an F ion transfer of the form R2++ -F-SF5
-
RF*
+ other products
'Author to whom correspondence should be addressed. 'Present address: Research Scientist, Whiteshell Nuclear Research Establishment, Pinawa, Manitoba, Canada ROE 1LO. 'Present address: Radian Corp., P.O. Box 201088, Austin, TX 78721.
there is no equivalent process possible in the Xe2+/C1-/Xe systema2 At higher gas pressures, the experimental data for the SFc recombination systems were found to converge to the predicted Langevin-Harperlimit,indicating that the ions always recombined upon their diffusing together. In contrast, the high-pressure rate constant data for Cl- recombination was seen to be parallel to, but far lower (- 50%) than, the predicted diffusion-controlled limit. This implied that, while the encounter rate was diffusion controlled under these conditions, there was much less than unit charge neutralization from the initially formed encounter complex. The discrepancy between experiment and theory for the recombination reaction
xe2++ ~ 1 +- Xe
products
was further investigated theoretically by Bates and Morgana8 Using Monte Carlo techniques they showed that at low/medium pressures the standard three-body recombination was aided by the two-body process Xe2+ + C1-
-
XeCl*
+ Xe
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 fluorescent exciplex. This behavior was termed the electrostatic tidal effect. This latter treatment was found to give very good agreement with the experimental data over the entire pressure range studied. The experimental data and all of the theoretical predictions for the Xe2+/C1-/Xe system are shown in Figure 1. The purpose of this study was to investigate the analogous Kr2+/Cl- ionic recombination in krypton to determine whether
0022-3654/92/2096-8858%03.00/0 0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 22, 1992 8859
Ionic Recombination Rate Constants of Kr2+/Cl-
Kr
--
Kr*, Kr', e-@)
e-(s) e-(th)
+ Kr
+ 'CFC13 C1-
Kr*
+ CFC13
Krt Kr2+
+ 2Kr
10'
103
10'
Prerrurr Xenon (torr)
Figure 1. Comparison of the experimental rate constants,aEXp, with the termolecular Bates, QBATB, diffusion-controlled Langevin-Harper, aLH, and electrostatic tidal assisted, CYTIDAL, calculated values for the reaction Xe2++ CI- + Xe XeCI* + 2Xe.
-
this system also showed significant electrostatic tidal pathway recombination. The behavior of the two systems is compared, and based on these observations, a criterion is proposed for the prediction of tidal recombination behavior in other recombining ionic systems.
Experimental Section For the determination of the rate constants for the reaction
+
Kr2+ C1-
+ Kr 2L KrCI* + 2Kr
with KrCl*
-
Kr + C1+ hu
over a wide range of krypton pressures, the established pulse radiolysis faci1ities2sin this Department were used. The kinetics of the recombination reaction were determined by monitoring the time dependence of the M I * luminescence. This was measured by conventional kinetic spectroscopic techniques, based on pulsed ionization of the component gases. Details of the experimental procedure have been published in full previously.1*2 The gases used, krypton (Matheson Rcsuuch Grade (99.995%)) and CFCI3 (C.I.G. Pure Grade), were subjected to several freeze (77 K)-pumpthaw cycles prior to usage. The potential energy curves used in this study were constructed from the available literature data at short bond lengths and by assuming a Coulombic attractive potential at greater lengths. For the latter, the energy of the ionic system, E, was calculated according to
-
(1)
(electron thermalization)
(2)
e-(th)
+ 'CFC12 (thermal electron capture) (3) KrCl* + 'CFC12 (rare gas excited state
-.
