hydrocarbon chain reactions: time-resolved

4962

J. Phys. Chem. 1982, 86,4962-4973

Laser-Initiated CI,/Hydrocarbon Chain Reactions: Time-Resolved Infrared Emission Spectra of Product Vibrational Excitation David J. NesbRt and Stephen R. Leone' Joint Institute for Laboratory Astrophysics, National Bureau of Standards and University of Colorado, Department of Chemistry, University of Colorado, Boulder, Colorado 80309 (Received: July 1, 1982)

Rapid gas-phase chain reactions of Cl,/hydrocarbon mixtures are initiated by selective laser photodissociation of C12 and investigated by time-resolved infrared emission spectra of chain products. The basic two-center chain chlorination reaction sequence is C1- + R H L HCl(u) + Re, R. + Clz 5 RClt + C1.. A t low hydrocarbon reagent pressures ([RH] 5 20 Pa), analysis of emission from HCl(u) is used to determine the chain rate constants kl and k2 under controlled room temperature conditions. At higher pressures of RH (2300Pa) the chain reaction generates vibrationally excited polyatomic products, RCl*,at rates comparable to or faster than relaxation of R,Cl*.Time- and wavelength-resolved emission from vibrationally hot RCl*is used to investigate chain reaction behavior in this regime of rapidly rising temperatures. Extensive vibrational emission from reagent molecules is also observed, indicating a rapid and complete sharing of product vibrational excitation with the reagent molecules. The dispersed emission spectra of the products (3.0-15.0 pm) is fit by a simple model that assumes a common vibrational temperature, Tvib, and varies the relative concentrationsof the emitters. Product isomer ratios obtained from these spectral fits are in good agreement with literature values. Vibrational temperatures as high as 700 K are observed. These are significantly hotter than the measured bulk gas temperatures (400-500 K), which suggests that the vibrational and translational degrees of freedom are not in equilibrium under the rapid burning conditions in these systems.

In several earlier works,13J4we presented experimental I. Introduction and mathematical analyses of real-time chain kinetics inGas-phase chain reactions play a key mechanistic role itiated by selective photolysis with low power laser pulses. in an impressively wide variety of chemical arenas, from The advantages of the technique for quantitative study ozone depletion in the atmosphere; to large scale industrial of chain reaction phenomena are several. (1)The system syntheses,2 to the highly involved mechanisms of comis prepared in a well-defined initial state on a time scale bustion phenomena? Interest in these varied systems has which is short compared to typical reaction times. (2) The stimulated a tremendous amount of research over the past evolution of the chain is monitored in real time, and condecades directed toward a detailed understanding of sequently the important chain features of induction, chemical chain processes from different experimental propagation, and termination can be temporally resolved. perspectives. Much of the early chain reaction literature This transient deconvolution of a complex chemical chain concentrated on the behavior of combustion of bulk gas reaction provides a key to quantitative kinetic analysis that mixtures as a function of temperature, pressure, reagent stoichiometry, and radical scavenger c ~ n c e n t r a t i o n . ~ ~ would be exceedingly difficult to obtain in the steady-state regime. (3) The radical densities, and hence chain comPostexplosion analysis of the products, although somewhat plexity, can be varied over several orders of magnitude by indirect, can be successfully used to infer the identity of suitable control of the laser beam pulse energy density. relevant chain radicals and combustion pathways.' More The technique has been successfully used to investigate recently, the ability to generate and detect radicals has linear kinetics in a number of chain chlorination systems, become sufficiently sensitive to probe individual chemical where a substantial diversity of chain behavior has been steps postulated from these bulk studies.8 Our underpredicted, observed, and quantitatively analyzed. standing of isolated radical reactions has been advanced tremendously by development of flow tube techniquesgJO and time-resolved photolysis experiments.l' The dilemma, (1) Stief, L. J.; Michael, J. V.; Payne, W. A.; Nava, D. F.; Butler, D. however, is that the majority of chain reaction processes M.; Stolarski, R. S. Geophys. Res. Lett. 1978, 5, 829. (2) Wolfrum, J. 'Process for the Production of Olefinic Double Bonds of practical significance, e.g., those present in combustion, by Hydrogen Halide Elimination", German patent, Max Planck Geoccur typically under very complicated chemical and selleschaft zur Forderung der Wissenschaften. physical conditions. Consequently, a complete analysis of (3) Benson, S. W.; Nangia, P. S. Acc. Chem. Res. 1979, 12, 223. (4) Bodenstein, M. 2.Phys. Chem. 1913, 85, 329. important chain reaction phenomena requires a careful (5) Semenoff, N. N. "ChemicalKinetics and Chain Reactions";Clarsynthesis of both isolated radical kinetic studies and bulk endon: Oxford, 1935. combustion characteristics such as rapid energy release, (6) Baldwin, R. R. Trans. Farady SOC.1956, 52, 1337, 1344. (7) Sagulin, A. 2.Phys. Chem. 1928, B1,275. transfer, and relaxation, local chain heating and temper(8) Voevodskii, V. V.; Kondrat'ev, V. V. "Determination of Rate ature gradients, explosive turbulence and mixing, etc.12 It Constants for Elementary Steps in Branched Chain Reactions", in is of practical interest, therefore, to develop better tech"Progress in Reaction Kinetics"; Pergamon: New York, 1960. niques for monitoring real-time chain kinetics in systems (9) Howard, C. J.; Evenson, K. M. J. Chem. Phys. 1974, 61, 1943. (10) Arrington, C. A,; Brennen, W.; Glass,G. P.; Michael, J. V.; Niki, whose behaviors range from simple to extremely complex. H. J. Chem. Phys. 1965,43, 525. Such techniques would aid in bridging the gap between (11) (a) Atkinson, R.; Hansen, D.A.; Pitts, J. N., Jr. Ibid. 1975, 62, studies of isolated radical chemistry and more complex 3284. (b) Atkinson, R.; Hansen, D. A.; Pitta, J. N., Jr. Ibid. 1975,63,1703. (12) Frank-Kamenetskii, D. A. "Diffusion and Heat Exchange in combustion phenomena. *Staff Member, Quantum Physics Division, National Bureau of Standards.

Chemical Kinetics"; Princeton University Press: Princeton, 1955. (13) (a) Nesbitt, D. J.; Leone, S. R. J. Chem. Phys. 1980, 72, 1722. (b) Ibid. 1981, 75, 4949. (14) Dolson, D. A.; Leone, S. R. J. Chem. Phys. 1982, 77, 4009.

