shock tube kinetics in homogeneous and heterogeneous reaction systems

Shock Waves (19951, 5:239-247

�9 Springer-Verlag 1995

Shock tube kinetics in homogeneous and heterogeneous reaction systems Paul Roth

lnstitut fiir Verbrennung und Gasdynamik, Gerhard-Mercator-Universitfit Duisburg, D-47048 Duisburg, Germany

Received April 19, 1995 / Accepted August 24, 1995

Abstract. The shock tube used as a high-temperature wave reactor has dominated high-temperature kinetics for more than 45 years. The nearly instantaneous heating to high temperatures, the accessible wide temperature and pressure ranges, and the diffusion-free reaction conditions are the main advantages of this technique for measuring rate coefficients at high temperatures. In this paper some applications of the shock tube technique for kinetic studies in homogeneous and heterogeneous reaction systems will be discussed. The examples to be presented were obtained in the author's laboratory. They include thermally and photolytically induced chemical reactions, which were studied by applying different optical absorption techniques.

Key words: Shock tube kinetics

1. Introduction

The scientific subjects presented in the last 4 decades at the shock wave symposia can roughly be divided into aerody- namically or kinetically orientated works. Going back to the e~xly history of research, the invention and the subsequent development of the shock tube were motivated by practical problems associated with explosion waves. In 1899, during his combustion studies on explosions in mines, Paul Vieille wrote his pioneering paper on discontinuities produced by the sudden expansion of compressed gas. In the next three decades shock tube research was mostly directed to an un- derstanding of detonation and explosion phenomena, ending in the forties with 1:he formulation of the popular ZND theory of one-dimensional detonation, which brought aerodynamic and kinetic aspects close together again.

Beginning in the early fifties, the two main shock tube applications started to separate from each other. Kineticists applied the shock tube as a high temperature wave reactor, characterised by a nearly one-dimensional flow with practically instantaneous heating of the initial gases. Reaction

An abridged version of this paper was presented as Paul Vieille Memoiral Lecture at the 20th International Symposium on Shock Waves, CALTECH, Pasadena 1995.

temperature could be extended far beyond the range covered by classic kinetic methods, and reaction time was available in the microsecond scale. After many years of extensive work, the shock tube technique was finally accepted as a reliable tool with a tremendous potential for the study of high-temperature and short-duration phenomena.

Many modern applications of shock tube technology for kinetic studies are characterised by two interrelated features: very high dilution of the reactants in an inert bath gas (mostly argon) and high sensitivity of the optical diagnostics used. The big advantage of highly diluted reactants is that the en- dothermicity or exothermicity of the chemical reactions have no effect on the structure and stability of the wave. Further- more, the number of elementary reactions, which determine progress in the shock-induced reaction system, is limited, thus facilitating the kinetic interpretation of measured properties. On the other hand, access to intermediate chemical species by the use of modern optical diagnostics (see Han- son (1993)) provides an insight into the details of chemical reactions, which are highly influenced by radical species.

Compared to homogeneous chemical reactions in shock waves, whose study was strongly stimulated by the G6ttingen researchers (see Wagner (1971)), heterogeneous kinetics in shock waves are at an early stage. The reasons are that both the degree of reaction complexity and the difficulties in the diagnostics are significantly higher. A precondition for this type of experiment is that the solid phase must be homogeneously distributed in the gas phase. The kinetic problems interfere to a high degree with the two phase flow" difficulties. Detailed access to the adsorption-desorption surface reactions is not possible in shock tube experiments so that rate parameters obtained are limited to global expressions. On the diagnostics side, sensitive optical methods for gas phase properties like laser schlieren or laser absorption are significantly disturbed by the dispersed particles.

In the present paper, some examples of different types of shock wave-induced chemical reactions all obtained in the author's laboratory will be illustrated: simple thermal decomposition reactions, thermally or photolytically initiated radical reactions, and reactions in dispersed systems (aerosols). In all cases, optical absorption ranging from vacuum ultra-violet (VUV) to the infrared region was used, to-

240

I Excimerlaser

Quartz Window I MW-Power [ Photolysis

Supply

MW-Discharge Lamp

Ar+Pump Laser ~ v Ring-Dye-Laser Frequency Stabil. 4 Intensity Stabil. Wavemeter

~l ~] ill ~ Pressure Transducer

Low Pressure Section

Filter n ,1 u

Monochromator

7

! Polarization

Filter

Fig. 1. Experimental arrangement for measurements in a shock tube: atomic resonance absorption spectroscopy (ARAS), ring dye laser spectroscopy (RDLS), and laser photolysis (LP)

gether with the Lambert-Beer-law, to measure time-dependent concentrations of reactive species.

