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Progress in Energy and Combustion Science 28 (2002) 151±192
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The shock tube as wave reactor for kinetic studies and
material systems
K.A. Bhaskaran a, P. Roth b,*
b
a
Department of Mechanical Engineering, Indian Institute of Technology, Chennai 600 036, India
Institut fuÈr Verbrennung und Gasdynamik, Gerhard Mercator UniversitaÈt, 47048 Duisburg, Germany
Received 8 January 2001; accepted 27 July 2001
Abstract
Several important reviews of shock tube kinetics have appeared earlier, prominent among them being `Shock Tube Technique in Chemical Kinetics' by Belford and Strehlow [Ann Rev Phys Chem 20 (1969) 247], `Chemical Reaction of Shock
Waves' by Wagner [Proceedings of the Eighth International Shock Tube Symposium (1971) 4/1], `Shock Tube and Shock
Wave Research' by Bauer and Lewis [Proceedings of the 11th International Symposium on Shock Tubes and Waves (1977)
269], `Shock Waves in Chemistry' edited by Assa Lifshitz [Shock Waves in Chemistry, 1981] and `Shock Tube Techniques in
Chemical Kinetics' by Wing Tsang and Assa Lifshitz [Annu Rev Phys Chem 41 (1990) 559]. A critical analysis of the different
shock tube techniques, their limitations and suggestions to improve the accuracy of the data produced are contained in these
reviews. The purpose of this article is to present the current status of kinetic research with emphasis on the diagnostic
techniques. Selected studies on homogeneous and dispersed systems are presented to bring out the versatility of the shock
tube technique. The use of the shock tube as high temperature wave reactor for gas phase material synthesis is also highlighted.
q 2002 Elsevier Science Ltd. All rights reserved.
Keywords: Shock tube; Diagnostics; Homogeneous kinetics; Pyrolysis; Material synthesis
Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. The basic shock tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1. Observation time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2. Measurement of shock velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3. Single-pulse shock tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3. Diagnostic techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1. Absorption spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1. Atomic resonance absorption spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2. Laser absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2. Mass spectrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3. Laser schlieren . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4. Laser light scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5. Laser light extinction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6. Laser induced incandescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7. Ignition delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
* Corresponding author. Tel.: 149-203-379-3426/3417; fax: 149-203-379-3087.
E-mail address: [email protected] (P. Roth).
0360-1285/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved.
PII: S 0360-128 5(01)00011-9
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4. Homogeneous systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1. Simple thermal decomposition reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2. Complex thermal decomposition reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3. Oxidation reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1. Initial oxidation steps in O 1 CH4 reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4. Precursor initiated reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1. Thermally initiated pre-cursors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.2. Photolytically initiated radicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5. Dispersed systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1. Heterogeneous±homogeneous systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2. Heterogeneous reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1. Preparation of the gas/particle mixture(aerosol) and its homogeneous distribution in the test
section of the shock tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2. Gas dynamic problems associated with shock wave heating of a two phase system . . . .
5.2.3. Determination of the reactive surface of the aerosol system . . . . . . . . . . . . . . . . . . . . . .
5.2.4. Suitable optical diagnostic technique to measure gas phase species in a particle loaded
system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3. Soot oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6. Shock wave initiated material synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1. Pre-particle kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2. Synthesis of Si-nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3. Gas phase synthesis of tin nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4. Production and sizing of soot nano-particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction
Shock tube based research has, over the last ®ve decades,
uncovered several potential areas for scienti®c investigation. Though the main thrust was focused on applying the
shock tube for aerodynamic and high temperature kinetic
studies, several interdisciplinary areas have also been
greatly bene®ted. A few examples of such interdisciplinary
research involving shock waves can be seen in many intriguing medical applications of shock wave focusing; shock
wave phenomena in geoscience and astrophysics; shock
waves in condensed matter and shock wave initiated material synthesis. Paul Vieille [2], who operated the ®rst
shock tube in 1899, to understand gas explosions in
mines, could not have foreseen the great potential of this
experimental tool.
Kineticists all over the world use the shock tube as a high
temperature wave reactor for obtaining rate coef®cient data
under diffusion free conditions, because it provides a nearly
one-dimensional ¯ow, with practically instantaneous heating of reactants. The temperature range under which the
reaction could be studied can be extended far beyond that
of the conventional ¯ow reactor (1000 K). The shock tube
technique has been used successfully to deduce kinetic data
on certain heterogeneous reaction systems also [3]. Though
low-pressure ¯ames have also been used to determine rate
coef®cients at high temperatures, dif®culties arising out of
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the ¯ame complexity, render the data that is not always
reliable. Use of the shock tube as a wave reactor for studies
on material synthesis is of very recent origin [4].
After Schott and Kinsey [5] demonstrated that the course
of an exothermic reaction like H2 1 O2 ! products, highly
diluted in argon, could be satisfactorily resolved using a
shock tube, several other investigators used the technique
to study many other reactions of varying complexity, covering a wide range of mixture ratios, temperature, pressure and
dilution factors. A variety of detection techniques to monitor
the molecule and radical concentrations during the short
microsecond range of reaction time available in a shock
tube, have been tried with varying degrees of success. To
mention a few, techniques like interferometric, emission or
absorption of molecules in the infrared, visible or ultraviolet
spectral regions have been tried out before the more sensitive atomic resonance absorption spectroscopy (ARAS) and
laser based diagnostic techniques emerged on the scene.
The shock tube has ®nally established its position as an
unrivalled experimental technique for gaining insight into
reaction mechanisms at elevated temperatures.
The gas phase homogeneous kinetic experiments carried
out in the recent past using shock wave reactor are characterized by two factors namely very high dilution of the
reactants by an inert gas (usually argon) and high sensitivity
of the diagnostic techniques employed to monitor species.
The main advantage of diluting the reactants with an inert
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
153
Fig. 1. x±t Diagram of a simple shock tube. (1) Initial test gas, (2) shocked gas, (3) driver gas behind contact surface, (4) initial driver gas,
(5) test gas subjected to re¯ected shock. Ref. [15].
gas is that the exothermicity or endothermicity of the reactants involved will not greatly alter the constant temperature
conditions during the investigation. Secondly, by using very
low initial reactant concentrations (up to 10 ppm), the in¯uence of subsequent reactions can be totally avoided or
reduced. This facilitates study of just one or two elementary
reactions with high accuracy and without being strongly
disturbed by fast secondary reactions [6].
Though shock tube based kinetic research in gas phase
homogeneous systems, strongly stimulated by Wagner et al.
[1] has been making steady progress over the last 40 years,
heterogeneous kinetic studies using the shock tube are still
at an early stage. The reasons for this are the degree of
reaction complexity involved and the dif®culties in diagnostics. A pre-condition for this type of experimentation is that
the solid phase (particles) are homogeneously dispersed in
the carrier gas. Interference between the complexities of
two-phase ¯ow and kinetics is another problem to be overcome in such investigations. Lack of detailed access to
absorption±desorption reactions on particle surfaces, limit
these studies to obtaining global rate parameters. Sensitive
optical methods of diagnostics are signi®cantly disturbed by
the dispersed particles. Roth and his co-workers [7±9] have
made some signi®cant contributions in heterogeneous shock
tube kinetics which is explained under dispersed systems.
