J. Phys. Chem. 1981, 85, 1091-1094
The results presented here are of significance for two reasons. First, they shed light on the triplet state chemistry of thiirane for which information is sparse, as is the case with three-membered ring compounds in general. Second, they represent a unique example of geometrical isomerization of an olefin induced by an electronically excited molecule, but without energy transfer. For this type of sensitization the sensitizer should have the following properties: (a) a long radiative lifetime, (b) resistance against collisional deactivation, (c) an excitation
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energy lower than the nonvertical triplet energy of the olefin, and (d) the ability to form a partial but not a full covalent bond with unsaturated carbon centers. At present, few molecules may be imagined which would fulfill these conditions. Acknowledgment. We thank the Natural Sciences and Engineering Research Council of Canada for continuing financial support.
Sequential Ion-Molecule Reactions in Acetylene Fred W. Brlll and John R. Eyler”7 Deparfment of Chemistry, University of Florida, Galnesvllle, Florida 326 1 1 (Received: December 1, 1980; In Final Form: March IO, 1981)
Reactions of C2H2+,C4H2+,C4H3+,C6H4+,and C6H5+with acetylene have been studied by using pulsed ion cyclotron resonance mass spectrometry. In the pressure range from 2 X lo4 to 3 X torr of CzHz,overall disappearance rate constants for C&+ and C4H3+of (3.3 f 0.8) X and (2.1 f 0.3) X cm3/s, respectively, have been determined. Formation of long-lived ion-molecule reaction complexes, stabilized by collisions at pressures near 1 X torr of CzH2and favored over H- or Hz elimination products, has been observed for C&,+ and C8Hn+species. The possible relevance of these reactions to soot formation processes in flames is discussed.
Introduction The existence of significant concentrations of ions in flames has been acknowledged for a number of years. Formation of the ions is generally accorded1 to take place in a very thin reactive zone via the chemi-ionization reaction CH(X211)+ O(3P) CHO+ + e(1) Extensive secondary ion-malecule reactions then lead ultimately to H30+,NO+, and electrons in the burnt gas region of the flame. Recent mass spectrometric sampling experiment^^-^ have confirmed the earlier identification of numerous flame ions, and have led to various reaction schemes3s4which explain the evolution of ion concentrations from an upstream region, through the reactive zone, and into the burnt gas region of certain laboratory flames. Whether these ions and ion-molecule reactions are relevant to any important combustion processes is, however, a subject of current controversy. One area related to combustion in which ions may play a crucial role is soot formation. Studies by Prado and Howard5 and by others have demonstrated the presence of large hydrocarbon ions (probably aromatic) in sooting flames. Experiments involving the effects of ionic additive@and of electric fields7on the amount of soot produced in such flames also indirectly point to participation of ions in these processes. However, almost equally compelling evidence has been given for the primary importance of radical-molecule as compared to ion-molecule reactions in the condensation reactions which lead to nucleation and ultimately to soot formation.s At least one groupghas postulated that rapid ionic polymerization of acetylenic species
-
t Camille and Henry Dreyfus Foundation Fellow, 1978-82.
is of crucial importance in sooting flames, since they observed large concentrations of polyacetylenic ions. Other workers2p3have detected similar ions in methane-oxygen and acetylene-oxygen flames, and large mole fractions of neutral acetylene have been foundlo in methane-oxygen flames. The techniques of ion cyclotron resonance (ICR) mass spe~trometry’l-~~ have been shown in the past 10 years to (1) See, for example, W. J. Miller, Symp. (Int.) Combust., [Proc.], 14th, 1972, 307 (1973). (2) A. N. Hayhurst and D. B. Kittelson, Combust.Flame, 31,37 (1978). (3) J. M. Goodin~s,D. K. Bohme, and Chun-Wai NE, Combust.Flame, 36, 27 (1979). (4) J. M. Goodings, D. K. Bohme, and Chun-Wai Ng, Combust.Flame, 36, 45 (1979). (5) G. P. Prado and J. B. Howard, Adu. Chem. Ser., No. 166, chapter 10 (1978). (6) E.’M. Bulewicz, D. G. Evans, and P. J. Padley, Symp. ( h t . ) Combust., [Proc.],14th, 1975, 1461 (1975). (7) R. J. Heinsohn and P. M. Becker, “Effects of Electric Fields in Flames” in “Combustion Technology, Some Modern Developments”, H. B. Palmer and J. M. Beer, Ed., Academic Press, New York, 1974. (8) H. G. Wagner, Symp. (Int.) Combust., [Proc.], 17th, 1978,3 (1979). (9) C. Vinckier, M. P. Gardner, and K. D. Bayes, Symp. (Int.) Combust., [Proc.],16th, 1976, 881 (1977). (10) J. W. Hastie, Combust. Flame, 21, 187 (1973). (11) J. D. Baldeschwieler and S. S. Woodgate, Acc. Chem. Res., 4,114 (1971). (12) J. L. Beauchamp, Annu. Reu. Phys. Chem., 22, 527 (1971). (13) J. M. S. Henis in “Ion-Molecule Reactions”, Vol. 2, J. L. Franklin, Ed., Plenum Press, New York, 1972, Chapter 9. (14) T. A. Lehman and M. M. Bursey, “Ion Cyclotron Resonance Spectrometry”, Wiley-Interscience, New York, 1976.