2. Thermal decomposit ion reactions

The classic application of shock-tube technology, which reached a certain state of completeness through many years, is to study the above type of reaction by observing the relaxation towards chemical equilibrium after shock heating of the test gas. The decomposition of molecules A can in those cases be described by the Lindemann mechanism, which considers a collisional activation or deactivation followed by the dissociation:

1 A* A + M ~ + M

A* 3 products

M is the collision partner. Besides temperature, the progress in the disappearance of A depends on pressure. Two limiting cases are possible: at low pressure the collisional deactivation of A* is much slower than its chemical reaction and the whole reaction obeys a second order rate law (low pressure limit). At high pressure, the rate of disappearance of A becomes independent of the concentration of the collision partner M and obeys a first order rate law (high pressure limit). The reality of the above type of reaction is normally much more complicated. The energy required for dissociation is transferred to the molecule by a large number of collisions, which can have different efficiencies. Also the internal dynamics of the energy transfer is of importance, i. e. the coupling between vibrational relaxation and dissociation can play a significant role resulting in an apparent delayed dissociation.

The thermal decomposition of diatomic molecules proceeds for most applications under conditions close to the low pressure limit. A good example is the dissociation of N2. Because of its importance in hypersonic flows, its rate coefficient was determined in numerous studies, all following the disappearance rate of N2. For this and other types

of decomposition reactions it seems useful to measure the rate of appearance of the atomic dissociation product and to determine in this way the dissociation rate coefficient of the mother molecule. In the case of N2, the low pressure decomposition is simply:

N 2 + M ~ 4 N + N + M

It is not an easy task to follow N atom formation under shock tube conditions. Since the middle of the seventies atomic resonance absorption spectroscopy (ARAS) for measuring H and O atom concentrations has been made available for shock tube research (see Just (1981)), which was later extended to other species like N, C, Si and S atoms. The diagnostic method is basically a spectroscopic line-emission/line- absorption technique. The respective atomic species have strong resonance absorption lines in the vacuum UV, which makes it possible to measure their ground state concentration with very high sensitivity.

A schematic diagram of the experimental arrangement employed for ARAS is shown in Fig. 1 together with other devices, which will be of interest later on. Microwave power is coupled into a low pressure flow of a He/N2 mixture. The high-temperature plasma formed contains the NI triplet radiation at 119.9 nm, which is single-passed through the shock tube about 10 mm back from the end wall. A one-meter VUV monochromator separates the strongest of the N atom lines from the radiation of the plasma lamp. N atoms formed in the shock tube during high temperature thermal decomposition absorb the resonance radiation very effectively. The absorption measured by a solar blind photomultiplier is then related to the N atom concentration. For a detailed evaluation of the signals a reliable calibration is needed, see Thielen and Roth (1986).

An example of data trace for N absorption (noisy line) and N concentration (dashed line with dots) from a reflected shock experiment in a mixture of 200 ppm N2/Ar at 5500 K and 1.43 bar is shown in Fig. 2a. The arrival time of the reflected shock is marked. After a certain de- lay the N atom concentration increases linearly with time

1.0 g?

E~ C)

i 2[ ?-;" 0.s- c: O

c'L

O (f) rq

<: 0.0

I I I

T = 5497 K .-'; p = 1.43 bar .'d "~

4, 200 ppm r,l~ in Ar ,.

Q.

shock ~ ' ' ~ ~ ' ~

;~ ~ -,,-induction period I I I I 0

6 E O

2 - 4 o

c- O

-2 (1) 0 C- O ro

0 z

200 400 600 800

Time//xs

10 '~

~0~ 10 ~- Z__

0

K 10 %

r

-~" 104"

10 ~

I I N~ + Ar-> N + N + Ar k - 1 .9 ' x 10" exp(-97850 K/T)

1.5 2.0 2.5

10 ~ K/T

3.0

Fig. 2a,b. N-atom ARAS signal and corresponding concentration during thermal decomposition of N2 (a). Rate coefficient of N2 dissociation (b)

T a b l e 1. Ra te coe f f i c i en t s o f va r ious h igh t e m p e r a t u r e d e c o m p o s i t i o n reac-

t ions ob ta ined by A R A S . ki = A i T - B i e x p ( - C ~ / T ) c m 3 m o l - l s - I

Reaction A~ Bi Ci CO2+Ar ----+ (;O + O + Ar 3,65 x 1014 0.0 52525 (20 +Ar ----+ C + O + Ar 4.30 x 1027 3.1 129000 )42 +Ar ~ N + N + Ar 1.97 X 10 TM 0.0 97850 1'40 +At ~ N + O + Ar 9.60 X 1014 0.0 74700 02 +Ar _I+ O + O + Ar 1.60 x 1018 1.0 59380 0 2 +N2 ~ (b + O + N 2 3.40 x 1018 1.0 59380 CN +Ar -----, C + N + Ar 2.50 X 1014 0.0 71000