The shock tube as a wave reactor provides an excellent
154
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
Table 1
Reactions studied with ARAS
Rate parameters
Reaction
log10 A (cm 3, s, mol) a
n
E/R
Temperature range
Ref.
H 1 NH3 ˆ H2 1 NH2
H 1 NH3 ˆ H2 1 NH2
H2 1 NH2 ˆ H 1 NH3
H 1 NH2 ˆ NH 1 H2
H 1 H2O ˆ H2 1 OH
H 1 O2 ˆ OH 1 H
H 1 O2 ˆ OH 1 H
H 1 O2 ˆ OH 1 H
H2 1 O2 ˆ HO2 1 H
H 1 O2 1 Ar ˆ HO2 1 Ar
D 1 D2O ˆ D2 1 OD
D 1 H2 ˆ HD 1 H
H 1 CH4 ˆ H2 1 CH3
D 1 CD4 ˆ D2 1 CD3
H 1 H2S ˆ H2 1 HS
H 1 C2H4 ˆ H2 1 C2H3
H 1 C7D8 ˆ C7H7D 1 H
O 1 H2 ˆ OH 1 H
O 1 H2 ˆ OH 1 H
O 1 H2 ˆ OH 1 H
O 1 D2 ˆ OD 1 D
O 1 C2H4 ˆ CH3 1 HCO
O 1 C2H4 ˆ CH3CO 1 H
±
±
±
±
±
±
±
2.0
±
±
±
±
±
±
±
8067
11,070
6492
5233
11,557
8118
8695
5172
34,277
±
10,815
4985
7577
11,221
1500
908±1977
1246±2297
962±1705
1700±2500
1100±2700
1100±1400
746±987
1285±2260
655±1979
1700±2300
1780±2440
1965±2560
2000
1410±1730
880±2495
1713±3532
2097±2481
2097±2481
1600±2300
[40]
[41]
[42]
[43]
[44]
[45]
[46]
[47]
[48]
[45]
[49]
[50]
[51]
[52]
[53]
[54]
[55]
[56]
[57]
[58]
[58]
[59]
O 1 N2 ˆ NO 1 N
O 1 COS ˆ products
O 1 CH4 ˆ OH 1 CH3
O 1 D2 ˆ OD 1 D
O 1 C2H2 ˆ CH2 1 CO
O 1 C2H2 ˆ CH2 1 CO
O 1 C2H2 ˆ HCCO 1 H
O 1 C2H2 ˆ HCCO 1 H
O 1 C2H2 ˆ products
O 1 C2N2 ˆ products
O 1 HCN ˆ OCN 1 H (a)
O 1 HCN ˆ CN 1 OH (b)
S 1 O2 ˆ SO 1O
14.3
14.1
13.5
13.7
14.4
14.2
14.4
7.0
16.6
15.4
14.2
14.4
14.9
15.3
13.0
13.2
13.5
14.3
6.5
14.4
14.2
13.5
Combined rate
constant for the two
channels
14.3
13.3
5.2
14.3
14.2
14.1
14.6
14.6
14.0
14.2
13.9
k…b† ˆ 0:6k…a†
12.6
2400±4100
1900
763±1755
825±2487
1500±2500
1500±2570
1500±2500
1500±2700
850±1950
1780±2285
1800±2500
[60]
[61]
[62]
[63]
[64]
[65]
[64]
[65]
[66]
[67]
[68]
Decomposition of small molecules
HCN 1 Ar ˆ H 1 CN 1 Ar
SO2 1 Ar ˆ SO 1 O 1 Ar
CH3 1 Ar ˆ CH2 1 H 1 Ar
H2S 1 Ar ˆ HS 1 H 1 Ar
NO 1 Ar ˆ N 1 O 1 Ar
N2 1 Ar ˆ N 1 N 1 Ar
NH3 1 Ar ˆ NH2 1 H 1 Ar
NH2 1 Ar ˆ NH 1 H 1 Ar
SiH2 1 Ar ˆ SiH 1 H 1 Ar
SiH 1 Ar ˆ Si 1 H 1 Ar
CD4 1 Ar ˆ CD3 1 D 1 Ar
CO2 1 Ar ˆ CO 1 O 1 Ar
N2O 1 Ar ˆ N2 1 O 1 Ar
N2O 1 Ar ˆ N2 1 O 1 Ar
C2H2 1 Ar ˆ C2H 1 H 1 Ar
16.8
16.5
16.3
14.7
15.0
4.2
16.3
14.7
14.2
13.8
16.3
13.4
15.0
14.7
16.6
±
±
2.17
±
±
±
1862
6854
4080
6915
7168
1425
±
8300
2.40
±
±
±
±
±
±
±
±
2838
7293
4975
3300
5365
6100
2714
7130
7460
900±1620
±
±
1900±2200
[69]
±
±
±
±
±
23.33
±
±
±
±
±
±
±
±
±
58,932
58,590
46,100
41,500
74,700
113,220
46,345
37,590
39,703
33,800
42,722
43,778
30,428
28,985
53,600
2200±2700
2500±3400
2150±2550
1965±2560
2400±6200
3390±6435
[70]
[71]
[72]
[53]
[60]
[73]
[41]
[43]
[74]
[74]
[52]
[75]
[75]
[76]
[77]
1700±3900
1700±3900
1780±2440
2300±3400
1600±2500
1500±2000
1850±3000
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
155
Table 1 (continued)
Rate parameters
Reaction
log10 A (cm 3, s, mol) a
n
C2H3 1 Ar ˆ C2H2 1 Ar
CF3Cl 1 Ar ˆ CF3 1 Cl
C2H3 1 Ar ˆ C2H2 1 Ar
C2H4 1 Ar ˆ C2H3 1 H 1 Ar
C2H4 1 Ar ˆ C2H2 1 H2 1 Ar
13.8
15.7
14.7
17.6
17.4
±
±
±
±
±
E/R
14,090
28,700
16,606
49,900
39,900
Temperature range
Ref.
1380±1750
1800±2500
1577±2177
1700±2200
1700±2000
[78]
[79]
[80]
[54]
[54]
a
Rate expressions are in the form of A…T†n exp…2E=RT† in units of s 21, cm 3 mol ±1 s 21, cm 6 mol 22 s 21 depending on the reaction order.