0022-3654/81/2085-1091$01.25/00 1981 American Chemical Society
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The Journal of Physical Chemistry, Voi. 85, No. 9, 1981
be quite useful in measuring ion-molecule reaction rates and in following ion-molecule reactive pathways. We have initiated ICR studies of several ion-molecule reaction pathways which might prove important soot formation mechanisms. Reaction rates, branching ratios, and consecutive ion-molecule reactions can and will be determined in the controlled ICR environment. We have begun this series of investigations with the acetylene system because of the suggestions presented aboveFgbecause the reaction rate for the first step in this pathway
+ H2 C4H3+ + H-
C2H2+ + C2Hz -+ C4Hz+ +
zoolh 160
(3a) Reaction Time / m s
(3b)
has been measured15and found to be quite fast (1.41 X lo* cm3/s), and because earlier workers had reported the occurrence of ion-molecule condensation reactions in acetylene studied by high-pressure mass spectrometry.16-19 In this paper, we report details of several additional reactions which consecutively follow (3), including rate constants which are found to be sufficiently rapid to suggest that ion-molecule condensation reactions are important in sooting flames.
Experimental Section Two pulsed ICR mass spectrometers, one at the National Bureau of Standards (NBS), and one at the University of Florida (UF), were used for these experiments. Descriptions of the pulsed ICR technique in general,20its application to the determination of ion-molecule reaction rates,21 and specific featuresz2of the instrument at the University of Florida have all been published. Purified acetylene (Matheson) was used as received after several freeze-pump-thaw cycles. ICR single resonance scans at very short delay times indicated no ions which could be attributed to impurities in the mass range ( m / e C 125) studied here. Because pressure in the UF ICR apparatus is measured by use of an ionization gauge located downstream from the analyzer cell, a means of calibrating the pressure in order to determine absolute rate constants was required. It was decided to use the previously reported15arate constant for (3) (assumed to be accurate) to calibrate the absolute pressure measurements in the ICR mass spectrometer. Using this procedure we found the measured pressures to be low by a factor of 4.2 f 0.5. The stated uncertainty reflects the combined error in the rate reported15afor (3) and in our rate measurements. This correction has been applied to all rate constants and pressures reported in this paper measured by use of the UF spectrometer. Pressures in the NBS ICR apparatus were obtained by calibrating the ionization gauge, used during kinetic runs, with a capacitance manometer, as previously describeda21 Rate constants calculated by using the two different pressure calibration schemes on the two different instruments agree to within their reported uncertainties. (15) (a) W. T. Huntress, Jr., Astrophys. J. (Suppl. Ser.), 33,495 (1977). (b) J. K. Kim, V. G. Anicich, and W. T. Huntress, Jr., J. Phys. Chem., 81, 1798 (1977). (16) P. S. Rudolph and C. E. Melton, J.Phys. Chem., 63,916 (1959). (17) M. S. B. Munson, J.Phys. Chem., 69, 572 (1965). (18) G. A. W. Derwish, A. Galli, A. Giardini-Guidoni, and G. G. Volpi, J. Am. Chem. Soc., 87, 1159 (1965). (19) J. H. Futrell and T. 0. Tiernan, J.Phys. Chem., 72, 158 (1968). (20) R. T. McIver, Jr., Rev. Sci. Instrum., 49, 111 (1978). (21) S. G. Lias, J. R. Eyler, and P. Ausloos, Int. J.Mass Spectrom. Ion Phys., 19, 219 (1976). (22) R. J. Dugan, L. N. Morgenthaler, R. 0. Daubach, and J. R. Eyler, Reu. Sci. Instrum., 50, 691 (1979).