This article not subject to US. Copyright. Published 1982 by the American Chemical Society

Laser-Initiated CI,/Hydrocarbon Chain Reactions

All of the previous chain studies have been carried out at low enough reagent pressures, slow enough propagation rates, and sufficiently large excess buffer gas concentrations to maintain the bulk gas temperature at a constant, room temperature value. In the studies described here, the chain exothermicities are several times greater and the chain rate coefficients are sufficiently large to allow rapid release of chemical energy on a time scale competitive with thermal moderation. Thus we can study the nonlinear effects associated with rapidly rising intemal temperatures, i.e., the onset of explosive behavior. The systems investigated here are C12/hydrocarbon chain reactions. The basic mechanism of the chain is C1. + RH HCl + R. Re Clz RC1+ C1*

+

--

AH z -130 kJ/mo115J6 where RH is an organic species with a suitably reactive hydrogen substituent e.g., butane). It is important to note that the overall chain exothermicity is quite large, -130 kJ/mol. Additionally, the chain reaction rates can be extremely fast, and reagent gas mixtures at pressures of several hundred Pa “burn” rapidly to completion on the millisecond time scale (1 Pa = 7.5 X torr). As a consequence of these two effects, the laser initiated Clz/ hydrocarbon chain reactions can liberate a substantial amount of chemical energy in a very short time. We take as a significant measure of the nearly explosive behavior of these chain reactions that pressure rises of up to 10% are observed in the flow cell when reagent pressures of a few hundred Pa are illuminated by a weak (dl mJ) pulsed laser. At higher reagent pressures (51300 Pa), even a sharp audible sound is heard from the cell. Internal and translational excitation of the chain products is anticipated to be quite high. As is described in detail below, sufficient energy is released in these laser-initiated chain reactions to observe infrared emission from chain products which have vibrational temperatures as high as 700 K. Hydrogen chain chlorination systems are of significant interest to study for several reasons: (1) Such chain reactions are of practical importance in industrial scale production of organic chlorides.” Analysis of chain reaction behavior in real time may prove useful in diagnosing and controlling product branching ratios, and thereby optimizing yields. ( 2 ) In the nearly explosive regime of chain reaction behavior, the high vibrational excitation of the products could dramatically alter the rates and mechanisms of the overall chain evolution via vibrational enhancement of thermoneutral or endothermic reaction channels. By monitoring the chain progress in real time, it may be possible to observe the onset of new reaction pathways and the enhancement of kinetic rate coefficients. (3) Techniques developed to probe the degree of polyatomic vibrational excitation in hydrocarbon chlorination systems may have significant application in studies of analogous hydrocarbon oxidation phenomena as well. This paper focuses specifically on chain reactions of Cl,/n-butane and Cl,/ethane. In particular, we confine our attention to three areas: (1)a chain kinetic analysis of the rate constants under room temperature conditions; ( 2 ) the spectral analysis of the higher temperature chain emission as a probe of isomer branching ratio and overall (15) ‘JANAF Thermochemical Tables”, 2nd ed. Natl. Stand. Ref. Data Ser., Natl. Bur. Stand. 1971, No. 37. (16) ‘Handbook of Chemistry and Physics”, Weast, R. C., Ed.; Chemical Rubber Co.: Cleveland, 1978; 59th ed. (17) Bender, H. U.S. Patent 2200254-5, May 14,1940 (to Dow Chemical Co.).

The Journal of Physical Chemistry, Vol. 86, No. 25, 1982 4963

chain evolution; and (3) the partitioning of chain exothermicity between vibrational and translational degrees of freedom. The interesting question of the effect of a sudden release of chemical energy on the chain kinetics is left for later investigation. The experimental strategy is as follows. The chain chlorination of hydrocarbons is initially investigated under conditions where thermal perturbations are successfully eliminated. This requires studying the chain reaction by emission only from HCl(u=l) at low, nonstoichiometrichydrocarbon/chlorine ratios in the presence of excess inert buffer gas. In this regime, polyatomic product emission is effectively quenched, analysis of the chain kinetics is greatly simplified, and detailed measurements of the relevant chain rate constants are obtained. The chain reactions are then investigated in the near stoichiometric, quasi-explosive regime. Under these conditions, bright infrared chemiluminescence from highly vibrationally excited polyatomic products of the chain is readily observed. The emission in the 3.0-15.0-pm region is spectrally resolved, and provides an infrared emission “fingerprint” of the chain products. From the wavelength dependence of the emission, we characterize the identity, relative concentration, and degree of internal excitation of the products. From the time dependence of these spectra, the full temporal evolution of the chain is monitored. Branching ratios into product isomers are measured in real time. The effects of reagent exhaustion as well as the concurrent generation of secondary chain products are observed and studied in detail. The partitioning of energy between vibration and translation is obtained from several independent measurements of the vibrational and translational temperatures of the rapidly heating system.

11. Experimental Section The basic apparatus has been previously described in the 1iterat~re.l~ We restrict ourselves to a brief description, with particular emphasis directed toward the modifications required for these studies. The apparatus consists of a pulsed laser photolysis source, flow reactor cell, infrared detector, and transient signal averaging electronics. Chlorine, argon buffer gas, and the desired hydrocarbon are mixed in a continuousflow and pumped at low pressure rapidly past the laser interaction region. The chain reactions are initiated by pulsed laser photodissociation of Clz to produce the initial C1- radicals. The UV laser pulses are generated from either a frequency tripled Nd:YAG (355 nm, 10-ns pulse) or a frequency doubled, flashlamppumped dye laser (300 nm, 2-ps pulse). So that the hydrogen abstraction reaction by C1. could be studied separately, pulses of frequency quadrupled Nd:YAG (266 nm, 10-ns pulse) are used to photodissociate SzClz SZCL+ CL. The SzC12precursor appears to block the second step of the chain mechanism.13J8 The laser beam is expanded to 1-3 cm in diameter and attenuated with neutral density filters (pulse energies typically 51 mJ). This ensures that only a minor fraction of the molecular Clz is photolyzed,lgand the subsequent kinetics can be monitored initially in a strictly pseudo-first-order regime. The quartz flow cell is coated uniformly with halocarbon wax to minimize radical recombination reactions. Both Clz and the desired hydrocarbon are injected into a flow of argon buffer gas through 1-mm2 nozzle inlets facing upstream to promote rapid mixing. Gas flows are measured with calibrated electronic flowmeters and regulated with monel metering valves. Partial pressures of the

-

(18) Braithwaite, M.; Leone, S. R. J. Chem. Phys. 1978, 69, 840. (19) Seery, D. J.; Britton, D. J. Chem. Phys. 1964, 68,2263.