Reaction order is dependent on number of molecules on left side of equation.
environment for the study of nucleation and growth of particles from the vapor phase at high temperatures. Apart from
providing nearly instantaneous and uniform heating of reactants, it allows rapid quenching of products leading to particle condensation and growth. The effect of varying initial
temperature, pressure, and mixture composition on the size
and yield of the particles produced, can be conveniently
studied in a shock tube. Frenklach et al. [10] have carried
out shock tube investigation of silicon particle nucleation
and growth during gas phase pyrolysis of silane and
proposed a reaction mechanism for the temperature range
900±2000 K. Formation of silicon particles was monitored
by light extinction measurements. A similar study on the
formation of Si atoms from thermal dissociation of disilane
(Si2H6) mixed with different additives was carried out
behind re¯ected shock waves by Mick et al. [11]. They
used the ARAS technique for detection of Si atoms and
ring dye laser absorption spectroscopy (RDLAS) to detect
SiH2 radicals. Herzler et al. [4] have investigated the formation of both TiN molecule and particles in TiCl4/NH3/H2
systems behind re¯ected shock waves. The relative TiN
particle concentrations were determined by ring dye laser
light extinction method.
Gas phase combustion synthesis of extremely ®ne particles (nano-particles) is a well established procedure [12].
These powders are used as reinforcing agents, opaci®ers,
and pigments, and in the fabrication of optical ®bers. The
high temperature ¯ame environment, in which these nanoparticles are produced, is self-purifying and the powder
requires no further processing, such as washing. The ¯ame
aerosol synthesis of nano-particle powders has created great
interest in extending the technique to the production of new
materials such as carbon black, fumed silica, pigmentary
titania, zinc oxide, and alumina. Though these powders
are being produced in large scale, the fundamental principles behind the formation and growth of the particles are
not yet fully understood. The shock tube as a wave reactor is
ideally suited for carrying out systematic high temperature
investigations into the particle formation, its shape, size
distribution and yield. Roth and his co-workers [13] have
started on a new series of investigations into the soot particle
formation behind shock waves from different hydrocarbon
sources, such as acetylene, benzene, and propane with the
view of optimising the production process. The new particle
sizing techniqueÐlaser induced incandescence (LII) is
being successfully used in these measurements [14].
An attempt is made in this paper to present a brief review
of the state of the art diagnostic techniques used in shock
tube research. Typical examples of shock wave initiated
reactions in homogeneous systems and dispersed systems
and methods of measurement used are discussed. Use of
shock tube as a wave reactor for nano-particle material
synthesis is illustrated. The experimental details are mostly
drawn from the facilities that exist at the Institut fuÈr
Verbrennung und Gasdynamik, Gerhard Mercator UniversitaÈt, Duisburg, Germany.
2. The basic shock tube
The shock tube in its simplest form consists of a uniform
cross-section tube divided into a driver and driven sections
by a diaphragm. The driver section is ®lled to a high
pressure with a low molecular weight gas (H2 or He) and
the driven or test section contains the test gas at low pressure
whose physical or chemical processes at high temperatures
are to be studied. When the diaphragm is suddenly allowed
to burst, a plane normal shock travels down the driven
section heating the test gas instantaneously. Simultaneously,
a rarefaction wave travels in the opposite direction through
the driver section. Fig. 1 shows the resulting wave pattern
and the pressure and temperature on an x±t diagram [15].
The incident shock is re¯ected at the end of the test
section and rams into the shocked gas ¯owing behind it,
which results in a further increase in temperature and
pressure of the test gas. The gas behind the re¯ected
shock will be at rest and is therefore ideal for observing
high temperature effects undisturbed. The rarefaction
wave, which traveled in a direction opposite to that of the
incident shock, also gets re¯ected at the end of the driver
section and starts traveling towards the test gas. The rarefaction fan, bounded by the head and tail of the rarefaction
zone, is characterized by falling temperature and pressure
below the initial conditions. The pressure and temperature
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K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
traces drawn in Fig. 1 show their corresponding values at a
given time t. The sudden jump to T2 and p2 from their initial
T1 and p1 is the result of incident shock heating.
2.1. Observation time
The time available for making measurements on the test
gas after the passage of the shock wave is called the observation time. This time is usually very short (order of milliseconds) and depends on the shock Mach number and the
distance of the observation station from the diaphragm. For
measurements behind incident shock waves, the observation
time available at a given station will be the time interval
between the arrival of the shock front and the contact
surface. If measurements are preferred behind the re¯ected
shock wave (where the temperature and pressure are much
higher), then it is advantageous to have the measuring
station as close to the end ¯ange as possible. The observation time in this case will be the time interval available
between the re¯ection of the incident shock on the end
¯ange and arrival of the re¯ected wave from the contact
surface. This is shown by DtR in Fig. 1.
The observation time available behind the re¯ected shock
can be increased by adopting what is known as `contact
surface tailoring'. By this the re¯ected shock, on meeting
the contact surface, does not re¯ect again, but becomes
stationary, allowing for constant temperature and pressure
to prevail for a longer time. The contact surface tailoring is
achieved by adjusting the densities of the gases on either
side of the contact surface.
The growth of the boundary layer behind the shock front
tends to accelerate the contact surface and this in turn
reduces the effective observation time available.
2.2. Measurement of shock velocity
The shock Mach number forms the basis for determining
all the other shock parameters. Making use of the conservation of mass, momentum and energy equations for an ideal
gas under inviscid ¯ow conditions, pressure, temperature
and density ratios across the incident shock wave can be
deduced in terms of the incident shock Mach number M
and speci®c heat ratio g of the test gas. The analogy can
be extended to derive pressure and temperature ratios across
the re¯ected shock wave also in terms of the incident shock
Mach number and speci®c heat ratio of the test gas.
The accuracy of the shock tube data very much depends
on the exact measurement of the incident shock velocity.
This is usually determined by measuring the time taken for
the shock wave to travel between four or more points separated by a known distance along the length of the tube and
taking the average value. Either thin ®lm resistance probes
or pressure transducers are used as sensors to detect the
arrival of the shock front and an electronic timer is used
for recording the time intervals.
2.3. Single-pulse shock tube
Single-pulse or chemical shock tube developed by Glick
et al. [16] is ideally suited for studying bond-breaking reactions of hydrocarbons. By suitable design, instantaneous
heating followed by rapid quenching of the reactive mixture
can be achieved. This enables samples to be drawn out at
desired intervals for detailed analysis.
In its simplest form the single-pulse shock tube consists
of an evacuated dump chamber at the end of the driver
section, separated by a second diaphragm. By timed rupturing of this second diaphragm, the rarefaction wave can be
expanded into the chamber, thus avoiding its re¯ection at
the driver section end ¯ange (as in a normal shock tube).
The test gas will be heated by the incident and re¯ected
shocks in the usual manner and later the expanded
rarefaction wave coming out of the dump chamber
quenches the reaction effectively and expands the
stationary test gas in the direction of the dump chamber.
By a suitable selection of the dump chamber volume
[17], the entire driver gas can be made to collect in
it, leaving the test section ®lled with the reacting
experimental gas. The ®nal mixing of the driver and
test gases takes place only through diffusion, thereby
allowing suf®cient time for samples of the test gas to
be drawn out for chemical analysis.