(dashed line). From the N atom slope the rate coefficient for the N2 dissociation can be determined. Results of a series of shock wave experiments in N2/Ar mixtures are summarized in Arrhenius form in Fig. 2b. Because of the high sensitivity of the optical diagnostics, the low temperature end is very much extended compared to other experimental results, the dam thus cover several orders of magnitude, and the rms deviation is quite :~mall. Results of other different rate coefficients with significants in hypersonic flows, all obtained from ARAS experiments, are summarized in Table 1, see also Roth (1992)

The thermal decomposit ion of triatomic molecules like H20, COS, or N20 is more complicated. They can dissociate directly out of the ground state or can dissociate in a spin-forbidden path from an electronically excited state, which requires a singlet-triplet transition. In the first case electronically excited atoms are formed whereas in the second case ground state atoms are the decomposit ion product.

24I

ca 1.0 E 2

I3..

cO 0.5- > ,

..Q

c- O ..i.--, Q .

B 0.0 CO

..Q <

I I I i E T=2110K , o

. - " _2-~o p = 1.5 bar ,.. 30 ppm COS " ' " ' -

O

,o (3) �9 r

C O (2

~" O ~ " - I V or)

I I I

0 1 O0 200 300

a Time/r

1 . 0 I I I ~ E ]T = 2738 K o 4p = 1.2 bar .... ; ..... "." ..... , - 4 ~o

/ 30 ppm C O S . . - ' " r --"-c o 0aj /

i -2 E (1) O c- O

F. . a O0 0 -~

I I I 03

0 100 200 300

b Time / / a s

Fig. 3a,b. Examples of measured S(3p) and S( 1 D) absorption/concentration during thermal decomposition of COS

g- g } q) c'~

<

A good example is the thermal decomposition of COS.

COS(1~) + M ~ CO(Is + S(3p) + M

J R h = 298.9kJ/mol

C O S ( I z ? ) + M 6 C O ( t ~ + ) + S ( I D ) + M

A R h = 409.2kJ/mol

The first decomposit ion reaction is energetically cheaper but requires a singlet-triplet transition of COS, not indicated in the above reaction, and the second reaction describes the direct formation of electronically excited S(JD) from the ground state potential.

We have recently performed experiments measuring both S(3p) and S(1D) concentrations during thermal decomposition of COS by applying ARAS. The examples in Fig. 3a,b illustrate that reasonable absorption signals by both elec- tronic states of S were obtained, see noisy lines. The conver- sion into concentration profiles by applying the calibration curves is also shown in Fig. 3a,b, see dashed lines with dots. The evaluation in terms of rate coefficients for this and all other decomposit ion experiments are summarized in Fig. 4. Both formation rates show Arrhenius behaviour, but the ab- solute values differ by about a factor of 150. It seems at first sight that S(3p) formation is the dominant reaction channel, but this cannot be concluded from the present experiments. The quenching and excitation reaction:

7 S ( J D ) + M = S ( 3 p ) + M ,.dRh = 1 10.3 kJ/mol

242

10 ~~ I I I I I

:e 109" ~ +

o ~ 10 7.

. . % 10 5 I I I I I

3.0 3.5 4.0 4.5 5.0 5.5 6,0 10' K/T

Fig. 4. Measured formation rates of S(3P) and S(ID) during thermal decomposition of COS

is very fast and contributes, in addition to the above direct formation reactions, to the balance between the two excited states of S. Reaction 7 is practically equilibrated under the present experimental conditions. This can be seen from the dashed line in Fig. 4, which represents the calculated formation rate of S(1D) based upon the equilibrium assumption and the measured S(3p) formation rate. So it must be concluded that the present results do not allow a decision as to whether reactions 5 or 6 dominate the thermal decomposition of COS.

Decomposition reactions of molecules with four or more atoms are more and more influenced by secondary and con- secutive reactions, which must - even under high dilution conditions - be described with kinetic mechanisms.

3. Precursor-initiated radical reactions

The second type of elementary reaction study is motivated by the strong interest in obtaining rate coefficient data for radical-molecule or radical-radical reactions. A chemical precursor undergoing a very fast "priming" reaction after shock heating seeds the test gas with reactive intermediate species at known concentrations. The reaction of interest then begins to proceed at a measurable rate only after this radical formation process is nearly finished. This idea of using the shock tube as a chemical reactor goes back to Gardiner et al. (1971). It is clear at once that the radical formation reaction must be fast compared to the reaction of interest. Over the years, many precursors were tested in our and in other laboratories. The application and success- ful use of such precursors depend on the detailed reaction conditions.