4964

Nesbitt and Leone

The Journal of Physical Chemistry, Vol. 86, No. 25, 1982

reagents are then calculated from relative flow rates and total cell pressures. Linear flow velocities of 220 cm s-l are used to eliminate prereaction of the reagent mixture, as well as to minimize effects from spatial propagation of the chain reaction upstream. These extremely long-lived chain reactions necessitate externally controlling the laser pulse repetition rate down to 0.5 Hz in order to prevent pulse-to-pulse accumulation of chain products. Under typical experimental conditions, the laser-initiated chain chlorination proceeds rapidly until either (i) the limiting reagent is exhausted in the laser illuminated volume or (ii) second-orderradical recombination processes significantly deplete the initial chain radical concentrations. All experiments are performed in a regime where the results are completely insensitive to further changes in gas flows or laser pulse repetition rate. Infrared fluorescence signals from the chain reaction products are observed as a function of time after the laser pulse by either a photovoltaic 77-K InSb or a photoconductive 4-K Ge:Cu detector. Both detectors have a rise time less than 1 vs. Chain emission signals vs. time from the infrared detectors are preamplified and collected by a fast transient recorder. The digitized signals from each laser pulse are then transferred to a signal averager, summed to enhance signal-to-noise, and recorded for later data analysis. Sufficient pulses are averaged to ensure S / N in excess of 20:l. In the low hydrocarbon pressure regime, where chain emission is predominantly from HCl(u=l-.O), the InSb detector is used with fixed interference filters to monitor the infrared fluorescence. A 1-cm cold gas cell containing approximately lo4Pa of HCl(1 Pa = 7.5 X torr) is used to identify unambiguously the emitting species as HCl(u=l) by resonantly absorbing the HCl(u=l-+) emission. In higher hydrocarbon pressure regimes, emission from highly vibrationally excited polyatomic chain products begins to predominate and can be observed at wavelengths over the entire "fingerprint" region of the infrared spectrum. In this case, the chain reaction emission is dispersed by rotation of 77-K cooled circular variable filters (CVF) in front of the Ge:Cu detector element. A full record of the emission intensity vs. time is obtained for each wavelength setting of the CVF. From these time-resolved records, after suitable normalization for laser power, number of laser pulses, and the wavelength-dependent detectivity, several spectra of the chain emission are constructed as a function of time after the laser pulse. Calibrations of both the InSb and Ge:Cu detectors for relative detectivity vs. wavelength are performed by measuring relative signal strength from a standard blackbody source. Details of the calibration procedure are described elsewhere.20 Gases are taken either from 12-L Pyrex storage bulbs or directly from a lecture bottle-regulator combination built permanently onto the vacuum system. Small amounts of noncondensable gases at 77 K (presumably air impurities) in the original gas cylinders can dramatically reduce the chain emission intensity. Thus the C12 (>99.5%), n-butane (>99.5%), and ethane (>99%) are scrupulously degassed via several freeze-pumpthaw cycles prior to experimentation. Extensive purification under vacuum by bulb-to-bulb distillation produces no further changes in the observed kinetics.

initiation: Cl2 22 c1. + c1.

C1.

+ RH R.

kl -+

R*

+ C1,

+ HCl(V=O,l)

k2

(20) Nesbitt, D. J. Ph.D. Thesis, University of Colorado, 1981.

AH,,, RClt

+ C1.

deactivation: HCl(u=l) + M

AH

= -34

kJ/mo115J6 (2)

= -96

kJ/mol

kQM

HCl(u=O) + M

(3)

(4)

kQlM

RClt + M RC1+ M (5) where RH is n-butane, and RC1 is either 1- or 2-chlorobutane. The $ indicates vibrational excitation. Laser pulse energies of 51 mJ are chosen such that of the limiting reagent density, radical densities are thus ensuring that the chain evolution can be accurately characterized by pseudo-first-order kinetics. Thermal perturbations of the chain reaction are eliminated by using a large excess of Cl2 [600 Pa] and Ar [650 Pa] to moderate the gas temperature. The excess C12and Ar also serve to relax the vibrationally excited polyatomic product efficiently. The evolution of the chain is monitored by infrared chemiluminescence from HC1 with an InSb detector and fixed interference filters. Observed emission in the 3.2-3.6-pm region is attributed solely to the HCl(u=l) product of reaction 2, which is verified by absorption in a HC1 cold gas filter cell. HCl(u=l) appears to be formed only in a small fraction of the reactive collisions, which is consistent with the fact that formation of even the thermodynamicallyfavored secondary butyl radical is only 34 kJ/mol exothermic, whereas excitation of the u = 1level requires 34.5 kJ/mol. The kinetic analysis of laser-initiated chain reactions in the simple, pseudo-first-order regime is well understood and has been rigorously tested in earlier work.13J4 The laser pulse generates an initial concentration of C1. radicals at t = 0, which react with butane to form HCl(u=O,l) and butyl radicals. The butyl radicals react in turn with excess molecular chlorine to regenerate C1- radicals. It is important to note that there are two possible chain reactions present, which form two product isomers, 1- and 2chlorobutane. A complete kinetic analysis of multiple chain reactions is presented elsewhere13band will not be addressed in this paper. For the present purposes it is sufficient to consider an effective total rate constant, k2, for the regeneration of C1. radicals, which represents a phenomenological average of the individual isomer rates. The chain radicals rapidly approach their steady-state concentration values

-

with an induction time constant Tind

111. Cl,/Butane-Low Butane Pressure: Chain Reaction Measurement of k , , k 2 For n-butane pressures 520 Pa, the relevant chain kinetic processes are

(1)

propagation:

= (kl[RHI + k!2[C1211-'

(8)

Once the steady-state concentrations have been attained, the C1. radicals generate HCl(u=O,l) by reaction with excess butane at a fixed chain rate


Laser-Initiated CI,/Hydrocarbon Chain Reactions I

-Ln

._

c

CI, CI'+C,H,, C,Hs'+ CI,

I

-f 1 lo)

I

-y k

I

C12-Cl+Cl C l +C,H,,4C,H,+HCI

iv:o,,i

[C12] = 581 Pa

Ci'+Ci' C,H,'+HCI(v=O,l) C4HsCI+CI'

[C4Hlo] = 4 0 P o

, r

-3

-

is

-

k,/k,s26?6

I

- -

-

_

-~ I

,

I

0 01

0 03

0 02

[C.HIOI'[C~*!

1

I

0

1

IO0

1

1

I

200

I

300

1

1

400

J

t (,used

Figure 1. Typical chain emission plot from the Cl,ln-butane chain reaction. The low butane pressure and the high chlorine and argon buffer gas pressures are chosen for rapid thermai moderation and also to eliminate interfering emission from polyatomlc chain products. The fast induction feature, which corresponds to initial equilibration of CI. and C,Hg. radicals, occurs within 1 ps of the laser pulse. The emission , reflects the competition between rises with a time constant T ~which steady-state chain production of HCI(v = 1) and vibrational relaxation by n-butane (seetext for details). The decline in emission at long times (>500 ps) is due to chain exhaustion of the rate limiting reagent, butane.