Tsang [18] in his article on comparative-rate single-pulse
shock tube studies on the thermal stability of polyatomic
molecules has given an extensive coverage for this technique. Though the experiments are similar to that carried
out in a fast-¯ow high temperature reactor (in which also
products are measured either by chromotograph or mass
spectrometer), the difference lies in the fact that the shock
heating takes only 1 ms or less, thus avoiding surface effects
and interference from side reactions. As the heating time in
the shock tube is ®xed, conversion of reactants to products
must be varied in order to obtain rate measurements over a
range of temperatures. At the lowest temperatures, concentration of products can be at trace levels. The limit for high
conversions is set by dead space effects described by
Lifshitz et al. [19] and Skinner [20]. The alternative possibility is to carry out studies at high dilutions and in the
presence of overwhelming amounts of a chemical inhibitor
so that the molecule under study can be isolated as it undergoes decomposition. Since the inhibitor traps all reactive
radicals, only unimolecular processes can occur. This is
the basis of the comparative rate technique described in
Ref. [18]. The decomposition of two molecules is effected
simultaneously and two unimolecular rate constants
obtained. If the rate expression for one of these has been
established, a reaction temperature can be immediately
deduced. Appendix A of Ref. [18] summarizes all the
published results using the comparative-rate single-pulse
shock tube technique. Similarly Appendix B of the quoted
reference summarizes rate constant data for a variety of
simpler saturated compounds while Appendix C lists bond
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
157
Fig. 2. Schematic arrangement of the ARAS technique.
energies and heats of formation determined from comparative-rate single-pulse shock tube experiments.
In a follow up review paper on shock tube techniques
Tsang and Lifshitz [21] have listed further work done on
organic compounds under inhibition and with internal standards. These are mostly bond breaking reactions with all
chain contributions suspended. Extensive decomposition
kinetic studies on organo-silicon compounds [22±25]
using single-pulse shock tube (SPST) technique have
revealed that the most important channel was 1,1 hydrogen-elimination. However, the quantitative interpretation
of the data from these studies is rendered dif®cult by the
lack of reliable mechanistic information. A set of prerequisites for this type of study include mechanism for decomposition and stability of the alkylsilyenes formed from 1,1
elimination and the reactivity and thermochemistry of Si H2
radicals [26].
Assa Lifshitz used the single-pulse shock tube to study
thermal decomposition and pyrolysis of many compounds
such as indene [27], benzene [28], propane [29], acrylonitrite [30]. Another promient user of the SPST is Mackie
who studied decompostition of benzyl radical [31] and pyrolysis of acetonitrile [32].
3. Diagnostic techniques
3.1. Absorption spectroscopy
3.1.1. Atomic resonance absorption spectroscopy
Resonance absorption is the most sensitive among the
spectroscopic absorption methods. This method of monitoring species concentrations has been extensively used by
many investigators, ever since the introduction of shock
tube in kinetic studies. Most investigators have measured
one species at a time, though from the kinetics point of
view, it would be good if several species could be monitored
simultaneously. But then, this desire will increase the
experimental complexity so much that it is not worth
pursuing [33].
In resonance absorption method, the light to be absorbed
comes from the same species that is to absorb it. This technique, ®rst used in a shock tube by Myerson and Watt [34],
has been further developed by Roth and Just [35] and
reviewed by Just [6]. A notable feature of this diagnostic
technique is the use of very low initial relative concentrations of reactants (from about 10 ppm to approximately
1 ppm or even less) thereby eliminating the effects of
exothermicity or endothermicity during the reaction.
Accurate measurements with such low initial concentrations
are possible because of the strong absorption in the line
center of atomic lines. Another advantage of using low
initial reactant mole fractions is the possibility of reducing
the in¯uence of subsequent reactions. One of the problems
in this technique is the preparation of accurate calibration
curves for the atoms to be measured covering the desired
temperature and concentration ranges. Because an intense
light source is required for good time resolution, the spectral
line emitted by the light source will tend to be broadened by
various effects. Therefore, a theoretical relation between
measured absorption and corresponding absorber concentration cannot be calculated for such line emission±line
absorption techniques. A combined theoretical and experimental approach to this problem has been developed by
Lifshitz et al. [36]. Prominent users of ARAS technique
together with the species they measured are as follows.
Just and co-workers (H, O), Roth an co-workers (O, H, N,
Si, S( 3P), S( 1D), S, Cl, Sn, C), Frank and co-workers (H, O,
I, C), Wagner and co-workers (O, H, Cl), Hippler and coworkers (H, O), Michael and co-workers (O, H, D, Cl, I),
Skinner and co-workers (O, H), Asaba and co-workers (H,
O, S), Matsui and co-workers(O, H, N, I, S( 3P), S), Takahashi and co-workers (O, H, I, Br). A schematic arrangement
of the ARAS technique used by Roth and Just [37] to monitor O-atoms during elementary hydrocarbon oxidation reactions is shown in Fig. 2. A microwave discharge lamp for the
158
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
Fig. 3. Typical O atom calibration curve.
emission of OI-triplet radiation at 130.5 nm is fed with low
pressure He±O2 mixture. The emission from the discharge
lamp is passed through a highly diluted (2 ppm N2O in Ar)
mixture contained behind the re¯ected shock wave
(T . 1600 K). The O atoms produced by the instantaneous
decomposition of N2O absorb the resonance radiation very
effectively. A 1 m vacuum UV monochromator separates
the strongest of the O atom lines from the radiation of the
discharge lamp. The absorption measured by a solar blind
photomultiplier gives a measure of the O atom concentration. A typical O atom calibration curve obtained from such
measurements is shown in Fig. 3.
Tsang and Assa Lifshitz [38] have summarized in their
review article `Shock Tube Techniques in Chemical
Kinetics ' the rate expressions that have been measured
via spectroscopic detection of products and of reactants
(Tables 1±3). An extract from this table that deals with
reactions studied by various research groups employing
ARAS technique is presented in Table 1. Some general
conclusions from the data in the tables can be summarized.
For unimolecular decomposition, even for relatively large
molecules at temperatures above 1200 K, fall-off effects
must be considered and are increasingly important as the
temperature is increased. On the other hand, for many
four- or ®ve-atom systems, the experimental results, under
the pressure conditions usually encountered in shock tube
studies, are not at the low-pressure limit. For fundamental
signi®cance the data must be extrapolated to the low- or
high-pressure limits. The Troe technique [39] has proved
to be popular in carrying out such extrapolations. Although
the methodology is very effective in determining intermediate pressure behaviour from results at the pressure extremities, the inverse, especially in the face of experimental
errors, is less certain.
3.1.2. Laser absorption
Though the ARAS played a key role in providing the bulk
of high temperature kinetic data, the introduction of laser
based absorption diagnostics by Hanson [81] has had a
major impact on the quality of kinetic data obtainable in
shock tube experiments. The increased sensitivity of laser
absorption and spectrally extremely small light source has
allowed use of more dilute reaction mixtures, leading to
lesser interference of secondary reactions. The increased
measurement accuracy with laser absorption has led to a
signi®cant reduction in the scatter of kinetic data. A further
improvement in the laser absorption approach was the introduction of a constant wavelength UV dye laser that enabled
precise measurement of intermediate species like OH.
