J. Phys. Chem. 1981, 85, 3989-3994
relations among the four coefficients because of the common functional dependence on r. The potential in region 1 only is needed, the solution for F1is then
,
3989
always less than unity, the fraction can be expanded in power series. Substituting into eq A7 allows one to identify each term as a potential due to a charge shifted in space. The potential for unit charge is therefore
where
Since the second term in the denominator of eq AS is
where d E tlh. A factor of count for self-energy.
112 has been included to ac-
Thermal Electron Attachment Rate to CCI,, CHCI,, CH2C12,and SF6 J. A. Ayala, W. E. Wentworth," Department of Chemistry, University of Houston Central Campus, Houston, Texas 77004
and E. C. M.
Chen
School of Sclence and Technology, University of Houston at Clear Lake City#Houston, Texas 77058 (Received: February 18, 1981; In Final Form: September 18, 198 1)
Thermal electron attachment rate constants have been determined for SF6,CC14,CHC13,and CHzClzby use of the pulse-sampling technique. The experimental results were obtained with nickel-63 and tritium foils as ,f3 sources under steady-state conditions (long pulse intervals)as well as the linear region (short pulse intervals). The rate constants determined with the tritium foil are generally larger than with nickel-63 and are in better agreement with the literature. The results with tritium from data in the linear region give the best agreement with the literature values except for CH2C12.Under these conditions the electron attachment rates at 298 K are as follows: SF6,(2.8 f 0.3) X lo-'; CC14,(4.4f 0.5) X lo-'; CHC13, (2.3 f 0.2) X lo-'; CH2C12,(6.5 1.1) x cm3 molecule-' s-l.
*
Introduction Thermal electron attachment to halogenated molecules has become of interest in various fields of investigation such as the chemistry of the upper atmosphere, gaseous electrical discharges, aerospace communications, electron scavengers in liquid solutions, and the study of chargetransfer reactions in general. The interest in electron capture by halogenated compounds is reflected by the numerous papers on this subject which are appearing in the literature. The purpose of this paper is the determination of the thermal electron attachment rate constants for CCl,, CHCl,, CH2C12,and SF, by use of the pulsesampling technique.lv2 Two different radioactive sources were utilized to generate the swarm of electrons: "Ni in metallic nickel and 3H as scandium tritide. Both of these sources are deposited on stainless-steel foils. The results obtained with both of these sources are compared with other published thermal electron attachment rate constants. It has been shown that the pulse-sampling technique can be used to determine absolute values for the thermal electron attachment rate constanL2 These measurements have been made at long pulse intervals so as to attain a steady-state condition. In much of our earlier work on halogenated aliphatic corn pound^^^^ we were not concerned
with determining the absolute rate constant. Instead we were interested only in the relative values for the rate constants and the temperature dependence which could be used to calculate the activation energy for dissociative electron attachment. In principle, it would appear that these relative values could be put on an absolute basis by assigning a known absolute value from another technique to one of these compounds. However, these relative rate constants are relative only within that experiment and experimental conditions can vary so that the results are not relative between experiments. In particular, the pseudo-first-order rate constant for electron loss in the absence of the electron-capturing species (kD) must be determined at the same time as the attachment rate constant is measured. This can be accomplished very simply by observing the change in electron concentration as a function of the pulse intervals as will be described shortly. If kD is determined at the time of the attachment study, the absolute rate constant for attachment can be determined.2 In principle, the use of the pulse-sampling technique at steady-state conditions appears to be quite simple for measuring thermal electron attachment rate constants. However, in practice the technique is subject to possible errors due to contamination of the carrier gas stream
(1) W. E. Wentworth, E. Chen, and J. E. Lovelock, J. Phys. Chem., 70, 445 (1966). (2) E. Chen, R. D. George, and W. E. Wentworth, J. Chem. Phys., 49, 1973 (1968).
(3) W. E. Wentworth, R. S. Becker, and R. Tung,J.Phys. Chem., 71, 1652 (1967). (4) W. E. Wentworth, R. George, and H. Keith, J. Chem. Phys., 51, 1971 (1969).