[C,H,,]

15

IO

05

llO"moIecu~e/cm'l

This constant production rate would generate a linearly rising concentration of HCl(u=l) were it not for the vibrational relaxation processes that remove HCl(u=l) from the system. From the exact solution of the k i n e t i ~ s , one '~~ finds kchain

-(1

kQ

- exp(-kQt))(10)

where the quantity

represents the concentration of HCl(u=1)produced during the rapid induction period, and k is the total phenomenological rate of relaxation of HC$u=l) by all the species in the chain mixture. Sample HCl(u=l) emission data from the C12/butane chain are shown in Figure 1, which can be seen to be in qualitative agreement with the predictions of eq 10 and 11. At t = 0, the C1. atoms are generated by the laser pulse and rapidly come into a dynamic equilibrium with butyl radicals. The induction period can be estimated with eq 8 and the values of kl and k2 obtained below to be less than 1ps, and is not observable at these experimental pressures. Once the steady-state concentration of C1. radicals is attained, the emission signal will increase according to eq 9 as HCl(u=l) is produced. The observed exponential rise to a steady-state HC1 emission intensity results from, and therefore provides a measure of, the collisional relaxation of HCl(u=l). On a much longer time scale of milliseconds, the steady-state emission slowly decays from termination processes which have not been considered in this linear kinetic treatment. In this low butane pressure regime the major contributor to chain termination is exhaustion of the n-butane reagent, which implies chain lengths in excess of several hundred cycles (see Appendix). The relative rate of HCl(u=l) production, kchain,is extracted by measuring the initial rate of growth of the emission ~ i g n a 1 . lBy ~ ~repeating this measurement for a variety of reagent concentration ratios, one obtains a family

Figure 2. Kinetic data plots for Cl,ln-butane chain processes. (a) Rate ratio of the two chain propagation steps, k , and k,. (b) Independent measurement of k ,, utilizing S,CI, hv S,CI CI- as the photolysis precursor of CI. radicals. (c) Vibrational relaxation of HCI(v=l) by n-butane.

+

-

+

of chain emission signals and corresponding values of k&. One full cycle of the chain involves a sequential reaction of both propagation steps. Consequently, kchain as a function of reagent pressures probes the relative propagation rates and can be used to extract kinetic information on the rate ratio, kl/k2. Equation 9 for kchaincan be reexpressed as [RH][Cl,] [laser energy]

c:

[i+L""']

(12)

k, [Cl,l

kchain

In eq 12 [Cl], is assumed to be proportional to both [Cl,] and the measured laser pulse energy, since the gas mixtures are optically thinlg and the fractional dissociation of C12 is small. A plot of the left-hand side of eq 12 vs. [RH]/ [Cl,] yields a straight line whose slope-to-intercept value is kl/k2. Data on kchain in the C12/butane chain system have been measured for approximatelyconstant [Clz],[Ar], and laser pulse energy, but with butane pressure varied from 0 to 20 Pa. The plot for eq 12, shown in Figure 2a, exhibits excellent agreement with the above predictions. The slope-to-intercept ratio, which we identify from eq 12 to be k1/k2, is found from a linear least-squares fit of the data to be 26 f 6. Uncertainties quoted for all measurements in this paper represent two standard deviations. An independent value for k , is obtained in a separate series of experiments with SZCl2as the photolysis precursor of C1- chain radicals. It has been shown previously'* that S2C12produces a clean source of C1 atoms via S2Cl2 2!+S,Cl

+ c1.

4966


but without sustaining the second chain reaction step analogous to eq 3. The C1. atoms generated in this fashion simply react once with butane at a rate k,[butane] to produce HCl(u=O,l). If the experiment is performed in a regime where production of HCl(u=l) is more rapid than deactivation, the rise time of the HC1 emission intensity is (k,[butane]J-'. A plot of reciprocal rise time of the HC1 emission vs. butane pressure is a straight line with slope k,, as is demonstrated in Figure 2b. The least-squares linear fit to the data is excellent, yielding a value for k, = 1.8(f0.2) X cm3 molecule-' s-'. This rate constant is essentially gas kinetic and is in good agreement with recent measurements with discharge flow tube, resonance fluorescence techniques,,' where kl was found to be 2.2 X cm3 molecule-' s-'. From the measured values for k l / k z and kl,we obtain kz = 6.8(i1.5) X cm3 molecule-' s-'. There are no previous measurements of this rate coefficient in the literature with which to compare. However, rates for CH,. + Clz (k = 1.3 X cm3 molecule-' s - ' ) ~ ~and CH3CHz. + C1, (k = 4.0 X cm3 molecule-' s-'),~are of a similar magnitude and establish the correct trend. As previously mentioned, the rise time of the chain reaction emission reflects the deactivation rate of HCl(u=l) by the gas mixture. Although Clz and Ar are the dominant components of the mixture, vibrational relaxation of HCl(u=l) by these species under our conditions is a minor contribution to the total dea~tivation.,~Near-resonant vibration-to-vibration (V-V) transfer to the CH stretch manifold of butane (ACH 3.35 pm,25AHCl 3.46 pm26) is anticipated to be extremely efficient, and thus should dominate the chain rise time behavior. A plot of reciprocal chain rise time vs. butane pressure, presented in Figure 2c, indicates excellent agreement with these predictions. A linear least-squares fit to the data yields a value for kgbume = 1.5(*0.2) X lo-'' cm3 molecule-' s-'. The intercept of the kinetic plot is zero to within the uncertainty of the fit. To the best of our knowledge, there are no previous measurements of HCl(u=l) relaxed by n-butane with which to compare. However, the rate is unexpectedly a factor of four slower than recent measurements of HCl(u=1-5) relaxation by isob~tane.~'

-

-

IV. C12/Butane-High Butane Pressure: Explosive Chain Evolution A . Initial Observations. As discussed above, chain reactions initiated in nonstoichiometric reagent gas mixtures at low butane pressures (i.e., [n-C4Hlo]5 20 Pa, [Cl,] 500 Pa) proceed slowly with respect to vibrational relaxation of the higher frequencies of the polyatomic species, and emission is observed solely from the vibrationally excited HCl(u=l) product. The intensity of HCl(u=l) chain emission is predicted from eq 10 and 11 to decrease with increasing butane pressure due to enhanced vibrational deactivation. Indeed, this effect is observed as the butane concentration is varied from 20 to 100 Pa. For butane pressures approaching 300 Pa, however, the chain reaction behavior begins to depart dra-

-

(21) Lewis, R. S.; Sander, S. P.; Wagner, S. G.; Watson, R. T. J . Phys. Chen. 1980,84, 2009. (22) Kovalenko, L.; Leone, S. R., to be submitted for publication. (23) Goldfiiger, P.; Huybrechta, G.; Mortens, G.; Meyers, L.; Olbregb, J. Trans. Faraday SOC. 1965, 61, 1933. (24) (a) Craig, N. C.; Moore, C. B. J. Chem. Phys. 1971,55, 1622. (b) Steele, R. V., Jr.; Moore, C. B. Ibid. 1974, 60, 2794. (25) Shimanouchi, T. J . Phys. Chem. Ref. Data 1977, 6. (26) Huber, K. B.; Herzberg, G. "Constants of Diatomic Molecules"; Van Nostrand-Reinhold: New York, 1979. (27) Berquist, B. M.; Dzelzkalns, L. S.; Kaufman, F. J . Chem. Phys. 1982, 76, 2984.