A good example for a precursor-initiated atom reaction, which also illustrates again the high sensitivity of ARAS, is the reaction of Si atoms with CO.

S i + C O 8 ~ S i O + C ARh=276 .1 kJ/mol

This reaction was studied in mixtures containing 0.75 to 20 ppm SiH4 and 0.2 to 5% CO diluted in Ar at temperatures 2720 K< T <_ 5190 K using the Si atom ARAS as given in Fig. 1. An individual example is represented in Fig. 5a showing Si atom absorption measurements in mixtures without and with CO. Immediately behind the reflected

1.0

o

0.5- C

.0

~ 0.o I~

<, _c

t -

II >-

I I I I

without CO

+ 2% CO

0 200 400 600

Time / H,s

dY/dt = -3530 s'

k= 6.4 x 10'~ cm3 mol ' s"

800

0 I O0 200 300 400 500

b Time //~s Fig. 5a,b. Si atom absorption measured in mixtures of Ar and 1 ppm SiN4 without and with CO addition, T = 3660 K, p = 0.8 bar (a). Evaluation of the absorption signal by the first order method (b)

shock wave the precursor Sill4 decomposes nearly instantaneously to form Si atoms (and H2) at a constant level. In the mixture with CO, the silicon atoms in turn react as given in the above equation, resulting in a decrease in the Si absorption.

The kinetic evaluation of the above type of absorption signal is facilitated by the fact that the disappearance of Si proceeds under first order conditions, because the CO concentration is practically constant.

d ln[Si]/dt = -ks[CO]o

The silicon atom concentration can be directly related to the measured absorption via the modified Lambert-Beer-Law with a concentration exponent of n = 0.8. The above equation rewritten yields:

d i n { r - I n ( 1 - A)] l /n} _ dY - - -ks [CO]0

dt dt

with A being the measured fractional Si absorption. The diagram of Fig. 5b shows the property Y as a function of reaction time. The linear behaviour of Y confirms the first order assumption for reaction 8 and allows determination of the rate coefficient from the slope. A summary of all rate coefficients thus obtained is shown in the Arrhenius diagram of Fig. 6. This also includes results of C atom measurements. The standard deviation of the data due to experimental scat- ter is again, at +10%, very low. Rate coefficients of several silicon reactions obtained in the author's laboratory are sum- marised in Table 2.

Another example of a precursor-initiated radical reaction, which illustrates some disadvantages of the technique, is the reaction

10 `3

"o~ 10 '~- L_

O

E 1 0 " -

r

"" 10 '~

' ' 1 ' ' ~ ' 1 . . . . I ' ' ' ' 1 ' ' Si + CO ~ SiO + C k - 73 x 10" exp(-34510 K/T)

[ ] C-a toms

�9 Si-atoms

10~ ' ' 1 . . . . I . . . . I . . . . I ' '

2.0 2.5 3.0 3.5

1 0 ' K / T

Fig. 6. Rate coefficienl of the reaction Si + C O ~ SiO + C

Tab le 2. Rate coefficients of var ious Si-containing reactions obtained by ARAS. /,:~ = .4~ e x p ( - U~ IT) cm ~ m o l - 1 s - 1

Reaction A i Ci I

Si + C O ~ SiO + C 7.8 x 1014 34510

Si + C O 2 ~ S iO + C O 6.0 x 1014 9420

Si + NO ~ SiO + N 3.2 x 1013 1775

Si + O2 ~ products 2.7 x 1014 1765

Si + N 2 0 - - ~ SiN + N O 5.0 x 1014 8100

- - ~ SiO + N 2 8.0 x 1013

9 CH + 02 ~ products

A precursor, which produces CH radicals instantaneously to a constant level as in the case of Si atoms is not known. We have examined several hydrocarbons with respect to their usefulness in serving as a CH source, but they all show a pronounced CH time profile. An example is given in Fig.7 where a gas mixture containing 20ppm C2H6 in Ar was shock heated to a temperature of 3000K. The CH concentration was measured at the overlap of the Ql/(7) and Q2[(7) resonance lines in the (0,0) band of the A2A - X2/-/transition at ~ = 431.1311 nm with the ring dye laser arrangement given in Fig.1. The detection limit is in the sub-ppm range, and the S/N ratio is better than 1000 on the short time scale of the experiment According to the upper curve in Fig. 7 (mixture without O2), the CH profile increases over about 30#s and decreases again for the remaining reaction time. The maximum CH yield is about 40% of the initial C 2 H 6

concentration. Both these experimental observations clearly illustrate the kinetic complexity of the CH source, which involves a large reaction mechanism. The addition of I00 or 500ppm 02 to ~:he C2H6/Ar mixture clearly shows a significant perturbation of the original CH profile, which can be: evaluated with kinetic methods. The rate coefficient k9 obtained from a series of experiments has a temperature- independent value of:

/,:9 = 7.5 x 1013cm3mol-ts --1

The detailed evaluation of those experiments is more com- plex and needs computer simulation.