0022-3654/81/2085-3989$01.25/0
0 1981 American Chemical Society
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The Journal of Physical Chemistty, Vol. 85, No. 26, 1981
passing through the electron capture (EC) cell. The basic kinetic model assumes that the carrier gas is pure and that ItD is simply a measure of the electron-positive ion recombination rate. However, if an electron-capturing impurity were present it is difficult to ascertain the effect it would have on the attachment rate measurement since the nature of the impurity is not generally known. For this reason we have made measurements only when the carrier gas is relatively free of electron-capturing impurities, as evidenced by a high standing current in the cell. Maintaining a clean carrier gas is not always easy to accomplish since the carrier gas passes through the gas chromatographic column in addition to pressure regulators and flow meters. On occasion we have even purchased argon that contained impurities far in excess of the specified limits. Recently, we have been making measurements under nonsteady-state conditions and in analyzing the data have realized an extremely simple mathematical analysis of the kinetic mechanism if very short pulse intervals are employed. At very short pulse intervals the electron-positive ion recombination can be neglected since the electron concentration increases linearly with pulse interval in this region. Furthermore, the attachment to impurities is less sensitive under these conditions and the results will not be subject to errors due to contamination of the carrier gas. However, as will be shown shortly, the linear relationship between the decrease in electron concentration and concentration of the capturing species is limited to the low capturing region and this will add some error to the determination of the thermal electron attachment rate constant. In this study we have determined the attachment rate constants using steady-state conditions at long pulse intervals as well as the data at short pulse intervals. From this study it appears that the data at short pulse intervals gives more reliable data, most likely as a result of the lower sensitivity to impurities. The limited linear relationship a t short pulse intervals does not appear to affect significantly the accuracy of the determined rate constant. As a result of this study we are presently considering the use of data at short pulse intervals in our other studies, including the determination of molecular electron affinities. A further complication can arise in regard to the positive ion concentration in the cell. In our earlier we assumed that the positive ion concentration remained constant during the electron attachment process. As will be discussed later, the positive concentration should decrease if the capturing species remains in the EC cell long enough to establish a true steady state. The time for this to occur has not been established as yet but it should be on the order of seconds. if the positive ion does decrease to its steady-state value, the capture coefficient should differ by a factor of 2 from the value when the positive ion concentration remains constant. In determining absolute thermal electron attachment rates this also introduces a possible uncertainty of a factor of 2. In this study we have assumed the positive ion concentration has decreased to its steady-state value and for this reason the calculated thermal attachment rate constants from data in the steady-state region could be high by this factor of 2.
Ayala et al.
experiments were made with a Gow Mac 550 gas chromatograph. High-quality electrometers, recorders, and oscilloscopes were used for all experiments. A Datapulse 102 square-wavepulse generator supplied a 40-60-V pulse of 2.8 ps duration at variable pulse times. The concentric electrode geometry6 was used for all but the tritium foil in the linear region which used a parallel plate geometry.' The collecting electrode was withdrawn from the region of the radioactive foil in the experiments with Ni-63 foil operated in the linear region. It is assumed that the geometry will not affect the results. Ar-10% CH4 was used for the primary carrier gas for all of the experiments and was passed through a 5-A molecular sieve trap. For data in the linear range, approximately 15 mL min-' of Nzwas used as the column carrier gas. The total flow rate was nominally 150 mL min-l but was accurately measured at the time of the experiment with a bubble meter and a stopwatch. All of the samples were injected into the system with a 1O-pL Hamilton syringe. Nanograde acetone, toluene, hexane, and xylene were used as solvents and were checked for electron-capturing impurities and coelution. A DC-200 GC column was used for the measurements in the linear region, a squalane column for measurements with tritium as steady-state conditions, and a porapak Q-S column for measurements with nickel at steady-state conditions. The ECD response was generally measured as a function of concentration at temperatures of 26 or 25 "C. For the steady-state runs, the electron concentration was measured as a function of time between pulses throughout the experimental run. The data taken in the linear region was obtained at 16.5 and 49.5 ps. The time between pulses was measured with an oscilloscope which was calibrated with a Hewlett Packard frequency counter. The values were obtained as a function of concentration but only the values giving less than 25% capture were used for the results. The reported values are the average from 6 to 15 injections and the errors are the standard deviations. Duplicate dilutions were made for SF6 and CC14 and there was good agreement in the results indicating that the sample preparation was not a major source of errors. The chart speed was measured directly so that the overall error in the rate constants should be less than f25%. The linear range data with the nickel source was obtained on the same solution and on the same day as the linear range data for the tritium source so that the differences are certainly real. For example, the sample sizes injected for SF6 were four times greater with the tritium source.