Nesbitt and Leone

m LL

t

i

i II

'\

(msec)

i

\,

,2 ------L -----

30

35

40

X (pm)

Figure 3. (a) Typical emission from Cl,ln-butane chain reaction in the 3.3-3.5-pm region under nearly stoichiometric reagent concentrations, where copious CH stretch emission from vibrationally excited chain products is observed. Signals are typically 100 times stronger than observed from HCI(v=l) under low n-butane pressure conditions, and appear on time scales of a few milliseconds. (b) By means of circular variable filters (CVF), the chain emission is dispersed as a function of wavelength. This emission spectrum in the 3.0-4.0-pm region (the resolution for this region of the spectrum (AX) is -0.05 pm) identifies the emission as originating from the CH stretch manifold. Line positions for HCI(v= 1-0) are shown for comparison. Higher vibrational levels of HCI would emit even further to the red and cannot account for the observed emission.

matically from the simple linear kinetic predictions. In this regime, pressure fluctuations in the flow cell of 1-1070 occur on each laser pulse because of the substantial chemical energy released by the chain. Infrared chemiluminescence in the 3.0-4.0-pm region that was originally dominated by weak HCl(u=l) emission is supplanted by intense emission that is essentially unblocked by an HCl cold gas cell and is found to arise from CH stretches of the hydrocarbon species. Figure 3a demonstrates a typical intensity vs. time signal observed in the 3-4-~mwavelength region. Of particular importance is the several millisecond time scale over which the emission develops. This time scale is insensitive to butane pressure but shortens with higher laser pulse energy densities. From a kinetic analysis of chain reagent exhaustion (see Appendix), one predicts that butane, the limiting reagent, should disappear with an exponential time constant given by (kl[C1]o)-l.This time is estimated from the C1, pressure, absorption cross section,I9pulse energy, and beam size for our conditions to be -1 ms. This same time scale is consistent both with the appearance of the bright emission at high butane pressures, as well as the decay of HCl(u=l) steady-state chain emission at low butane pressures (see Figure 1). As predicted in the Appendix, the time scale for reagent exhaustion does not depend on the concentration of the limiting reagent but only on the density of free radicals and the rate constant


for the propagation step that involves the limiting reagent. Second-order recombination of butyl radicals may also contribute to the observed chain termination behavior at high butane pressures. For perspective, this rate of chain burning of reagent (i.e., -300 Pa in 1 ms) translates into roughly 60 million chain cycles per second. By further increase in reagent concentration and laser pulse energy density, one can raise the rate of chain cycling by several orders of magnitude. In the interest of maintaining the chain burning in a regime that can be analyzed, our further studies are carried out under relatively low reagent con500-1000 Pa) centrations ([RH] 250-500 Pa, [Cl,] and with very weak, defocused laser excitation (51-2 mJ, -4-cm2 beam size). B. Time-Resolved Infrared Chain Emission Spectra. The infrared chemiluminescence from the chain reaction is monitored with a Ge:Cu detector equipped with a circular variable filter to obtain low-resolution (AA I0.2 pm) emission spectra. The emission at 3 ms after the laser pulse in just the 3.0-4.0-pm region is displayed as a function of wavelength in Figure 3b. This emission is assigned to vibrationally excited CH stretch modes of the polyatomic hydrocarbon species. HCl(u= 1-0) emission from the first chain step at this resolution would exhibit a double peak from P- and R-branch structure centered at 3.46 pm. For purposes of comparison,the predicted line positions of HCl(u=l+O)emission are shown in Figure 3b. Minor residual effects of this HC1 emission may be present underneath the CH emission. Emission from higher vibrational levels of HC1 would be shifted even further to the red of the observed CH stretch emission due to anharmonicity effects and cannot be the cause of the observed emission. More complete infrared emission spectra obtained in this fashion contain a wealth of information on the identity of the polyatomic emitters. Additionally, since the emission at each wavelength is recorded as a function of time, the full temporal development of the spectrum is obtained. Spectra from the Cl,/butane chain reaction over the range 3.0-15.0 pm and for t = 50 ps to 3.0 ms are displayed in Figure 4. Discontinuities in signal strength in the raw data displayed in Figure 4 at 7.8-8.0 pm result from a change in transmission between adjacent CVF filter segments. This is accurately taken into account by the calibration proceduremfor the spectral fits. Several features are worth noting from Figure 4: (1)The spectra exhibit detailed structure characteristic of highly vibrationally excited chlorinated hydrocarbons. There is a well-resolved CH stretch feature at 3.3 pm, a series of CH bend peaks in the 6.0-8.0 pm region, and finally several CC and CCl stretch features at longer wavelengths. (2) On closer inspection, comparison with standard infrared absorption spectra indicates a particularly interesting result-emission peaks can be found from the two product isomers (1- and 2chlorobutane) as well as reagent (n-butane). Several bands which are primarily due to each species are indicated in Figure 4. (3) The time dependence of the spectra indicate a general “heating up” of the vibrational modes as the chain reaction progresses. All the peaks grow monotonically, but the ratio of high frequency CH stretch emission to low frequency CH bend emission, for example, increases with chain evolution time. (4) The CH stretch emission at long times is intense and comparable to the CH bend emission. In light of the -1500-cm-l energy difference between these modes, this would indicate that the effective vibrational “temperature” must be high. (5) The observed emission, particularly at longer wavelengths, exhibits only broad structure and never goes to zero between major

-


: I

I

t=300psec

-

Figure 4. Full timedependent chain emission spectra (D) from the Cliln-butane chain reaction over 3.0-15.0 pm for four-delay times after the laser pulse. All spectral features are assigned as either emission peaks of one molecule or as contributions from severai bands of (a) n-butane, (b) 1-chlorobutane, or (c) 2-chlorobutane. The break in the emlssion intensity at 8.0 pm corresponds to the transition between CVF I1 and 111. The evolution of the chain emission from 50 to 3000 ps demonstrates a dramatic increase in the CH stretch population (3.3 pm) relative to other emlssion features. This is evidence for substantial vibrational heating of the chain mixture. Further evidence for a rapidly rising temperature can be noted in the loss of peak contrast in the 11-14-pm region. This broadening of spectral features may be attributed to a hotter rotational distribution, as well as anharmonically shifted emission from higher vibratlonai levels.

features. This is most likely due to thermal rotational broadening and anharmonic shifts of higher bands adjacent to the main peaks, an effect observed also in arrested relaxation studies on hydrocarbon substitution reactions.% The time dependence of the spectra also tends to support this; at early times the emission peaks have noticeably more contrast and resolution than at later times. This effect is particularly visible in the CC1 stretch region of the spectrum (11-14 pm). C. Spectral Fits t o the Chain Emission. All major peaks in Figure 4 are identified as belonging to either reagent (n-butane) or product (1- and 2-chlorobutane). The chain emission can be separated into its contributing components in order to obtain information on the relative concentrations of emitters and the degree of vibrational excitation. An approximate method of resolving the spectrum into components is described below. The emission intensity P of the ith species at frequency v is proportional to the product of Einstein A coefficients for each vibrational mode n times the population in each state (N,,,JZ9 (28) (a) Durana, J. F.; McDonald, J. D. J. Chem. Phys. 1976,64,2518. (b) Moehlmann, J. G.; Gleaves, J. T.; Hudgens, J. W.; McDonald, J. D. Ibid. 1974, 60, 4790.