-
reaction with the halogen source gas) (4)
Kr2+ + Kr
-
+ C1- + Kr KrCl* + 2Kr
-
KrCI*
101' 10'
-
(initial species production)
Kr
(rare gas cation dimerization) (5)
(three-body ionic recombination) (6)
+ C1 + hu
(7)
(exciplex emission)
To measure the ionic recombination rate constants it was essential to ensure that reaction 6 was the rate-limiting step in the exciplex formation mechanism. This was achieved by using the following experimental conditions. The hot electrons, e-(s), were thermalized by both the rare and halide source gases, 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 CFC13 (k = 1.55 X IOl4 M-'s-I to form the atomic anion. Fast cation dimerization (relative to recombination) via
Kr+
+ 2Kr
-
Krz+
+ Kr
k = 8.70 X
1Olo
M-2 s-l
I2
was achieved by using high rare gas pressures, or at lower gas pressures, by observing the recombination on microsecond time scales. The identities of these recombining ions, Kr2+and C1-, have been established previously,'J where, based on kinetic arguments, it was shown that further complexation of these ions with either impurities or the constituent gases was not possible on the time scale of the observed emission. The lower ionization potential of CFC13 (1 1.77 eVI3) than that of krypton (13.999eV14) allows the charge-transfer reaction Krz+
+ CFC13
-
2Kr
-
+ (CFC13)+
to occur in competition with the recombination reaction KrZt
+ C1- + Kr
KrCl*
+ 2Kr
This problem was minimized by using a very small pressure of the halide source gas, 0.10 Torr, and keeping the ion concentrations as high as possible to maximize the rate of the ion recombination reaction, relative to the charge-transfer reaction. However, in this system the ionic recombination process was so rapid that measurements were not possible with the initial ion concentration higher than 10-* M. The initial ion concentration was typically kept between 0.3 X 10-9 and 9 X 10-9 M,and within this range, the obtained values showed a slight dependence on the initial ion concentration. The maximum estimated error of the measured data points is less than 15%, the problem being worse at higher pressures. The data obtained are possibly higher than the real values by this amount. The M I * 22+1/222+1/2 transition covers the range 202-228 nm,I5 with a maximum at 222 nm. All rate constant determinations were done at the peak wavelength. Ionic Recombination Rate Constants. The technique used to determine ionic recombination rate constants has been well established At longer times after the initiating pulse of electrons, the formation of the exciplex is only by ion-ion recombination? and by applying a steady-state analysis for KrCl*, it has been shown that1
-
where E. is the energy of the two ions at infinite separation, e the electronic charge, eo the permittivity of free space, and r the distance between the two ions (A). Excellent agreement was obtained for all potential energy curves between the literature data and the assumed potential for exciplex bond lengths greater than 6 A.
Results and Discussion The KrCl* exciplex was produced by the pulsed electron beam irradiation of Kr/CFC13 gas mixtures. Under the experimental conditions of this study, the mechanism for KrCl* production has been shown to bel*2
where I is the photon intensity observed by the detection system
8860 The Journal of Physical Chemistry, Vol. 96, No. 22, 1992
Mezyk et al.
(= millivolts of intensity on the kinetic trace oscilloscope), K the proportionality constant for the light detecting efficiency of the experimental setup, a! the recombination coefficient, and [R+l0 the initial cation concentration. Using charge balance gives CY
C
= m(i,l/z/n,)
Thus, to eliminate K and obtain a!, the gradient, of the transformed kinetic plot, m, must be multiplied by the square root of the observed kinetic trace emission intensity (millivolts) at any time t , I,, and divided by the ion concentration, n,, at that time. The total emission was found to consist of the following components:lS2 X-rays, dimer rare gas fluorescence, rare gas excited state formed exciplex fluorescence, and ionic recambination formed exciplex fluorescence. The X-ray component was small and followed the time profile of the electron pulse (- 5 ns). The dimer rare gas fluorescence was typically complete within 100 ns, and its intensity varied greatly with rare gas pressure. At low rare gas pressure, its contribution was small, but at higher pressures (>lo00 ToK), it accounted for up to 90% of the total signal. The reproducibility of subtraction of this fluorescence determined the upper pressure limit of rate constant measurement. The exciplex fluorescence formed by the