Experimental Section Three different sets of ancillary equipment were used in these experiments. The steady-state measurements for Ni were carried out with the system described in ref 5 while the steady-state tritium measurements were made with the same type of system described in ref 1;the linear region
Kinetic Analysis For the molecules considered in this study, electron capture is dependent kinetically on the rate of electron attachment. For SF6only nondissociative capture to give SF6- occurs at thermal energies (25 "c). Dissociative capture to SF, F- and SF6- F can occur but only at higher energies. For CHZClz,CHCl,, and CC14dissociative capture to C1- and the corresponding radical occurs at near thermal electron energies. For these molecules both dissociative and nondissociative modes of electron capture are kinetically indistinguishable, and are described as the /3 mechanism in the literature related to the pulse-sampling technique at steady-state conditions.' In these earlier studies the electron-capture coefficient, K , was related to the instan-
(5) J. A. Ayala, W. E. Wentworth, and E. C. M. Chen, J.Phys. Chem., 85,768 (1981).
(6)J. A. Ayala, W. E. Wentworth, and E. C. M. Chen, J. Chromatogr., 196, l(1980).
+
+
Electron Attachment to
SF, and Halogenated Molecules
The Journal of Physical Chemistry, Vol. 85, No. 26, 1981 3991
p + (Ar + 10% CHI)
v1
m
E 3
-
kdia
e-
$
+
AB- or A + BThe differential rate expressions are simply db/dt = kpRa e-
m u
0 7 ,
v
-2
Y
+ AB
-+
kl
de/dt = kpR, - kle[AB]
m
E 1
(4) (5)
(6)
(7)
where b and e are the concentrations of electrons at the time of the applied pulse (t,) in the absence and the presence of the capturing species, respectively. Integration of eq 6 and 7 give
5
b = kpR,t,
(8)
Flgure 1. Graphs of integrated response vs. moles of CCll injected with a nickel-63 source and with a Sc3H, source.
taneous concentration of the capturing species and the ECD response by means of the following equation: -b -- e - K[AB] e where b is the concentration of electrons at steady-state conditions, e is the concentration of electrons at any given time, and [AB] is the concentration of the capturing species. For the p mechanism the electron capture coefficient is related to the electron attachment rate constant, k, through the equation k. k. where kD’ is the electron-positive ion recombination coefficient, and [$I0 is the concentration of positive ions in the absence of capturing species. Recently, Wentworth and Chen7 have revised the initial model developed to explain the behavior of the ECD. In the revised model, which is discussed in detail in ref 5 and 7, the electron capture coefficient is still related to kl, as in eq 2. However, K is no longer related to the ECD response as in eq 1, but rather as follows: b2 - e2 -- K[AB]
(3) be In an earlier publicatioq2 the kl for SF6was obtained through eq 1and 2. In this report, the same experimental results from ref 2 are analyzed through eq 3, as shown later. In must be pointed out that, in order to obtain values for kl under steady-state conditions, it is necessary to know the value of kD at the time of the experiment. The values by meafor kD are calculated, as described el~ewhere,~ surement of the standing current in the ECD2s4 as a function of the time between pulses (t,), or pulse period. A graph of kDSb2- e 2 / ( b e )dVvs. moles of A B injected should give a straight line passing through the origin with a slope equal to kl. Figure 1 shows the results of such graphs for CC14run with nickel-63 and Sc3H3sources in the ECD. The line is the least-squares fit to the equation y = ax + b. The intercept for the nickel source is not zero and the data do no appear to fit a linear relationship as well as for the Sc3H3source. For the analysis of the data collected at short pulse intervals we need to consider only the rate of production of electrons by the p particles and the attachment to AB. (7) W. E. Wentworth and E. C. M. Chen, J. Chromatogr., 186, 99 (1979).