4 . P h o t o l y t i c a l l y i n i t i a t e d r a d i c a l r e a c t i o n s

The method of generating radical species by photolysis and following their fllrther reaction, is an old and well es-

24~

E 2- 2 O

2"1 o

T = 3000 K

p = 1 2 bar

20 ppm C;,H~_ ~ hout O~

0- . . . . I ' ' r , I '

0 50 100

T ime/ / . ts

Fig. 7. Measured CH concentrat ions in shock heated C2H6/Ar lllixtures without and with addit ion of ():

tablished technique in chemical kinetics, mostly used in room-temperature static cells. In the shock wave commu- nity, flash lamps were first used to photolyse molecules in shock-heated gases. With the availability of high intensity pulsed UV lasers, which have a higher spectral intensity and a greater monochromaticity compared to flashlamps, these light sources were also used in shock tube experiments, see e.g. Hanson (1993), Matsui et al. (1992). Compared to the chemically formed radicals, described in the previous section, pulsed laser photolysis is an effective and instantaneous source allowing direct preparation of radical species widely independent of the properties of the shocked gases. An extension to low temperatures is therefore unproblematic. A disadvantage is that the energy transfer or the absorption coefficient during photolysis are not known in detail, ren- dering prediction of the identity or the energy states of the photofragments produced more difficult.

To illustrate a photolytically initiated radical reaction behind the reflected shock wave, I have chosen the reaction:

S + H2 ~ HS + H ~/r = 80.3 kJ/mol

for which no experimental high-temperature data were available. S atoms were photolytically produced by an excimer laser pulse at 193nm in mixtures of 25 or 30ppm CS2 and 1000 to 4000ppm H 2 diluted in At. The laser was coupled into the measurement plane of the shock tube through an end plate made of quartz glass, see Fig. 1. The original rect- angular beam was expanded by a cylindrical lens allowing illumination of the whole ARAS diagnostic path; for more details see Woiki and Roth (1993). The temperature range of the present experiments was 1260 to 1840K. Progress of the chemical reaction studied was followed by applying S(3p) ARAS at 147.4 nm.

The absorption profile of a typical experiment is shown on the upper part of Fig. 8. The arrival of the reflected shock, which is associated with a temperature discontinu- ity does not initiate any measurable S atom formation in the mixture. Only the laser photolysis pulse of about 13 ns duration, which was delayed with respect to the reflected wave by about 50#s, causes a quasi step-like peak in S atom absorption. Subsequently the signal decreases due to S consumption by the above reaction with H 2 . Data reduction could again be achieved by, assuming first order decay of S,

244

1.0- i ~ i i d) T = 1447 K. p = 1.15 bar

~: 30 ppm CS2 + 4000 ppm H, O �9 ~ laser

09 pulse

x~ 0.5- c- O c3 g 03

'~ Aa

0 2 0 0 4 0 0 6 0 0 8 0 0

a Time/,u,s

10" I I I I I

S + H 2 - ~ S H + H

= 10 ~3- " k = 6.0 x 10" exp(-12070 K/T)

is o E 10 '2-

~E o ~ s i s

"~ 10"-

1 0 ' ~ ' I ' I ' I ' I ' I

3 4 5 6 7 8

b 104 K / T

Fig . 8a ,b . S - a t o m A R A S signal af ter photolys is o f a shock-hea ted

CS2/H2/Ar mixture (a). Rate coefficient of the reaction S+H2 ~ HS + H (b)

as illustrated in the last section. Results of all the experiments are summarized in the Arrhenius diagram of Fig. 8, lower part. The data points can be approximated by the Ar- rhenius expression

klo = 6.0 x 10Mexp(-12070 K/T) cm3mol-ls -1

In this diagram the results of another series of experiments are also included, where the S atoms were chemically formed by pyrolysis of COS. Both data sets agree quite nicely and illustrate the high potential of photolysis experiments at low temperatures, as well as the good applicability of pyrolysis- generated reactive species for high-temperature reaction conditions.