4988

Nesbitt and Leone


Ii(v)

mA,'(u)Ni,,

0 :

(13)

Nbutane ' O.30

Two simplifying harmonic oscillator approximations have been made: (i) the A coefficient is appreciable only for single quantum transitions, and (ii) the transition probability for the higher transitions of the same mode n vary as the quantum number m times A, for the 1-0 transition. The 1-0 Einstein coefficients, A,, are obtained directly from the absorption spectrum via3"

N1-chiorobutane=o25 N2-chiorobutane= 0.45

40 where ani(v) is the molar extinction coefficient of the ith species a t frequency v for mode n. Equation 14 does not properly account for hot band absorption effects; however, for the range of frequencies investigated, room temperature population of excited vibrational levels is at most a few percent. For butane and chlorinated butanes, there are ?lo4 rotational states in each vibrational manifold, which implies many overlapping transitions inside the Doppler width. Thus the emission appears completely smooth and continuous, and motivates the following approximation. Since there is an absorption transition a t virtually every frequency, we treat the A coefficient as a continuous function of v that represents the density of these transitions. The infinitesimal contribution to the emission strength at v is then given by the derivative of eq 14, where we remove the distinction of specific modes, n aA' Ai(u)du = - dv

au

a

v2ai(u) dv

(15)

Equation 15 makes a very simple statement: the emission strength maps out the absorption strength, appropriately weighted by v2. This one-to-one mapping permits the reconstruction of an emission spectrum from the absorption spectrum without further spectroscopic information. The assumptions involved in this derivation will be valid if each mode is somewhat sharply defined, the anharmonicities of the vibrations are small, and thermal rotational broadening can be neglected. If the molecules have established a common sharing of vibrational energy via either inter- or intramolecular V-V transfer, the system may be appropriately characterized by a vibrational temperature. In light of the eventual V-T bulk heating processes that occur simultaneously, a true vibrational equilibrium may not exist, but this approximation permits us to characterize the chain emission with a single temperature and the populations of just a few emitting species. We make this assumption, therefore, in the interest of simplicity, but note that this introduces considerable limitations in the analysis of the spectral data. In this limit, Nnmi, the population of species i with m quanta in mode n is simply proportional to the Boltzmann factor:

The expression for observed intensity becomes I'(v)

a

i

I

n,m

Mv2ffi( v) xme-hum/kTvib

(17)

m

where N' is the density of species i. The sum over m can (29) Herzberg, G. 'Infrared and Raman Spectra"; Van NostrandReinhold: New York, 1945. (30) Strickler, S. J.; Berg, R. J. Chem. Phys. 1962, 37, 814.

60

80

100

120

1 +

140

A",( Flgure 5. Chain emission spectrum from the Cl,/n-butane chain reaction at [Cl,] = 1050 Pa, [n-butane] = 300 Pa, laser pulse energy = 2 mJ, 3.5 ms after the laser pulse. The data (B)have been least-squares fit (solid line) by assuming the emission is from n-butane, 1-chiorobutane, and 2-chlorobutane, and that all species are at a common Vibrational temperature, T., The fft reproduces the spectrum qualitatively quite well but systematically overestimates the contrast between peaks due to neglect of thermal rotational broadening and anharmonicity (see text for details of the fitting procedure).

be performed analytically to yield e - h u f k T n b / (1- e-hu/kTnb)2. The final result, therefore, is

for the ith species in the mixture. A least-squares fitting of eq 18 to the observed emission spectrum can now be carried out; the procedure is summarized as follows: (1) An absorbance spectrum, i.e., &), is taken for each of the species presumed to be in the chain reaction mixture. (2) A trial vibrational temperature, Tvib, common to all species is chosen. Equation 18 then predicts emission intensity as a function of v. (3) This predicted emission intensity is convoluted with the measured detector response function, which takes into account the relative detectivity and the wavelength resolution and transmission of the CVF. (4) With this, the detector signal as a function of wavelength is predicted for each component in the mixture. The best choice of N' is determined from linear matrix inversion techniques. (5) Another temperature Tvibis chosen and the process repeated until the best fit for Tvib and the N' is obtained. This procedure is applied to one set of emission spectra from the C12/butane chain reaction, where reagent n-butane as well as products 1- and 2-chlorobutane are included as the species in the fit. The fit for a 3-ms spectrum is presented in Figure 5. Note that this spectrum is from an experiment with different conditions than Figure 4. See the figure captions for details. Several features are worth noting: (1) In light of the several approximations utilized, the fit is satisfactory. All the observed peaks are represented in the synthesized spectrum, and the relative intensities of the peaks are reproduced semiquantitatively. (2) The fit appears to underestimate the breadth of the peaks in the measured spectrum; this is due primarily to neglect of thermal rotational broadening and anharmonic shifts of higher vibrations that will broaden the emission features. A more detailed analysis that includes rotational broadening and anharmonic shifts would obtain a more nearly quantitative fit to the spectrum and could be used to extract further dynamical information from the data. However, this would require further substantial spectroscopic information as well. (3) The vibrational temperature of the best fit in Figure 5 is 710 K, which accounts for the


The Journal of Physical Chemistty, Vol. 86, No. 25, 1982 4969

TABLE I ; Time-Dependent Emission Fits to the Cl,/n-Butane Chain Reaction t , ms T ~ ,K a % I B ~ %I,.cB~ % 1 2 - c ~ u R b Run lC 0.125 0.250 0.625 1.o 1.33 1.75 2.13

390 410 4 30 440 450 460 470

0.60 0.56 0.51 0.49 0.46 0.43 0.41

0.12 0.14 0.15 0.16 0.17 0.18 0.18

0.28 0.30 0.34 0.35 0.37 0.39 0.40

2.22 2.18 2.22 2.21 2.21 2.19 2.18

0.5

560 640 680 710

Run 2d 0.45 0.20 0.36 0.23 0.33 0.24 0.30 0.25

0.35 0.41 0.43 0.45

1.76 1.84 1.82 1.80

1.5 2.5 3.5

a Uncertainties in the least-squares temperature fit are estimated t o be i 2 5 K. R is the ratio of 2-chlorobutane t o l-chlorobutane. Conditions: [n-butane] = 427 Pa, Conditions [Cl,] = 827 Pa, laser pulse energy = 1 mJ. [n-butane] = 300 Pa, [Cl,] = 1 0 5 0 Pa, laser pulse energy = 2 mJ.