Figure 1. Ion intensity curves as a function of delay (reaction) time between ion formation and detection for C2H2+,C4H2+, and C,H,+. Ions were formed by impact of 1 4 4 electrons during a 3-ms grid pulse. Neutral C2H2 pressure was 8.5 X lo-' torr, magnetic field strength -1.3 T, emission current 1 X IO-' A, trapping potentials +1.25 V, and other cell potentials -1.0 V.
-
4 ion 40$ Intensity
/ Arb. Units
,
0
0
0 Reaction Time / m s
Figure 2. Ion intensity curves as a function of delay (reaction) time for C6H4+and C6H5+taken under identical conditions to those in Flgure 1. In additional experiments the intensity of both ions was seen to remain constant from -200 ms to >400 ms reaction time.
For calculation of neutral number density, a temperature of 330 K has been used. Thermocouples mounted at one end of the NBS ICR cell and directly across the cell from the electron-emitting filament were used to obtain this average temperature in the center of the cell.
Results Ion cyclotron double resonance (ICDR) experiments and intensity vs. time plots were used to confirm the rapid conversion of CzH2+to C4H2+ and C4H3+. As reported p r e v i o ~ s l y , l ~these - ~ ~ secondary ions were found to react further with neutral acetylene via (4) and (5). This deC4H2' + C2H2 -+ C6H4' (4) C4H3'
+ CzHz
+
C&5+
(5)
termination was made by using ICDR and intensity vs. time plots. We see no evidence for products such as C6H3+ or C6Hz+which would result from Hz or H. loss from the intermediate ion-molecule complexes formed in (4) and (5). We presume that these products, formed by condensation, are collisionally stabilized. In the pressure range studied here, the product ions in (4) and ( 5 ) undergo approximately one ion-neutral collision every 5 ms, assuming a collision rate constant of 1 X lo* cm3/s. Reactions 4 and 5 were seen at pressures as low as 5 X lo4 torr and no contribution to the C6H4+signal intensity from C4H3: was found by using ICDR techniques, indicating that (6) is not C4H3+ + CzH2 ++ C&4+
+ H*
(6) an important channel. Figures 1and 2 display intensity vs. time plots at 8.5 X lo4 torr which demonstrate the
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The Journal of Physical Chemistty, Vol. 85,No. 9, 198 1 1093
Intensity 5o
/ Arb.
IO
and NBS, lead to 3.3 f 0.8 X and 2.1 f 0.3 X 10-lo cm3/s23for the disappearance rates of C4Hz+ and C4H3+, respectively. Over the pressure range 2 X lo4 to 3 X torr, we see no pressure dependence of the apparent disappearance rate constant for these two ions.
i'\ I
15
I
45
30
,
60
75
Reaction Time / rns
Semilog plots of C4H2+ and C4H3+signal intensity as a delay (reaction)time at a C2H, pressure of 8.5 X lo-' torr. Data were taken directly from Figure 1. Flgure 3. function of
behavior expected from the sequential reaction scheme (3), (41, and (5). When the cell pressure was raised to -2 X 10" torr and the ion intensities monitored at longer delay times, reactions 7 and 8 were also observed. Decay of C6H6+and CGH4+ + C2H2 C & 3 + (7) C&6+
+ C2Hz
--
-
C8H7+ C & j + -t He (8)
C6H4+due to these reactions can be seen in Figure 2 in the 50-160-ms reaction time region. No evidence was seen for H. or H2 loss from the [C8Hs+ltcollision complex, which would lead to C8H5+or C8H4+.Under these conditions low intensities of CloH6+and CloH8+ ions were also detected, suggesting yet another step in this sequential reaction chain. However, definitive experiments as to the exact ion-molecule reactions forming these species have not yet been carried out. Because C4H2+ and C4H3+are intermediates in a sequential reaction scheme, and because they are certainly produced initially via (3) with excess internal energy, care must be taken in extracting quantitative disappearance rate data. Using a pressure determined as indicated in the Experimental Section, we analyzed semilog plots of the signal intensity of these two ions vs. time, taken from Figure 1and nine other curves similar to those in Figure 1, to provide absolute reaction rates for (4) and (5). Data from Figure 1 is plotted in Figure 3. For most decay curves analyzed, curvature was evident in the semilog plots at short reaction times. This may be seen particularly for C4H3+in Figure 3. We believe such behavior can be attributed to the shorter lifetimes of (C6H5+)*and (c6H4+)* collision complexes due to excess internal energy in the C4H2" and C4H3+reactants and thus in the collision complexes. The shorter-lived collision complexes cannot be stabilized at the pressures of these experiments and thus dissociate back into reactants, leading to the lower apparent reaction rate at shorter reaction times. Support for this explanation is provided by our observation that the curvature becomes much less pronounced at higher pressures (Le., the decay of C4H3+and C4H2+become exponential at earlier times), since both the reactant ions and the shorter-lived collision complex are more likely to be collisionally stabilized at higher pressures. We thus analyzed only the linear portions of the semilog plots such as shown in Figure 3 to obtain disappearance rate constants for C4H2+and C4H3+.A least-squares fit to the points in Figure 3 (shown as the two straight lines on the figure) leads to 3.3 X and 2.2 X 10-locm3/s, respectively, for C4H2+ and C4H3+disappearance. These rate constants and those from nine similar semilog plots, collected at both UF
Discussion The extensive ion-molecule condensation reaction sequences seen previously at high p r e s ~ u r e s land ~ ' ~ reported torr) suggest quite here at much lower pressures (13 X strongly that an ionic path to soot formation may be important in certain flames. One might speculate that this should be particularly true in flames which have reactive regions containing relatively high concentrations of olefins. The first reactions in the sequence, (3), (4), and (5), have rates (reported15and measured here) which are quite rapid. While the initial step in this sequence, (3), may or may not be important in flames, relatively high concentrations of C2H3+have been formed presumably via the reaction CHO+ C2H2 C2H3++ CO (9) The C2H3+ species reacts with C2H (klo = 2.5 X cm3/s) to form C4H3+e x c l ~ s i v e l y ~ J ~ ~ C2H3' + C2H2 --+ C4H3' + H2 (10) thus providing an additional channel feeding into the condensation reactions discussed here. The behavior of C6H5+signal intensity vs. time seen in Figure 2 strongly suggests that two noninterconverting isomers, one reactive and one nonreactive, are formed in this reaction chain. Similar behavior has recently been seen for C4H4+ions produced from benzene by electron impact.24 Our experiments to date do not offer further information as to the identity of the two isomers. Although the possibility that gaseous C6H5+ions are acyclic has been suggested,25most recent work26has been interpreted by assuming a phenylium structure. Addition of C2H2to the C8H6+species reported here to produce (presumably naphthalenic) CloH8+ions, suggested by our results but not yet confirmed, is quite exothermic and certainly a reasonable process. Thus mono- and bicyclic aromatic ions, postulated5 as important soot precursors, appear to be reasonable products of this ion-molecule reaction chain. I t was somewhat surprising that reactions such as (4) and (5), involving collisional stabilization of a (presumably) long-lived collision complex, are observed at such relatively low pressures, while the more straightforward reactions such as ( 6 ) or (ll),in which H- or H2 is eliminated from C4H2' + C2H2 * C6H3+ + He x* CGH2" + H2
+
-
(11) the complex, are not seen. Examination of existing thermochemical data27indicates, however, that reactions such as (6) and (11)are endothermic by 35-100 kcal/mol. I t is interesting to note that the similar Ha and Hz elimination reactions (reactions 3a and 3b) are by contrast exothermic and the C4H4+collision complex formed is apparently sufficiently short-lived that it cannot be col(23) Reported uncertainties are 3 times the 95% confidence limits for the mean of 10 determinations, reflecting our assessment of both the scatter in rate constant measurements and the possible systematic error in absolute pressure determination. (24) P. J. Ausloos, submitted for publication. (25) A. W. Johnstone and F. A. Mellon, J. Chem. SOC.,Faraday Trans. 2, 1209 (1972). (26) M. Speranza, M. D. Sefcik, J. M. S. Henis, and P. P. Gaspar, J. Am. Chem. SOC.,99, 5583 (1977), and references contained therein. (27) H. M. Rosenstock, K. Draxl, B. W. Steiner, and J. T. Herron, J. Phys. Chem. Ref.Data, 6, Suppl. 1 (1977).