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
159
Table 2
Rate expressions determined with the laser schlieren method
Rate parameters
Reaction
log10 A (cm 3, s, mol) a
SO 1 O 1 Kr ˆ SO2 1 Kr
CH4 1 Ar ˆ CH3 1 H 1 Ar
CH3OH 1 Ar ˆ CH3 1 OH 1 Ar
C3H6 1 Kr ˆ CH3 1 C2H3 1 Kr
C3H8 ˆ CH3 1 C2H5
C2H4 1 Kr ˆ C2H2 1 H2 1 Kr
C2H4 1 Kr ˆ C2H3 1 H 1 Kr
1,3-C4H6 ˆ 2C2H3
CH3 1 CH3 ˆ C2H5 1 H
C6H6 ˆ C6H5 1 H
Ethylbenzene ˆ C7H7 1 CH3
c-C6H10 ˆ 1,3-C4H6 1 C2H4
C4H4 ˆ 2C2H2
Toluene ˆ C6H5 1 CH3
Pyridine ˆ C5H4N 1 H
24.8
17.0
42.71
75.73
17.17
15.18
15.15
16.61
11.89
17.3
15.95
15.57
15.11
12.95
14.89
n
22.6
27.08
215.7
±
±
±
±
±
±
±
±
±
±
E/R
Temperature range
Ref.
±
43,200
45,300
60,380
43,500
27,900
41,180
47,000
6562
59,380
37,590
33,060
41,500
36,500
47,800
2900±5200
1950±2770
1800±2600
1650±2300
1400±2300
2300±3200
2300±3200
1600±1900
2400±2800
1900±2400
1300±1800
1200±2000
1700±2400
1550±2200
[126]
[127]
[128]
[129]
[130]
[131]
[131]
[132]
[133]
[134]
[135]
[136]
[137]
[138]
[139]
a
Rate expressions are in the form of A…T†n exp…2E=RT† in units of s 21, cm 3 mol 21 s 21, cm 6 mol 22 s 21 depending on the reaction order.
Reaction order is dependent on number of molecules on left side of equation.
Subsequently the cw dye laser absorption technique was
extended to measure CH, CH3, CO, NO, CN, NH, NCO, etc.
Hanson et al. [82] demonstrated for the ®rst time how a
tunable cw CO electric-discharge infrared laser could be
used for NO absorption. Subsequently the tunable laser
technique was used by the same group for the detection of
H2O and N2O. An important further improvement in the
laser absorption approach was provided by Hanson et al.
in 1983 [83] when a cw dye laser was used to monitor
OH. Fig. 4 shows a schematic of the experimental arrangement for cw laser absorption used by Hanson et al. [81]. An
argon-ion laser is used to pump a single frequency ring dye
laser, which emits 0.1±0.5 W at visible wave lengths. For
several species the laser light is frequently doubled internal
to the ring cavity in a non-linear crystal, yielding a ®nal
output power of 1±50 mW. The spectrally narrow laser
light is single-passed through the shock tube about 1.9 cm
from the end wall, and low levels of absorption are monitored using a two beam differencing scheme. The nominal
laser wave length is monitored with a wave meter, but the
®nal wave length selection is typically made by peaking
absorption signal of a small fraction of the beam passed
through either a ¯at burner, a static absorption cell or a
low pressure electrical discharge tube. Further details of
the experimental arrangement can be taken from the paper
of Davidson et al. [84]. Ring laser absorption spectroscopy
has been used by Schading and Roth [85] for detecting OH
during the dissociation of cyanuric acid aerosol behind
re¯ected shock waves.
3.2. Mass spectrometry
Use of a time-of-¯ight mass spectrometer to make realtime measurements of species concentrations in a shock
Table 3
Rate coef®cients of various Si-containing reactions obtained by
ARAS ki ˆ Ai exp…2Ci =T† cm3 mol21 s21
Reaction
Ai
Ci
Si 1 CO ! SiO 1 C
Si 1 CO2 ! SiO 1 CO
Si 1 NO ! SiO 1 N
Si 1 O2 ! Products
Si 1 N2O ! SiN 1 NO
Si 1 N2O ! SiO 1 N2
7:9 £ 1014
6 £ 1014
3:2 £ 1014
2:7 £ 1014
5 £ 1014
8 £ 1013
34,510
9420
1775
1765
8100
±
Fig. 4. Schematic of laser absorption arrangement. Ref. [81].
160
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
Fig. 5. Schematic of a typical laser-schlieren set-up. Ref. [99].
tube was pioneered by Bradley and Kistiakowski [86].
Subsequently Kistiakowski and co-workers [87] applied
the technique to study the reaction of methyl and ethyl
radicals. The method has the advantage that several species
can be monitored simultaneously. The masses aid in
identi®cation of substances although identi®cation is not
altogether simple since molecules may dissociate in ionization. Chemiions may also be found which cannot be easily
distinguished from molecules and radicals. Problems associated with drawing of samples through nozzle/skimmer and
boundary layer interference are still to be solved. The
method is not highly sensitive, and small concentrations of
atoms and radicals formed during pyrolysis reactions cannot
be easily followed.
Despite the limitations pointed above, mass spectroscopic
(MS) diagnostic attached to shock tubes can prove a valuable tool for qualitative product analysis. Dove et al. [88]
have shown that the shock tube can be used as a source of
vibrationally excited molecules for studies of mass spectra.
Using a time-of-¯ight (TOF) mass spectrometer they
sampled high temperature (900±3300 K) gas samples of
carbon dioxide, diazomethane and azomethane directly
from the shock tube and recorded the mass spectra. The
results indicated a substantial temperature effect on the
obtained mass spectra.
Akiva Bar-Nun and Dove [89] have studied the oxidation
of acetylene by water vapor and its pyrolysis at 2650 K by a
shock tube coupled to a TOF mass spectrometer. Time
dependent pro®les of C2H2, C4H2, C6H2, C2H4, H2O and
CO at an average T ˆ 2650 K were obtained. Comparing
the experimentally obtained pro®les with model calculations, they were able to deduce a rate coef®cient for the
reaction OH 1 C2H2 ! C2 H2 O 1 H.
The formation of a thermal boundary layer immediately
after shock re¯ection leads to serious uncertainities in the
reacting gas temperature. A discussion of the problems associated with the boundary layer and its effect on gas
sampling from the re¯ected shock zone can be found in a
paper by Teshima et al. [90].
Recent mass-spectroscopic shock tube experiments have
dealt with the pyrolysis of various unsaturated organic
molecules in order to gain insight into mechanisms of soot
formation [91±93]. In all of these studies, attempts were
made to ®t measured TOF pro®les to kinetic models. An
important contribution is the detection of benzene as a major
product in allene pyrolysis [94]. Kern et al. also found a
good correlation between TOF pro®les of benzene growth
in various organic molecules and production of soot form
the same molecules from laser extinction experiments [95].
The other use of the method has been to determine ignition delay times in fuel±oxygen mixtures by observing with
a quaderupole mass spectrometer the sudden decrease in
oxygen concentration that occurs at the onset of combustion
[96±98].