substantial emission, even in the high-frequency CH stretch region. (4) The relative populations of the emitters are 0.30:0.25:0.45 for butane, l-chlorobutane, and 2chlorobutane, respectively. The observation of vibrational excitation in reagent as well as product molecules is attributed to rapid sharing of the vibrational energy among all the molecules in the system. In light of the several approximations involved in the fitting procedure, a number of comments are in order. (1) Convergence in the “temperatures” determined by the least-squares fit is quite good. Changes in the vibrational temperature of more than *25 K lead to visibly poorer fits. (2) Vibrational temperatures obtained by fitting only the short wavelength (3.0-9.0 pm) or long wavelength data (9.0-15.0 pm) agree to within 50 K, although the short wavelength data generally predicts a slightly hotter temperature. (3) The predicted ratio of 1-to 2-chlorobutane emission is determined predominantly by emission in the 9.0-15.0-wm region, since that is where the major differences in their emission features occur. In summary, the vibrational fitting procedure does not characterize all features of the emission with a single vibrational temperature. However, the procedure does appear sufficiently accurate to establish clear trends in vibrational temperatures as well as ratios of emission from various species in the chain mixture. D. Time Dependence of the Chain Emission Spectra. The chain emission spectra described above also contain relevant information in the time as well as wavelength domain. The full temporal evolution of the chain reaction can be mapped out by performing the spectral fitting procedure for a series of data taken at different delay times after the laser pulse. Results for several of the C12/butane chain reactions are presented in Table I. The major difference in the two runs is a factor of two higher laser energy in the second run, which produces a factor of two more C1 atoms initially. Several interesting features are worth noting. (1)The best fit vibrational “temperature” exhibits a distinct rise throughout the course of the chain. The temperatures in the first series are cooler than the highest values observed in the second series (-710 K) because of weaker laser excitation. Higher temperatures can be achieved by increasing the reagent pressures as well. (2) The fraction of the emission that is due to reagent butane steadily diminishes with time, whereas the product 1-and 2-chlorobutane emission fraction steadily increases. The time dependence of the spectral fits, therefore,

qualitatively follows the evolution of the chain as reagent is consumed and products are formed. An interesting comparison can be made between the two runs in Table I. Under the hotter burning conditions of run 2, the fraction of product to reagent emission is substantially higher than observed in the cooler chain data of run 1, indicating a more rapid consumption of the reagent. Whereas the products are likely to be formed with initial vibrational excitation from the reaction exothermicity, the vibrational excitation in reagent butane comes about necessarily by energy transfer. Because of the large number of near-resonant vibrational frequencies in these polyatomic molecules, we expect that all species in the reaction mixture will come into rapid vibrational equilibrium by V-V transfer. Thus the spectral fits can provide direct information on relative product populations, i.e., product isomer ratios. From the first run of Table I the ratio of 2-chlorobutaneto l-chlorobutane product emission is observed to be approximately 2.2 and nearly constant over the full chain duration. This compares extremely favorably with previous literature mea~urements~l of the branching ratio which vary between 2.05 and 1.95 over the temperature range of 390-460 K. The good agreement suggests the possibility of monitoring yields of different product isomers in even very complex combustion mixtures. For C12/butane chain reactions run under hotter experimental conditions, one anticipates a decrease in this isomer ratio, since there are more methyl hydrogens (6) than methylene hydrogens (4) to substitute, and the selectivity for abstraction will become more nearly statistical at higher temperatures. This prediction is verified in the literat~re,~’ where isomer ratios are observed to decrease from approximately 2.0 at 473 K to 1.1 at 723 K. The chain reaction data listed in run 2 of Table I are obtained over this range of temperatures. The observed ratio of 2to l-chlorobutane emission is significantly lower ( 1.8) than is observed under the cooler chain conditions of run 1 (-2.2). If the observed emission ratio reflected the instantaneous product rates of 1-and 2-chlorobutane, one would anticipate a time-dependent decrease, rather than the essentially constant value observed. The explanation is that the observed emission amplitudes arise from the time-integrated products. Consequently, the emission ratio reflects an average over the product isomer ratio formed at varying temperatures, and the possibility of real-time measurements by this method is unlikely. E . Evidence for a Disequilibrium between the Translational and Vibrational Temperatures. The good fit of the emission spectrum in Figure 5 to a 710-K vibrational distribution is direct evidence of the elevated vibrational temperature in the chain reaction mixture. The magnitude of this temperature rise is quite reasonable in light of the large amounts of energy released by the chain reaction. Pressure fluctuations of 1-10% are also observed with the electronic capacitance manometer on s time scales. This indicates that at least some of the reaction exothermicity is either rapidly degraded by V-T,R processes or appears directly as translational heating of the gas mixture. It is not immediately clear, however, whether V-T,R relaxation pathways are sufficiently rapid with respect to production rates of vibrationally excited molecules to ensure that a local thermodynamic equilibrium is established. In this section we address the question of whether or not the entire system can be characterized by the same temperature; i.e., are the translational and vibrational degrees

-

-

(31) Maillard, A.; Deluzarche, A.; Levy, G. Bull. SOC.Chim. Fr. 1961, 1640.

4970

The Journal of Physical Chemistry, Vol. 86,No. 25, 7982

of freedom always in equilibrium? Direct measurements of transient translational temperatures in low pressure gases are difficult as a result of the very low heat capacities of the sample. An alternative is to infer the translational temperature spectroscopically from a distribution of molecular state populations by using states which rapidly equilibrate with translation. A good example would be to measure rotational state populations of some molecule by laser-induced fluorescence to monitor a local rotational-translational temperature. Since a suitable species for this was not available in these systems, we chose to use a low-lying vibrational state instead. The population of the low frequency C 0 2 ( v 2 )mode (667 cm-') is used as a nonintrusive gas-phase "thermometer" to measure the time-dependent translational temperature of the system. C 0 2 is doped into the chain reagent mixture at very low pressures ( N 1 Pa). V-T,R relaxation rates of the v2 (010) bending mode of C 0 2 by several collision partners have been r e p ~ r t e d . ~Values ~ ? ~ ~vary from cm3molecule-I s-' for pure C02to several thousand times this value for more complex molecules. To the best of our knowledge, relaxation of C02(v2)by butane and chlorinated butanes has not been measured. However, relaxation of u2 by large organics such as toluene has been shown to be extremely rapid, ktoluene= 3.7 X 10-l' cm3 molecule-' s-'.~~ The rate constant may be similarly rapid for the butane species. Relaxation of C02(u2)is expected to be even more rapid at elevated temperature^.^^ Equilibration of the u2 mode of C02should occur, then, on a time scale very short compared to the -millisecond duration of the chain at the reagent pressures used. The v2 mode may not actually come to equilibrium a t the translational temperature of the bath if near-resonant vibrations in the organic species are significantly "hotter". Therefore it is safer to consider the measurement as an upper bound on the translational temperature. V-V energy transfer from the excited organic molecules populates the asymmetric stretch mode ~ ~ ( 0 0of 1 )C02,35 which fluoresces rapidly to the ground state at 4.3 pm, and is readily detected with the InSb detector. Low pressures of C 0 2 in the cell are necessary to prevent radiative trapping on this strong infrared transition. If we interpose a C 0 2 cold gas cell between the flow cell and the detector, the (001) (OOO) transition will be blocked, while the (Onl) (OnO)transitions ( n 2 1)will be transmitted. The ratio of C 0 2 emission intensities with and without the cold gas cell provides a direct measure of the v2 population, and thus an estimate of the effective chain reaction translational temperature. The cold gas cell has roughly 7.9% population of the (010) level at room temperature. It is therefore crucial to adjust the cold gas cell C02pressure so that essentially all (001) (000) transitions are blocked, but (011) (010) and higher states are passed. This is possible since the absorption strengths of the v2 and v3 transitions differ by more than a factor of ten.34 Empirically this pressure regime is found to be 670 Pa in a 1 cm length cell by monitoring room temperature v2 equilibrated 4.3-pm emission from a Br*(2P, 2) + C 0 2 E-V transfer experiments over a series of cod gas cell pressures. Spontaneous radiative cooling of the (010) level is on the order of 0.4