Obviously from eq 8 the electron concentration varies linearly with time and we frequently refer to this as the linear region where electron-positive ion recombination is not significant. Experimentally, this region is easily defined and measurements to be used in this analysis must be confined to this region. Generally, this linear region is on the order of 50-200 ps, depending upon the purity of the carrier gas. Equation 9 can be simplified by expanding the exponential term into a MacLaurin’s series.
If we neglect higher order terms than the second term and substitute b for k$,t, from eq 8, we obtain be b
klt~
- +AB]
The quantity ( b - e ) / b represents the fractional loss of electrons and this is linearly related to [AB] and t,. Of course the linear relationship with t , is restricted to the linear region for b and the linear relationship to [AB] will be restricted to the region where the higher order terms can be neglected. The response ( b - e ) / b has been found to be linear with t, up to 50 ps. The dependence on [AB] is shown in Figure 2. Note that the data for SF6 and CH2C12appear to be linear up to approximately 0.2 to 0.3 capture. Obviously, the thermal electron attachment rate constant, kl, can be determined from the initial slope of the graph of ( b - e ) / b vs. [AB]. The pulse period, t,, should be accurately measured at the time of the measurement in order to obtain an accurate estimate of kl.
Results Sulfur Hexafluoride. The result for SF6found in ref 2 has been recalculated by using the revised kinetic model at steady-state conditions and eq 3. The result are reported in Table I. The thermal electron attachment rate constant determined by the pulse sampling technique (steady state) is larger than other reported values. The (8) K. G. Mothes and R. N. Schindler, Ber. Bunsenges. Phys. Chem., 75, 936 (1971). (9) B. H. Mahan and C. E. Young, J. Chem. Phys., 44, 2182 (1966). (10) L. G. Christophorou, D. L. McCorkle, and J. G. Carter, J.Chem. Phys., 54, 253 (1971). (11) F. C. Fehsenfeld, J. Chem. Phys., 53, 2000 (1970). (12) F. J. Davis and D. R. Nelson, Chem. Phys. Lett., 6, 277 (1970). (13) R. W. Fessenden and K. M. Bansal, J. Chem. Phys., 53, 3468 (1970).
3992
The Journal of Physical Chemistry, Vol. 85, No. 26, 1981
Ayala et al.
TABLE I: Rate Constant for SF, at T = 300 K k , cm3 molecule-' 5-l carrier
a
method
ref
pulse sampling (steady state) 3.9 x 10-7 A r + 10%CH, pulse sampling 3H (linear region) (2.8 t 0.3) x 10-7 Ar + 10% CH, pulse sampling 63Ni(linear region) (5.4 i. 1.7) x Ar + 10% CH, 2.6 x 10-7 Ar ECR microwave 3.1 x 10-7 He swarm 2.7 x 10-7 NZ swarm 2.8 x 10-7 1 ' H4 flowing afterglow 2.21 x 10-7 He 2.0 x 10-7b various swarm microwave 2.21 x 10-7 C3H8 The original data from ref 2 was fit to eq 3. Average value of k , with different carrier gases.
Za present work present work 8 9 10 10 11 12 13
TABLE 11: Rate Constant and Activation Energy for CCl, k , , cm3 molecule-' s-l
4.1 x 10-7 4.1 x 10-7 4.0 x 10-7 3.55 x 10-7
E*, kcal mol-'
carrier Ar
+ NO
2.9 x 10-7 2.9 x 10-7 1.5 x 10-7
CO,, CH,OH, C,H, N, -0.05 Ar + 10% CH, -0.6 Ar + 10% CH, 4.20 x 10-7 A r t 10%CH, 1.57 x 10-7 Ar + 10% CH, Ar + 10% CH, (4.4 i. 0.5) x 10-7 (1.3 f 0.2) x 10-7 Ar + 10% CH, 1.6 x 1 0 - 7 a Nl a Value calculated from model given in ref 20 at 0.05 eV.