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lisionally stabilized (and thus observed) in the pressure range of these experiments, although it has been observed in high-pressure work.lg We also see no C6H6+ions at any delay times in our low-pressure studies. These ions have been reported in acetylene at higher pressure^,^^ presumably arising from reaction of the collisionally stabilized C4H4+ion with C2H2. Previous low-pressure ICR studies26 of C6H5+reactions have also noted the existence of longlived complexes produced in reactions such as (12) and (13). C6H5+ + Hz C&7+ (12)
--
C6H5+ + CH4
C,HS+
(13) The fact that we see no pressure dependence of the C4H2+and C4H3+disappearance rate in the high lo* and low torr range indicates that the "high pressure" limit for these association reactions has been attained at these relatively low pressures. Thus the lifetimes of the [C6H5+It and [CsH4+It,except at shorter reaction times as mentioned above in the Results section, must be sufficiently long ( - 5 ms) that a significant fraction of them are sta-
bilized by collisions even at the low pressures of our experiments. Our initial experiments involving ion-molecule condensation reactions in acetylene have confirmed at low pressures interesting sequential processes which may be of definite relevance to soot formation. We are currently studying other reactions of these and similar ions with flame gases. We plan both reactivity studies with ions produced from different neutral precursors and laser photodissociation studies in order to confirm the structures of the larger ions reported here. Following the condensations as even larger, possibly bicyclic, species are formed is also of great interest and we are working actively in this area.
Acknowledgment. J.R.E. thanks the personnel of the Naval Research Laboratory, especially Dr. J. R. McDonald, for hospitality and helpful discussions during his 1980-81 Intergovernmental Personnel Act sabbatical appointment. He is also indebted to Drs. P. J. Ausloos and S. G. Lias for use of the NBS pulsed ICR spectrometer and for additional suggestions and comments about this work.
Dynamical Calculation of the Temperature Dependence of the Activation Energy for a Chemical Reaction from 444 to 2400 K Normand C. Blals," University of California, Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87545
Donald G. Truhlar," and Bruce C. Garrettt Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455 (Received: January 3 1, 198 1)
The quasiclassical trajectory method with Monte Carlo and importance sampling and with the Tolman interpretation of the activation energy has been used to calculate the activation energy for a bimolecular reaction at three temperatures in the range 444-2400 K. The activation energy is found to increase by 6 kcal/mol over this range.
It is unusual for the temperature dependence of a chemical reaction rate to be measured over a temperature range of 2000 K or more. Yet for many applications, such as combustion, it is necessary to estimate reaction rates at very high temperatures even though measurements may exist only at temperatures much closer to room temperature. The most common method has been to assume a linear Arrhenius plot [In h(T) vs. 1/27, Le., a temperature-independent activation energy. Recent experimental results, however, have shown many deviations from linear Arrhenius behavi0r.l This is a situation where theoretical guidance can be very helpful. Transition-state theory often indicates a significant temperature dependence of the activation energy,lb4*gbut transition-state theory may suffer from errors due to trajectories that recross the transition-state dividing surface. Recrossing effects become more important as the temperature increases and this lessens our confidence in the predicted high-T rate constants and activation energies. Recrossing effects can be minimized by using variational transition-state theory,2 'Chemical Dynamics Corporation, 1550 W. Henderson Road, Suite N140, Columbus, Ohio 43220.
or they can actually be calculated by using quantal-scattering theory or performing trajectory calculations. These methods, as applied over wide temperature ranges to collinear model reactions, have also predicted significant temperature dependences of the activation energy in some cases.3 In this communication we report a direct calculation of the temperature dependence of the activation energy from three-dimensional trajectory calculations employing an accurate potential energy surface. The results are compared to a transition-state theory prediction and to available experimental results. ~~~~~
~
(1) See, e.g., (a) D. G. Truhlar and R. E. Wyatt, Annu. Reu. Phys. Chem., 2 7 , l (1976); (b) B. Perlmutter-Hayman, Prog. Inorg. Chem., 20, 229 (1976); (c) W. C. Gardiner, Acc. Chem. Res., 10,326 (1977); (d) T. C. Clark, J. E. Dove, and M. Finkelman, Acta Astronaut., 6,961 (1979); (e) R. Zellner, J. Phys. Chem., 83,18 (1979); (f) A. R. Ravishankara and P. H. Wine, J. Chem. Phys., 72, 25 (1980); (8) R. F. Heidner, 111, J. F. Bott, C. E. Gardner, and J. E. Melzer, ibid., 72, 4815 (1980); (h) and references therein. (2) D. G. Truhlar and B. C. Garrett, Acc. Chem. Res., 13,440 (1980). (3) See, e.g., (a) D. G. Truhlar and A. Kuppermann, J. Chem. Phys., 56, 2232 (1972); (b) G. C. Schatz, J. M. Bowman, and A. Kupperman, J. Chem. Phys., 63, 674, 675 (1975); (c) D. G. Truhlar and J. C. Gray, Chem. Phys. Lett., 57,93 (1978). See also J. C. Gray, D. G. Truhlar, and M. Baer, J. Phys. Chem., 83, 1045 (1979).
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