5. Thermal ly initiated reactions in dispersed systems.

The reactions of solid particles homogeneously dispersed in gas mixtures at high temperature is of interest in many tech- nical applications, for example, soot oxidation, pulverized fuel combustion, or SO2 reduction by limestone particles. The degree of complexity in such heterogeneous reactions is much higher than in the case of gas phase reactions, and the availability of kinetic data, even for global processes, is poor. The idea of applying the shock tube technique to reactive aerosol systems seemed to suggest itself, because a di- lute suspension of particles behaves essentially as a gas. The initially unreacted mixture can be heated by a shock wave, thus initiating chemical reactions, which can be recorded by optical methods. But there are some difficulties compared to experiments with gas mixtures:

- preparation of the gas/particle mixture (aerosol) and its homogeneous distribution along the low pressure part of the shock tube,

- gasdynamic problems during shock wave heating of the two-phase system,

- determination of the reactive surface of the aerosol system,

- application of an optical diagnostic for gas phase species in a particle loaded system.

The first problem was solved by developing an expansion wave driven aerosol generator allowing dispersion of small amounts of powders, see Roth and von Gersum (1993). The second difficulty can be overcome by choosing sub-#m particles having low overall particle load. In this case the effect of particles on the fluid flow properties is very weak, i.e. gas temperature and pressure increase almost instantaneously behind the shock wave to nearly constant levels. Because of the small size of the particles, the slip flow region behind the shock wave, in which heat and momentum transfer from the gas to the particle phase occurs, is very small compared to the extension of the heterogeneous reaction zone, i.e. the suspended particles are also almost instantaneously heated up to a constant level behind the shock wave. If gas phase reactants are either initially available in the mixture or chemically formed during a fast homogeneous rate process, their reactions with the hot solid particle surface can proceed. The rate of a heterogeneous reaction depends, besides other surface properties, on the size or the reacting area, i.e. the particles must be characterized with respect to these properties. This can be done by applying laser light scattering or laser light extinction at different wavelengths, which will not be discussed here; for details see Brandt and Roth (1989).

The remaining problem in the above list is determining the progress of the heterogeneous reaction by measuring the formation of gas phase products or reduction of gas phase educts. A well suited technique is tunable IR-diode laser absorption spectroscopy, because interference by the particles is small, as light extinction by small particles is weak in the infrared region. The optical arrangement used is shown in Fig. 5. It consists of a pulsed, tunable IR-diode laser, the shock tube arranged as a multipass optical cell, a 0.5 m infrared monochromator for mode filtering, and an InSb detection system. The laser is pulsed with a frequency of 25kHz and can additionally be tuned in each pulse over one or two lines, thus producing a series of highly resolved absorption lines, from which time-dependent species concentration can be determined, see Brandt and Roth (1989).

An example of a thermally initiated reaction in a dispersed system is the oxidation of soot particles by O atoms. The expected oxidation products are CO and CO2, but the only clearly detectable product on the time scale of the present experiments was CO, i.e. the oxidation proceeds, in the present case, mainly via the global heterogeneous reaction:

Cs + 0 > CO

where Cs represents the solid carbon in the soot particles. The O atoms were generated by the fast thermal decomposition of N20 that was present in the initial gas/particle

245

I Filter

~ ~ e D r ~ e ] - ~

*" (] V6 q

[ b_talon j :/ ~ RingeDY e

I [ Zuna 'e @ Power H Infrared Supply ][Diode Laser

Multipass ~ Spectrat Absorption

~ [[] [J] Pressure Transducer

Low Pressure Section

Infrared Monochromator

Fig. 9. Experimental arrangement for measurement in a shock tube: ring dye laser spectroscopy (RDLS) and infrared diode laser spectroscopy (1RDS)

mixture. According to the above reaction, the rate of formation of CO is:

1 dlCO] _ c~oZoap Z0 : ~ ~ [O] dt

In this equation c~o, Z0 and ap are the reaction probability of O atoms with the soot surface, the collision number of O atoms per unit time and area, and the reacting particle surface area per unit volume of suspension, respectively. The collision number Zo can be calculated from the Hertz- Knudsen equation with ~ being the mean thermal veloc- it 5, of O atoms. The desired kinetic property is the reaction probability c~0, which can be determined from the measured properties [CO] and ap, for known [O].

A typical example of an individual shock tube experiment in a soot/N20/Ar mixture at 2490 K is shown in Fig. 10. The laser was tuned in a wavelength range close to the (0,1) P8 line of CO, and the pulse frequency was about 25 kHz. The arrival of the shock front is marked. In the lower part of Fig. 10a selected scans of the same experiment are shown in more detail with an enlarged time scale. The strong absorption lines in scan A were caused by spectral absorptior, of N20 under pre-shock conditions. Be- ginning with the first post-shock scans, sharp spectral lines of CO appear shewing increasing absorption. These illustrate the formation of an increasing amount of CO during the heterogeneous soot oxidation.