reaction of krypton electronically excited states (reaction 4) was again complete typically within 100 ns but was more intense at low krypton pressures. The ionic recombination formed exciplex fluorescence had the slowest rate of production, being observed for many hundreds of nanoseconds. Its intensity was also dependent on the total gas pressure, being comparable to the direct reaction fluorescence intensity at low gas pressures, but accounting for nearly 100% of the exciplex fluorescence at high gas pressures. As expected, the presence of these extraneous emissions caused the initial part of the transformed kinetic curve (l/il/zvs t) to be nonlinear. Thus, the gradient determination, by linear least-squares fitting, was done only on the limiting linear portion, and the time, t, at which the analysis began was noted. It has previously been shown that, from time t onwards, there was only ion recombination formed exciplex fluorescence occurring.2 The square root of the millivolt intensity on the kinetic trace, il/z, at that time, was simply determined from the digitized oscilloscope trace. Ion ConcmtmtiooDetenninatioa The ion concentration at time t was calculated by the following method, involving integrated kinetic traces. Total emission yields were obtained by filling a standard cell with the gas mixture of interest and measuring the integrated intensity under the entire exciplex fluorescence spectrum at 2.0-nm intervals. This was done using the experimental satup described previously,lJ but with one oscilloscope continuously monitoring the peak emission wavelength as a means of correcting any pulse to pulse variations. To isolate the exciplex fluorescence in the integrated kinetic traces, the X-ray and dimer rare gas fluorescence intensities had to be subtracted. This was done by the method described previously;2 by irradiating the gas mixture a second time to measure the total intensity at a wavelength just outside the exeiplex 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. For M I * , the X-ray and dimer rare gas fluorescence intensities were calculated using a background wavelength of 230 nm. After subtraction, the remaining integrated emission consisted only of exciplex fluorescence. However, for M 1 * the resolution of the exciplex fluorescence into its excited state formed and ionic recombination components could not be determined directly from the integrated trace, as before.2 Thus, these fractions were obtained by the following procedure. The total exciplex fluorescence yield, YT,as a function of CFCI, pressure over the range 0.02-1.0 Torr, at a constant krypton pressure of 100 Torr,was determined as described above (see
g
? .-
s
-
20
m c
b b
-
10
b
00
02
06
04
08
10
12
'0
12
Pressure CFCI3 (torr)
.
'0°1
.
lff, 1"
02
00
06
04
08
Pressure CFCI, (torr)
F i p e 2. (a) The total emission yield, YT,as a function of CFCI, pressure at a constant krypton pressure of 100.0 Torr. (b) The CFCI, pressure dependence of the calculated excited-state reaction P contribution to the measured KrCl* YTvalues at a krypton pressure of 100.0
Torr.
Figure 2a). This plot shows a limiting linear slope at high CFC1, pressures, where the charge-transfer reaction
-
Krz+ + CFCl,
2Kr
+ (CFC13)+
dominates and thus all the KrCl* fluorescence is formed by the direct reaction of krypton excited states with the halide source molecule2J6
+ CFCl,
Kr*
KrCl*
+ products
Deviation from the higher CFCI, pressure linearity is due to the ionic recombination process Krz+
+ C1-
KrCl*
+ Kr
becoming important.I6 An exact value for the charge-transfer rate constant could not be found in the literature: however, the rate constant for the analogous reaction Ar+
+ CFCI,
-
Ar
+ (CFCl,)+
k = 5.2 X 10" M-I s-] I I
and the measured values for the reaction of Krz+ with species of similar ionization potential to CFCl,, e.g.
Krz+ + COS
-
2Kr
+ (COS)+
k = 5.1
X 10"
M-l s-l
suggests that the charge-transfer rate reaction is essentially collision controlled. Using the Ar+ rate constant, the CFCl, pressure at which the first half-life for ionic recombination (from at 100 Torr of Kr, with typical Figure 4,a 2.6 X loi5M-' initial ion concentration 3.0 X o+l' M) and that for charge transfer have the same value is 0.19 Torr. From Figure 2a, the experimental Y, value at this pressure is 0.110. while the linear extrapolation of the higher CFC1, pressure values gives P = 0.062, in reasonable agreement with this prediction.
-
'..-.'1
Ionic Recombination Rate Constants of Kr2+/Cl-
The Journal of Physical Chemistry, Vol. 96, No. 22, 1992 8861
0.3 i
e
I-
1.:
10'
-
F
0.1
0.0 0.0
1.0
a.o
2.0
1 0 ' Prsesure [Krj' (lorr')
: I .
$ 0
,
100
10"
:
.