best agreement is with the microwave method reported by Mahan and Young? The value for SF6is 25% larger than the microwave value. The pulse-sampling technique has also been used to determine kl for SF6for data in the linear region. A value of (2.8 f 0.3) X cm3molecule-1 was obtained with a tritium EC detector and this value agrees well with the other experimental determinations. However, a similar determination with a nickel-63 EC detector gives a value of (5.4 f 1.7) X cm3 molecule-I s-l which is considerably below the values obtained by other established techniques. Carbon Tetrachloride. Carbon tetrachloride has been the subject of numerous studies. It has a high rate constant, very close to the theoretical limit14of 5.0 X cm3 molecule-l s-l. It undergoes dissociative attachment, and it is a well-established fact that the electron capture cross section rapidly decreases with increasing electron energy. A summary of the reported values for the rate constant at T = 300 K is given in Table 11. The values for the activation energy for attachment are also summarized. Lee,15 in his pioneer work relating flame inhibition properties to electron attachment rates of halocarbons, reports an electron attachment coefficient a = 9 attachments cm-l ppm-l in an electron swarm experiment using nitrogen as carrier gas, and a mean electron energy of 0.2 eV. The electron attachment rate constant in swarm experiments is given by aw,where w is the electron drift velocity. The value quoted in Table I1 is based on the thermal attachment rate as calculated by Blaunstein and Christophorou.16 In order to obtain rate constants cor(14)J. M.Warman and M. C. Sauer, Int. J. Radiat. Phys. Chem., 3, 273 (1971). (15)T.G.Lee, J. Phys. Chem., 76,360 (1963). (16)R.P.Blaunstein and L.G. Christophorou, J. Chem. Phys., 49, 1526 (1966).
method ECR microwave microwave
DDD swarm swarm swarm pulse-sampling pulse-sampling pulse-sampling pulse-sampling pulse-sampling pulse-sampling swarm
ref 8
300 300 300 300
14 19 18 16 17 15 3 4
3H 3H 3H (steady state) 63Ni(steady state) 3H (linear region) 63Ni(linear region)
T,K
300 300 300
300 300 present work present work present work present work 20
299 299 298 298 298
s ($> Flgure 2. Response (b - e ) / b vs. concentration (volume solute injected) for a tritlum source with data in the linear region. S is sample size in microliters.
responding to thermal electron energies (average energy of 3 / 2 K T )in swarm experiments, it is necessary to extrapolate the data for aw to the limit as the EIP ratio goes to zero, where E is the electric field strength and P the pressure. Swarm experiments on carbon tetrachloride have also been performed by Bouby et al.17and by Blaunstein and Christophorou.16 There is excellent agreement for the (17)M.Bouby, M.Fiquet-Fayard,and M. H. Abgrail, C. R. Acad. Sci., 261,4059 (1965).
The Journal of Physical Chemistry, Vol. 85, No. 26, 198 1
Electron Attachment to SFB and Halogenated Molecules
3993
TABLE 111: Rate Constant and Activation Energy for CHCl,
k,, cm3 molecule-' s-' 2.6 x 10-9a 2.2 x (2.2-2.6) x 4.9 x 10-9 3.8 x 10-9 3.8 x 10-9 2.66 x 10-9 (2.3 f 0.2) x 10-9 (2.0 + 0.5) x 10-9
E*, kcal mol-' 2.4 2.2 3.1
carrier Ar + NO n-hexane NZ
NZ
Ar t 10% CH, Ar + 10% CH, Ar + 10% CH, Ar t 10% CH, Ar + 10% CH,
ref
method ECR microwave swarm swarm pulse-sampling (steady state) pulse-sampling, (steady state) pulse-sampling, 63Ni(steady state) pulse-sampling, 3H (linear region) pulse-sampling, 63Ni(linear region)
a Reaction followed in time at a fixed concentration of CHCl, = 1.5 x 10'' molecules ern-,. Pressure dependent. function of concentration at constant reaction time.