3.3. Laser schlieren
The laser-schlieren method has been reviewed in great
detail by Kiefer [89], who introduced this technique in
1967 [100]. It is applicable to reactions that occur in very
short times, typically up to 10 ms. Since such short times
imply very high rates, the laser-schlieren method typically
provides data at the highest temperatures of any shock tube
methods. Best results are obtained for strongly endothermic
reactions, such as thermal dissociation. Because substantial
thermal effects are needed to produce measurable results,
high concentrations of reagents (up to 10±20%) are needed.
Coupled with the high temperatures, this sometimes leads to
complicated secondary reactions even at short times. This
dif®culty is compounded by the fact that the method gives
no direct indication of what reactions cause the observed
thermal effects. Therefore the observed effects must be
interpreted in terms of reaction mechanisms, which have
been already studied in detail by other methods at lower
temperatures.
The technique works on the well known principle that a
ray traversing any medium having a refractive index gradient, normal to the propagation direction will be de¯ected
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
(refracted) in the direction of increasing index. When an
endothermic rate process is initiated by shock heating, an
axial density gradient is established in the post-shock gas. In
a laser-schlieren experiment, a narrow laser beam passing
through the shock tube perpendicular to the tube axis, is
de¯ected and the extent of de¯ection determines the density
gradient. The measured density gradient is often linearly
related to the rate of reaction.
Fig. 5 shows the schematic of a typical laser-schlieren
apparatus developed by Kiefer, and his co-workers for
their determination of dissociation rate coef®cients. The
cw He±Ne gas laser operating in the TEM-OO (uniphase)
mode at 632.8 nm at which the beam has a Gaussian power
distribution over the plane normal to its propagation
direction. This beam, accurately aligned normal to the direction of ¯ow, passes through the shock-heated gas and
emerges being de¯ected. The differential detector in which
two photodiodes detect the beam and the difference signal is
recorded.
Laser-schlieren technique has been extensively used for
the study of vibrational relaxation or molecular decomposition. The ®rst application of the technique was to study the
vibrational relaxation of D2 and H2 [101,102]. Though the
enthalpy associated with the vibrational modes can be quite
small, relaxation is often rapid, at least for shock temperatures, and the gradient generated is observable over a wide
range of temperatures for many of the smaller molecules.
The available relaxation studies which have used laserschlieren are summarized in Tables 1 and 2 of the review
article contributed by Kiefer [99]. Two studies cited in the
tables (relaxation of O2 [103] and CO2 [104,105]) are of
signi®cance because they not only serve to establish the
validity of Bethe±Teller [106] equation, but also for their
demonstration of the accuracy of schlieren measurements.
From the information provided in the tables cited above,
it is evident that the technique has made a substantial contribution to our knowledge of relaxation at high temperatures.
Particularly notable are the extensive series of experiments
using a wide range of collision partners with CO2 [107,108]
and COS [109±111] and the set of hydrogen and deuterium
halide studies [112±114], both of which have helped establish the importance and behaviour of R±V energy transfer.
The basis for the use of laser-schlieren in the investigation
of chemical reaction rates is the linear relation between rate
and angular de¯ection. If the reaction, composition and
other state variables are known, then a direct connection
between observed gradient and reaction rate can be derived
[99]. Since the only states that can be speci®ed without prior
knowledge of the kinetics are the initial or frozen condition
and ®nal equilibriumÐand there is no rate at equilibriumÐ
most schlieren experiments have sought to determine the
`initial' rate of reaction.
The ®rst application of this technique to reaction kinetics
was an extensive study of O2 dissociation by Breshears et al.
[115]. From the density pro®les obtained in the study, the
coupling of relaxation and dissociation could be clearly
161
seen. Immediately following the start of the readings,
there is a local minimum or `dip' in gradient. At this point
vibrational relaxation is virtually complete and dissociation
is clearly underway and Breshears et al. took the gradient at
the dip minimum as indicating the initial rate, i.e. the rate
corresponding to vibrational equilibrium, but no dissociation. The coupling of relaxation and dissociation may be
such that, although relaxation is apparently complete, the
upper levels have not yet quite achieved their full steady
populations and the dissociation rate is consequently less
than its full steady value. This could give rise to a local
gradient minimum, and the gradient at this point would
then not re¯ect a true steady reaction rate. Evaluation of
this possibility requires a full master-equation analysis of
the relaxation±dissociation coupling.
The values of the effective dissociation rate coef®cient
obtained for mixtures of O2 in Kr by Breshears et al. exhibit
extremely high precision levels which allows detection of
very slight differences in rate between various mixtures. The
laser-schlieren technique has subsequently been used to
study the dissociation of several diatonic molecules like
H2 [116], F2 [117], Cl2 [118] and Br2 [119,120].
Methane was one of the ®rst polyatomic molecules whose
decomposition was studied using laser-schlieren [121]. No
indication of a dip in gradient was observed during its pyrolysis and a perfect match of the gradient records with
computer simulation was achieved. The decomposition of
CO2 [122] was again similar to that of methane. The other
polyatomic molecules studied using this technique are N2O
[123], SO2 [124], and NF3 [125]. Of all the kinetic studies
using the laser-schlieren technique, the work of Dove et al.
[123] on N2O pyrolysis most impressively illustrates its
possibilities. From an extensive series of experiments covering the range 450±3590 K, these authors derived relaxation
times, rates of primary dissociation, summed rates of two
secondary reactions and induction times for the primary
dissociation. Table 2 contains summary of recent work in
which laser-schlieren technique was used.
The laser-schlieren technique has also been used in collaboration with ARAS and mass spectroscopic detection
techniques [132,134,139,140] to examine the later stages
of hydrocarbon pyrolysis. Of special interest was the
demonstration of molecular mechanisms for vinylacetylene [141] decomposition C4 H4 ! C4H2 1 H2 and
C4H4 ! 2C2H2. The latter suggests, through microscopic
reversibility, a bimolecular reaction mechanism for the
condensation of acetylene molecules.
Kiefer, who poineered the use of laser-schlieren technique for reaction kinetic investigations, continues to be
active in this area. His recent publications of the dissociation
of methane [142], acetylene [143], carbon tetrachloride
[144], toluene [145] are examples of this.
3.4. Laser light scattering
Laser light scattering can be applied to gaseous systems
162
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
Fig. 6. Laser light scattering technique.
containing solid or liquid particles in highly dispersed form.
The gasdynamic behaviour of such dispersions is very similar to that of gases, so that thermal processes can be initiated
by shock waves as in gases. Aerosol droplet evaporation is
of great practical signi®cance in understanding spray
combustion in diesel engines and gas turbines. If the
droplets are of submicron size with very low particle volume
fraction (Knudsen Number , 1), the reduction in their size
due to evaporation behind an incident shock wave can be
measured using the laser light scattering technique. When a
shock wave runs through an aerosol (characterized by very
low droplet volume fraction in a gas) the mass, momentum
and heat exchange processes are relatively weak and do not
affect the gas phase properties signi®cantly. This is quite in
contrast to shock waves in dusty gases (with high particle
volume fractions), where the interphase ¯uxes are strong.