.
10.24
.
.
1
0
500
VT
V'
.
I
1000
I
.
I
2000
1500
aEXP
2500
Pressure Kr (torr)
Figure 3. (a) The krypton pressure dependence of the calculated excited-state reaction, P, contribution to the measured KrCl* YTvalues for a constant CFCll pressure of 0.10 Torr. (b) Determination of the (k,/k,) rate constant ratio in the given excited-state formed reaction scheme from the KrCl* measured YT values. The production of exciplex fluorescence by only the excited-state process (corresponding to the region of higher CFCl, pressure in Figure 2a) has been previously shown'5 to be accurately modeled by the following general mechanism, using the rate constants: Kr*
+ CFCl,
Kr*
+ Kr
&CI*
+
+ Kr
KrCl* + 2Kr
KrCl*
products
---
+
Kr* CFClS
KrC1*
-
k, = 1.2 X 10I2 M-' kb = 1.0
X
1Olo M-I
s-l s-I
hv k, = 5.1 X lo6 s-I products kd 6.7 X 10" M-'
(a) (b)
'
'
'
v "
' ' I
Pressure Kr (torr) Figure 4. Comparison of the experimental rate constants, cyBxp, to the
-
termolecular Bates, cyeATES, and diffusion-controlled Langevin-Harper, aLH,values for the reaction Kr2+ + C1- + Kr KrCl* + 2Kr. where Yo*is the maximum possible yield of excited-state KrCl* production and Ri the rate for the ith reaction in the scheme. The Yo*value was determined by measuring P yields under the conditions where only excited state formed fluorescence occurred (the linear region in Figure 2a) and then allowing for the effects of all the quenching/emission reactions via the expression
S-l I *
products
k, = 3.3
products
kf = 1.3 X 10" M-2 s-I (0
lo9 M-l s-l (e)
KrCl* .-+ hv k, 3.7 X lo7 s-I l9 (g) Very few kinetic parameters for KrCI* could be found in the literature. The rate constants for reactions a-c were assumed to be the same as determined for KrF*.2 The lifetime of KrCI* has been measured as 19 ns,I9 and the quenching reaction KrCP CF2C12 products
+
'
aLH
(c) (d)
X
101'4
a~~~~~
-
previously studied,16in which the parameter kT = 2.1 X 10-l8cm3 (where k is the quenching rate constant and T the lifetime of KrCl*) was determined. Using the above lifetime measurement, this gives a value of k = 6.7 X 1O'O M-' SI, which was assumed to be equivalent to kd, the exciplex quenching by CFCI,. No quenching rate constants for KrCl* by krypton could be found. The three-body quenching value, kf,was determined in this study from the measured YTvalues as for XeCl*,Z by plotting YT-Ivs [KrI2 and obtaining the slope/intercept ratio (equal to kf/k,);see Figure 3b. The ratio obtained was 3560 and from k = 3.7 X lo7 s-I, a value of kf = 1.3 X 10" M-2 s-l is derived. Tkis value is in fair agreement with the three-body quenching coefficients used previously2for KrF* (2.1 1 X 10" M-2 s-l) and XeCl* (2.65 X 10" M-2 s-l). The two-body quenching of KrCl* by krypton, k,, could not be determined in this study. This value was calculated by assuming the ratio k f / k ewas 40, the average of the values for the Xe2+/ Cl-/Xe (44.0) and Kr2+/SF6-/Kr (37.5) systems.2 This gave k, = 3.3 x 109 M-1 s-1. From the above reaction scheme, the excited-state yield of fluorescence is given by
This equation allows us to test the sensitivity of the assumed rate constants kd and k, above. From the ratio in the second pair of brackets, it can be seen that, at low krypton pressures, R, is the dominant term in the sum, while at high krypton pressures Rf becomes the major component. The Rd term is seen to have a very small contribution at all pressures studied, and thus the value for kd is not critical. Similarly, the sensitivity for k, is low; at a krypton pressure of 100 Torr, an error of 50% in this value (giving k, = 1.6 X lo9 M-' s-l ) would produce an error of approximately 16% in the calculated P value, but this corresponds only to an error of