Nesbitt and Leone

ri

444'K

40!

a

-

- -

-

(32) Cottrell, T. L.; McCoubrey, J. C. "MolecularEnergy Transfer in Gases"; Butterworths: London, 1961. Lambert, J. D. "Rotational Relaxation in Gases"; Clarendon: Oxford, 1977. (33) Eckstrom, D. J.; Bershoder, D. J. Chem. Phys. 1972, 57, 632. (34) Gribov, L. A.; Smirnov, V, N. Sou. Phys. Usp. 1962, 4, 919. (35) Rao, I. V.; Babu, S. V.; Rao, Y. V. C.; Subba Rao, V.; Lalita, K. J . Chem. Phys. 1978, 68, 2933. 136) Reisler, H.; Wittig, C. J. Chem. Phys. 1978, 68, 3308.

0,5t I

P

0

c

50

100

t

(msec)

15.0

20 0

-

Flgure 6. Timedependent measurement of the translational temperature in the Cl,lbutane chain system. The ratio of (On 1) (OnO) fluorescence from a small dopant concentration of C 0 2 viewed with and without an external cold gas COz filter provides a spectroscopic means of monitoring translationaltemperatures of the chain mixture (see text for details). The undulations In the emission intensity are real and appear to be due to acoustic pressure waves created in the flow cell by rapid chain burning.

s34and can be totally neglected in the analysis. The estimate of the chain reaction translational temperature is calculated as follows. We measure the ratio (r) of C02(v3)emission intensities with and without the cold gas cell, first correcting for the weak background chain emission in the 4.3-pm region. The value of r equals the probability at temperature T of having one quanta or more in the v2 mode. This is given by 1 minus the probability of having no quanta, which by equilibrium statistical mechanics is r = 1 - (1 - e-hu/kT):! (19)

The square results from the twofold degeneracy of the v 2 mode. Inverting eq 19 for Tone finds (remembering that this temperature represents an upper bound) Ttrans I- ( h v / k ) In (1- (1- r)1/21 (20) Equation 20 provides a simple connection between r, which can be measured directly as a function of time, and the estimated translational temperature of the chain reaction system. Typical results observed with the C 0 2 ( v 2 )thermometer for the C12/butane chain are shown in Figure 6. Emission viewed through a fiied COzcold gas cell is attenuated only by a factor of 4, which immediately indicates a v 2 population well in excess of the 7.9% observed for a room temperature distribution. The temperatures calculated from these data via eq 20 demonstrate a rapid initial heating followed by a gradual cooling as the chain evolution is limited by reagent exhaustion. The effective range of translational temperatures in this data sample is 420-485 K. Translational temperatures measured under a wide variety of experimental conditions vary typically between 400 and 500 K, depending on laser pulse energy, reagent concentrations, etc. However, even under experimental


Laser-Initiated Ci,/Hydrocarbon Chain Reactions

TABLE 11: Time-Dependent Emission Fits to the Cl,/Ethane Chain Reactiona

Nethane ' o.72 Nchloroethane

b

t a

'O 28 0.0625 0.125 0.25 0.625 1.00 1.38 1.75 2.13

-g I-

40

60

100 (pm)

80

120

140

470 480 500 530 550 560 570 580

V. C12/Ethane Analysis of the CIP/butanechain reaction is complicated by the presence of two product isomers in the emission spectrum. This motivates an investigation of time-dependent chain behavior in a chemically simpler system, C12/ethane, where only a single product, chloroethane, is generated at early times. One anticipates, therefore, that a chain emission spectrum can be fit by considering emission from only two species, ethane and chloroethane. Chain behavior in the C12/ethanesystem is qualitatively quite similar to that observed in C12/butane. At low ethane pressures, chain emission is predominantly due to vibrationally excited HCl(u=l) product from the first propagation step. For ethane pressures in excess of a several hundred Pa, however, chain production of vibrationally excited product occurs sufficiently rapidly to generate strong chemiluminescenceover the 3.0-15.0-pm region. A sample chain reaction emission spectrum from C12/ethane is shown in Figure 7 along with the best fit to the emission calculated in the manner described in section 1V.C. The vibrational temperature of the fit is 580 K, somewhat lower than many of the typical C12/butane chains for similar reagent and laser power conditions. Once again, a significant fraction of the emission is due to reagent ethane as well as product chloroethane, a clear indication that sharing of the vibrational excitation from product to reagent occurs. Additionally, the emission peak at 9.4 pm is definitely identified as due to dichloroethane chain product as well. The observed spectrum again exhibits broader peaks than predicted by the fitting procedure. This is most likely a reflection of significant emission from high rotational states as well as hot bands that are neglected in the fit. The results of fits to the emission spectra at various times are shown in Table 11. The reagent fraction of the

0.16 0.18 0.20 0.23 0.25 0.26 0.27 0.28

a Conditions: [ethane2 = 605 Pa, [Cl,] = 715 Pa, laser pulse energy = 2.3 mJ. Uncertainties in the leastsquares temperature fits are estimated t o be ? 25 K.

Flgure 7. Chain emission spectrum from the Ci,/ethane chain reaction at [Ci,] = 715 Pa, [ethane] = 605 Pa, laser pulse energy = 2.3 mJ, 2.13 ms after the laser pulse. The data (m) have been least-squares fit (solid line) by assuming that emission is solely from ethane (peaks marked (a)) and &loroethane (peaks marked (b)), and that both species share a common Vibrational temperature, T,. The peak marked (*) corresponds to emission from 1,ldichloroethanewhich grows in only as ethane reagent is consumed (see Figures 8 and 9).

chain conditions that produce quite high vibrational temperatures (700 K), the highest translational temperatures measured via the COPemission are on the order of 500 K. It is worth noting that these estimates of a translational temperature of 400-500 K (i.e., roughly a 50% increase over room temperature) are consistent with the observed maximum pressure rises in the cell, ,

hydrocarbon chain reactions: time-resolved

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