However the velocity of the aerosol droplets decreases
because of momentum transfer with the carrier gas, the
droplet temperature rises because of heat transfer from the
surrounding gas and the droplet size decreases due to
evaporation. The measured time-dependent droplet sizes
can be interpreted in terms of evaporation rates.
The shock tube arrangement used by Roth and Fischer
[146] for studying aerosol droplet evaporation is shown in
Fig. 6. The gas droplet mixture was generated by evaporation and subsequent condensation of dioctyl phthalate
(DOP)ÐC24H38O4. The initial droplet size and size distribution were independently measured using an optical particle
counter (OPC) and a differential mobility analyzer (DMA).
The time dependent change in the droplet size during
evaporation behind incident shock waves was measured
by laser light scattering. The optical arrangement consisted
of four light ®ber probes, adjusted at ®xed angles of 20, 30,
45 and 608 relative to the outcoming laser beam. The scattered light ¯ux signals were recorded by photo-multipliers
that were shielded from direct laser light. From the time
dependent scattered light ¯ux, the radius of the evaporating
droplet can be deduced.
3.5. Laser light extinction
Laser light extinction by particles is a variant of particle light
scattering. The method has been used by several investigators
(Wagner, Frenklach, Roth and others) to measure the induction
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
163
Fig. 7. Optical arrangement for measuring laser light extinction.
time for soot particle formation, soot growth rate and soot yield
during high temperature pyrolysis of hydrocarbons. This
optical diagnostic technique combined with laser-induced
incandescence can provide precise information on soot
concentration and soot particle size, down to a few nanometers.
The principle behind the laser light extinction method is
attenuation of light by the particles present in the shocked
gas. The laser beam passed through the particle forming
pyrolyzing gas at right angle to the shock tube axis. It is
detected by a photomultiplier and the signals are analyzed
applying Beer±Lambert Law relationships. Fig. 7 shows the
experimental arrangement used by Roth et al. [13] for
measuring soot induction times and soot volume fractions.
The laser used is a 15 mW He±Ne laser. The beam is directed perpendicular to the tube axis and focused on a photodetector. A narrow bandwidth interference ®lter in front of
the photo diode inhibited any thermal emission of the soot
particles from reaching the photomultiplier window.
Frenklach [10] who used this technique to investigate the
mechanism of silicon particle nucleation and growth in gas
phase pyrolysis of silane behind shock waves concluded that
his kinetic model predictions were found to be extremely
sensitive to the values of optical constants assigned to the
silicon particle material. This implies that the optical data of
the particle under investigation must be established with
higher certainty before a detailed analysis of the results
becomes possible.
3.6. Laser induced incandescence
Gas phase synthesis of nano-particles is a fast growing
area with potential industrial applications. The ultra®ne
particles produced in this way have several attractive
physico-chemical properties. Accurate in situ measurement
of the particle size is important to analyse the effect of
variables on the formation of these particles. The laser
light scattering method of particle size determination will
not be satisfactory for nano-particles because of its extremely reduced sensitivity with decreasing particle size.
LII is an attractive alternative that allows particle sizing
down to a few nanometers [147].
LII technique is based on the principle that larger particles
need more time for cooling than the smaller ones. When a
cloud of particles of different sizes is suddenly heated by an
intense laser pulse, they start to emit thermal radiation. As
the particles are rapidly cooled through heat transfer to the
carrier gas, larger particles with larger volume to surface
ratio take longer time for cooling than the smaller particles.
Therefore, the characteristic time of temperature decay can
be used as a measure for the particle size [9].
A schematic of the LII technique used by Woiki and Roth
[14] for measuring TiN particle sizes behind re¯ected shock
wave is shown in Fig. 8. The optical arrangement consists of
a Nd/YAG laser, end-wall mounted quartz window, two
plane convex lenses, a monochromator, and a photomultiplier.
Fig. 8. Schematic of the LII technique.
164
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
Fig. 9. Ignition delay times of various fuels. Ref. [153].
A single laser pulse of about 15 ns duration at l ˆ 1064 nm
and pulse energy of 70 mJ was used to irradiate the particles
in the reacting mixture behind the re¯ected shock wave. The
laser energy absorbed by the suspended particles causes a
fast increase in their temperature before they cool back to
the original post-shock temperature. The time dependent
thermal radiation of the particles detected at a wave length
of l ˆ 450 nm perpendicular to the laser path is taken to
represent particle cooling. This new diagnostic technique of
particle sizing is illustrated later under Section 6.4.
effect of inert diluent, such as argon, on the ignition delay
of benzene was studied by Bhaskaran and co-workers [150].
By comparison of the time±temperature curves, empirical
equations relating ignition delays to concentrations and
temperatures are obtained. An example is the empirical
equation deduced by Lifshitz et al. for methane±oxygen±
argon ignition
194:5 kJ
‰ArŠ0 ‰CH4 Š0:33 ‰O2 Š21:03 s
t ˆ 3:62 £ 10214 exp
RT
…1†
3.7. Ignition delay
where concentrations are expressed in mol cm 23. The
expression is valid over a temperature range 1500±
2150 K, a pressure range 2±10 atm, and for mixture equivalence ratios of 0.5±2.0.
A large number of papers relating measured ignition
delay to modeling of combustion processes have been
published. Notable contributors include Burcat [151],
Gardiner [152], Adomeit [153], Tsuboi [154], Bhaskaran
and co-workers [155±157], Westbrook [158]. Shock tube
ignition delay data has been related to the detonation properties of hydrocarbon fuels, through modeling and important
conclusions on detonation limits were deduced. GroÈnig
[159] has published several articles on pneumatic transportation of reactive dusts. Similarly the rate of ignition of
fuel±air mixtures at elevated pressures has been related to
the susceptibility of a mixture to engine knock. The shock
tube data provides a means of testing detailed reaction
mechanisms under conditions that are dif®cult to achieve
under other methods.
Adomeit and co-workers [153] have carried out exhaustive ignition delay studies under engine relevant conditions
When any combustible fuel±oxygen±argon mixture is
suddenly heated by shock wave, nothing happens for a
while (induction period or ignition delay) after which
there will be an abrupt increase in the rate of reaction,
coinciding with large temperature and pressure changes as
also emission of light. The rate of reaction increases almost
exponentially towards the end of the ignition delay period.
This time interval is a characteristic quantity for any fuel
and is a function of the initial temperature, pressure, and
mixture composition. The measurement of the dependence
of ignition delay on temperature and reactant composition
provides a powerful tool for modeling and understanding of
the combustion mechanism of a given fuel [148].
Considerable information pertaining to ignition delay
data on technical hydrocarbon fuels is available, mainly
because the experiments are fairly easy to perform. Lifshitz
and co-workers [149] re®ned the method by measuring
ignition delay times for several hydrocarbons over wide
ranges of temperature and mixture concentrations. The
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
165
Fig. 10. Experimental arrangement for measurements using ARAS, ring dye laser spectroscopy (RDLS), and laser photolysis.
on several hydrocarbon fuels (n-heptane, benzene, isooctane, methanol and methyl-tert-butylether (MTBE)) in a
high pressure shock tube. They have used fuel±air mixtures
of different stoichiometry without any inert gas dilution so
as to obtain delay data directly applicable to modeling of
engine combustion.The investigations were conducted at
two pressure levels, 13 and 40 bar so as to determine the
pressure effect on the strong ignition limit. A comparison of
the ignition delay times of all the fuels investigated under
stoichiometric mixture conditions is presented in Fig. 9.