The reduction of the spectroscopic data to CO concentration can be done using the Lambert-Beer law. The necessary spectral absorption coefficient depends on the line strength and the line shape factor. The latter was determined by fit- ting a Voigt profile to the measured absorption line. Taking this into account, I:he sequence of absorptions obtained can be transformed inlo a time-dependent CO concentration, as illustrated in Fig. ]0b. From the initial slope together with the above equation, or from computer simulation of this and other oxidation experiments, reaction probabilities c~0 were determined. A summary is given in the Arrhenius diagram

/

A B C D

shock 40ps time A "~q

Ill N2 0 I / CO i J . L ;

V V

/ / i CO // CO I

�9 -' L_ a V' V

I I

4.5 % N20/sool/Ar mixture T=2490K, p= 1 bar

oE2. �9 j , , J -

C ) �9 �9

R �9 1 o

0 ' i ' i ' i 0 500 1000 1500

b Time / ,u,s Fig. lOa, b. Example of pulsed IR diode laser scans in a shock heated soot/N20/Ar mixture showing increasing CO spectral absorptions (a). Cor- responding CO concentration (b)

of Fig. 11, which also contains results of soot oxidation by OH and NO. The c~o values obtained are nearly independent of temperature and can be approximated by a mean value of c~0 = 0.23. For more details see Roth and w)n Ger- sum (1993).

246

10 ~

d

3 1 0 " ~ z

s

1 0 2 ~

-

1 0 -3

3500K I I

2000K

i I

z~

,t, ~ �9

2.5 5.5 I ' I '

3.5 4.5

104 K / T

Fig. 11. Reaction probabilities of soot oxidation by O, OH, and NO obtained from shock tube experiments

A further example of shock-initiated reaction in an orig- inally dispersed system is the thermal decomposition of fullerene C60. This material, which has been known to be a new carbon modification for about 10 years, is, at room temperature, a black powder like soot. There is some interest, from both the scientific and the industrial point of view, in the thermal stability and the chemical resistance of fullerenes to high temperatures. We therefore have dispersed a C60 powder in Ar using the expansion wave-driven aerosol generator mentioned earlier. The aerosol mixture was loaded into the shock tube and heated to a temperature of about 2500 K. Two main observations were made: the solid particles evaporate in a very short time forming fullerene vapor, and the measured emission behind the shock wave contains strong bands of C2 and very weak bands of C3.

To make this last spectroscopic observation more quan- titative, the formation of C2 during the thermal decomposition of C6o in mixtures with Ar was studied in detail in the temperature range 2450 K to 3450 K. Time-dependent C2 formation in the post-shock mixture was measured with the ring dye laser system shown in Fig. 9. The spectrome- ter was connected to the measurement section of the shock tube by an optical fiber. The intensities of both the incident and the transmitted laser light were recorded by two fast Si-detectors. The laser was fixed to line center of the over- lapping R1(35), R2(36), and R3(35) lines in the (1-0) band of the d3Hg-a3H~ transition of C2.

A problem for the present experiments was the quan- titative characterization of the amount of fullerene, which is in the pre-shock situation a dispersed powder and in the post-shock reacting mixture a vapor compound. We have therefore performed some experiments with C60/Ar mixtures enriched with 6% of 02. The aerosol mixtures were heated by the shock wave to conditions similar to those of the pyrolysis experiments and we observed a very effective oxidation of C60. The combustion products CO and CO2 were quan- titatively measured by the tunable IR diode laser described earlier, see Fig. 9. Assuming a complete oxidation of all carbonaceous material, which is justified under the present high-temperature conditions, the post shock C60 concentration can easily be determined from the measured oxidation products.

8

6- ~E

( 3 2 0 4 - , r -

0 " 2 -

O -

a

106

1 0 5 -

"700

1 0 4 - _~

103 --

102

2 . 5

b

I ' I ' I ' I

T = 3040 K

0 200 400

Time//~s

I I

C8o ~ Css + C2

I I

3.0 3.5 4,0

10 4 K/ I - Fig. 12. Examples of measured C2 concentrations during the thermal decomposition of C60 (a). Arrhenius diagram of the C2 abstraction reaction from C6o (b)

Detec tab le C2 absorption could only be recorded at temperatures above 2600 K. Typical examples of time-resolved C2 formation in C60/Ar mixture are shown in Fig. 12a. The weak schlieren-signal at time zero can be ignored. It is obvious that both the rate of appearance of C2 and the final amount of C2 depend on temperature. At conditions T > 3000 K the C2 profiles show a characteristic maximum.