21 14 15 16 3 present present present present
T,K 300 300
300 work work work work
299 299 298 298
Reaction followed as a
TABLE IV: Rate Constant and Activation Energy for CH,Cl,
k , , cm3 molecule-' s-' 4.1 x 5.4 x 10-'2b 4.7 x 1.6 x lo-'' 2.88 x 10-l2 3.45 x 1 0 4 3 (6.5 + 1.1)x 10-13 (2.3 i 0.6) x lo-',
E *, kcal mol-'
ref
ECR
21
T. K 300
microwave swarm pulse sampling pulse-sampling (steady state) pulse-sampling 63Ni(steady state) pulse-sampling ,H (linear region) pulse-sampling 63Ni(linear region)
22 15 3 present work present work present work present work
3 00 298
carrier
+
4.1
Ar
NO
7.5
propane NZ Ar + 10% CH, Ar + 10% CH, A r + 10%CH, A r t 10%CH,
method
a Reaction followed in time at a fixed concentration of CHZC1,= 2.4 X function of concentration at constant reaction time.
values of the rate constant quoted in Table 11. The value shown in Table I1 for ref 17 is an average of the values obtained for LYW (attachments s-l torr-l) at E / P = 0 in different carrier gases (a= 8 X logfor C2H4,13 X lo9 for COz, and 5.8 X lo9 for CH30H). The drift-dwell (DDD) technique is a modified swarm experiment where the electrons remain in the reaction chamber for a period of time under zero field conditions. It has been used by Davis et al.lSto study thermal electron attachment to CC14,and other polyatomic molecules. The value in Table I1 is an average of the values obtained by using H2, He, CO, CH4, and C2H4as carrier gases, and pressures ranging from 2 to 6 torr. The results obtained by Warman and Sauer14J9with the microwave conductivity technique, and n-hexane carrier, and Mothes et al.,S with the electron cyclotron resonance (ECR) technique with argon as carrier, are in excellent agreement. Warman and Sauer14have also shown that the rate constant is invariant over a pressure range from 0.1 to 100 torr. The temperature dependence of the rate constant has been investigated by Wentworth et al.374and by Warman and Sauer.14 These results are also summarized in Table 11. The results are consistent in that the measured activation energy is close to zero. It should be noted that all 0. values have E* The pulse-sampling value for lzl obtained by use of the tritium source at steady-state conditions is in good agreement with the higher results obtained with the other techniques. On the other hand, the value obtained with the nickel source at steady-state conditions agrees with the lower value reported by the swarm method. The difference between the results obtained with 3H and 63Niat steadystate conditions is outside of the expected error and could be due to a slightly higher electron energy distribution with (18)F. J. Davis, R. N. Compton, and D. R. Nelson, J. Chem. Phys., 53, 2324 (1973). (19)J. M.Warman and M. C. Sauer, J.Chem. Phys., 53,6428(1970).
lo1, molecules ~
299 299 298 298
followed as a m - ~ Reaction .
the nickel-63 source. The pulse sampling values from data in the linear region agree quite well with the steady-state values. Again the tritium value is in good agreement with the ECR and microwave data whereas the nickel-63 value is quite low. Chloroform. Good agreement for the rate constant for electron attachment to chloroform exists in the literature. A summary containing the rate constants and activation energies is given in Table 111. The value attributed to Lee15 is that reported in ref 16. Lee reports an electron attachment coefficient a = 0.6 attachments cm-l ppm-' at a mean energy of 0.2 eV. The results obtained with the microwave14and electron cyclotron resonance techniquez1 are in excellent agreement. Warman and Sauer, however, have found that the rate constant is pressure dependent in the range from 33 to 80 torr. The rate constants obtained by use of the pulse-sampling technique under steady-state conditions are in reasonable agreement with the literature values. The difference between the results obtained by using 3H and 63Niis much less than with CCl& Again the 3H value is greater. In this case the rate constant obtained by use of 3H is in better agreement with the swarm result16 and that obtained by use of 63Niis in better agreement with the ECRzl and microwave14 results. The pulse-sampling values from data in the linear region are lower than the values at steady-state conditions. Again the nickel-63 value is lower than the tritium value. The tritium value agrees well with the ECR and microwave results. The activation energy has been measured by Schultes et al.,21Warman and Sauer,14and Wentworth et al.4 The discrepancy of