A first step towards an interpretation of the measurements is to assume a simple C2 abstraction followed by other reactions not discussed here.

C6o + M ~ C 2 -t- C58 "4- M ARh = not known

An apparent rate coefficient for the appearance of C2, which can easily be extracted from the present experiments without any computer simulation, is:

_ d[C2]/dt

kapp [C60]0 t~0

For such a big molecule like C60 it is quite within the bounds of probability that the C2 ejection proceeds near the high pressure limit. This is the reason why the above data reduction was chosen. In so far the scientific circle to the Linde- mann mechanism mentioned earlier, is closed. All the individual rate coefficients obtained from the C2 measurements are summarized in Fig. 12b. They can be approximated by the Arrhenius expression:

kapp m 4.25 x 1012 exp(-516 k J / m o l / R T ) s -1

247

The apparent activation energy of 516kJ/mol is between value:s determined in molecular beam and in photolysis studies, which indicates some remaining open questions. For more details see Sommel ~, Kruse and Roth (1995).

6. Conclus ion

Modern applications of shock tube technology for kinetic studies in both homogeneous and heterogeneous reaction systems were illustrated in several examples. It was shown that the trends are in the direction of studying rate processes in highly diluted .';ystems, partly as low as 1 ppm of re- actant. The availability of highly sensitive optical, mostly laser-based, diagnostics make such experiments possible. Care is required concerning the influence of impurities in the: test gases as well as in the shock tubes, which are here constructed and used as ultrahigh vacuum apparatuses. Wall adsorption of strorgly polar reactants in the highly diluted systems can also be a problem. Nevertheless the high temperature wave reaclor will continue to be of great importance in high-temperature kinetics.

Acknowledgement. The author like to thank Prof. John Kiefer, University of Hlinois at Chicago, for helpfull discussions. The financial support of the German Science Foundation is gratefully acknowledged.

3. Hanson RK (1995) The Rate of Lasers in Shock Tube Studies of Chem- ical Kinetics. In: Bran R, Dumitrescu LZ icds) Proceedings of the 191h lnt. Shock Wave Symposium

4. Just T (1981) Atomic Resonance Absorption Spectrometry in Shock Waves In: Lifshitz A (ed) Shock Waves in Chemistry. Marcel Dekker lnc., New York, p 279

5. Mick H J, Roth P (1994) Shock Tube Study of Silicon Atom Oxidation by CO and CO2. J Phys Chem 98:7844

6. Rolh P (1992) Experimental Determination of Kinetic Coeflicients with Significants in Hypersonic Flows. In: Brun R. Chikhaoui AA (eds) Proceedings of the IUTAM Symposium on Aerolhermochenlislr? of Spacecraft and Associated Hypersonic Flows. Universitd de Provence. Marseille, p 267

7. Roth P, yon Gersum S (1993) High Temperature Oxidation of Soot Par- ticles by O, OH, and NO. In: Takeno T (ed) Turbulence and Molecular Processes in Combustion. Elsevier, Amsterdam. p 149

8. Sommer T, Kruse T, Roth P (1995) C2 fl3rmation during high temperature pyrolysis of fullerene C6~} in shock waves J Phys Chcm {to be published)

9. Thielen K, Roth P (1986) N Atom Measurements in High-Temperature N 2 Dissociation Kinetics. AIAA Journal 24:ll02

I 0. Vieille P (1899) Sur tes Discontinuitt~s Produites par la Ddtcnte Brusque de Gaz Comprimds. Compte Rendus 129:1228

I1. Wagner HG (1971) Chemical Reaction of Shock Waves. In: Stollery JL, Gaydon AG, ()wen PR (eds) Proceedings of the 8th Int. Shock Tube Syrup. Chapman and Hall. London, p 4/I

12. Woiki D, Rnth P (1993) ARAS Measurments on S( l D) Formation in Shock Heated COS/Ar Mixtures. Ber. Bunsenges. J Phys Chem 97:996

13. Yoshimura M. Koshi M, Matsui H. Kamia K, Hideaki U (1992) Non- arrhenius temperature dependance of the rate constant lk~r lhe reaction H+H2S. Chem Phys Lett 189:195

References

1. Brandt O, Roth P 11989) A tunable IR-diode laser technique for measuring reaction rates of high-temperature aerosols. Comb Flame 77:69

2. Gardiner W C, Mc Farland M, Morinaga K, Takeyama T, Walkes B F (1971) The Shock Tube as a Chemical Reactor. In: Stollery JL, Gaydon AG, Ower~ PR (eds) Proceedings of the 8th Int. Shock Tube Symposium Chapman and Hall, London, p 23/1

shock tube kinetics in homogeneous and heterogeneous reaction systems

Documents