For n-heptane, the ignition delay dependence upon
temperature both in the high and low temperature regions
can be expressed approximately by straight lines. In an
intermediate range, the dependence becomes strongly nonlinear and is represented by the well known s-shaped dependence. In this region of negative temperature coef®cient, the
alkylperoxy radical reactions become dominant. The sshaped dependence of the ignition delay for n-heptane is
connected with a two-step self-ignition process [160]. The
full kinetic scheme by Chevalier et al. [161] and reduced
mechanisms by MuÈller et al. [162] are able to model this
behavior by the inclusion of peroxy reactions.
The ignition delay data are quite reproducible. Though
the data obtained under different experimental conditions
may differ, the differences tend to be small when rationalized with empirical correlation equations. It has been
tried by many to deduce reaction mechanisms, and determine individual rate coef®cients, from ignition delay times.
But one should be careful in reaching ®nal conclusions,
unless a complete understanding of the reaction mechanism
involved is available. However, the delay data can be used
effectively in carrying out sensitivity analysis of all the reactions involved in a given mechanism. This can help in
consolidating and sometimes simplifying the combustion
mechanism of a complex hydrocarbon fuel.
4. Homogeneous systems
4.1. Simple thermal decomposition reactions
The shock tube as a high temperature wave reactor has
been extensively used for the study of molecular decomposition. When a test gas containing a molecule A is suddenly
heated to a high temperature, the gas relaxes towards a new
equilibrium according to the Lindemann mechanism
A 1 M $ Ap 1 M
…2†
Ap ! Products
…3†
where M is the collision partner (usually the carrier
gas). The rate of disappearance of A depends on both
the temperature and pressure. At low pressures the collisional deactivation (reaction (2)) is much slower than
its chemical reaction and the reaction obeys the second
order rate law or low pressure limit. At high pressure,
166
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
Fig. 11. (a) N-atom ARAS signal and corresponding concentration during the thermal decomposition of N2, (b) rate coef®cient of N2
dissociation.
the rate of disappearance of A becomes independent of
the concentration of the collision partner M and obeys a
®rst-order rate law, also called high pressure limit. In
reality, the reaction is much more complex than
described above. The energy required for dissociation
is supplied to the molecule through a large number of
collisions of different ef®ciencies. The intramolecular
energy transfer is also very important. The coupling
between vibrational relaxation and dissociation can
play a signi®cant role in delaying dissociation.
The thermal decomposition of diatomic molecules
proceeds under conditions close to the low pressure limit.
A good example is the dissociation of N2. Because of its
importance under hypersonic conditions as in space vehicle
re-entry, its dissociation rate coef®cient has been determined in numerous studies, all following the rate of
disappearance of N2
N2 1 M ! N 1 N 1 M
…4†
However, a more sensitive method of measurement will be
to monitor the rate of appearance of the atomic dissociation
product N using ARAS technique and hence deduce a more
accurate rate coef®cient.
A schematic diagram of the experimental arrangement
employed for ARAS is shown in Fig. 10, together with other
devices, (an excimer laser) which will be explained later.
A microwave discharge lamp fed with a low pressure ¯ow
of He/N2 mixture supplied the required NI triplet radiation at
119.9 nm, which is single passed through the shock tube about
10 mm back from the end wall. A 1 m 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
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
167
Fig. 12. Typical measured traces of (a) S( 3P) and (b) S( 1D) absorption/concentration during thermal decomposition of COS.
temperature thermal decomposition absorb the resonance
radiation very effectively. The absorption measured by a
solar blind photomultiplier is then related to the N atom. For
detailed evaluation of the signals a reliable calibration curve is
needed, see Thielen and Roth [163].
An example of the absorption signal obtained (wavy line)
and corresponding N concentration (dashed line with ®lled
circles) from a re¯ected shock experiment with a mixture of
200 ppm N2/Ar at 5500 K and 1.43 bar is shown in Fig.
11(a). The time of arrival of the re¯ected shock is marked
by an arrow, and after a certain time delay, the N concentration increases linearly with time. From the slope of the N
concentration line, the rate coef®cient for N2 dissociation
can be determined. Results obtained from a series of experiments in N2/Ar mixtures are summarized in an Arrhenius
form in Fig. 11(b). The rate coef®cient deduced for N2 dissociation is in good agreement with theoretical calculations of
Troe [164]. Because of the high sensitivity of the ARAS
technique, the low temperature end is very much extended
compared to what can be obtained by other measurement
techniques. Though the data covers several orders of magnitude, the rms deviation in the value of k is quite small.
The thermal decomposition of triatomic molecules like H2O,
COS or N2O 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 ®st case, electronically excited atoms
are formed, whereas in the second case ground state atoms are
the decomposition products. A good example for this type of
reactions is the thermal decomposition of COS
COS…1 e† 1 M ! CO…1 e1 † 1 S…3 P† 1 M;
DR h ˆ 298:9 kJ mol21
COS…1 e† 1 M ! CO…1 e1 † 1 S…1 D† 1 M;
DR h ˆ 409:9 kJ mol21
…5†
…6†
168
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
Fig. 13. Measured formation rates of S( 3P) and S( 1D) during the thermal decomposition of COS.
The ®rst decomposition reaction is energetically easier,
but requires a single triplet transition of COS (not indicated
in the above reaction). The second reaction describes the
direct formation of electronically excited S( 1D) from the
ground state.
Woiki and Roth [165] have measured both S( 3P) and
1
S( D) concentrations during thermal decomposition of
COS by applying ARAS. Fig. 12(a) and (b) show the absorption signals measured by both electronic states of S (wavy
lines). The conversion into concentration pro®les by applying calibration curves are also shown by dashed lines. The
evaluation of rate coef®cient values for this and other
decomposition experiments are summarized in Fig. 13.
Both S( 3P) and S( 1D) formation rates show Arrhenius behavior, but their absolute values differ by about a factor of
150. It seems at ®rst sight that S( 3P) formation is the dominant reaction channel, but this cannot be concluded from the
present experiments. The quenching and excitation reaction
S…1 D† 1 M $ S…3 P† 1 M;
DR h ˆ 110:3 kJ mol21 …7†
is very fast and contributes, in addition to the above direct
formation reactions. Reaction (7) is practically equilibrated
under the present experimental conditions. This can be seen
from the dashed line in Fig. 13 obtained for the formation of
S( 1D) based on the equilibrium assumption and the
measured S( 3P) formation rate. It is therefore to be
concluded that the present results do not allow a decision
to be arrived at on whether reaction (5) or (6) dominate
during the thermal decomposition of COS.
4.2. Complex thermal decomposition reactions
Thermal decomposition of polyatomic molecules with
four or more atoms are even more complex and the in¯uence
of subsequent reactions cannot be ignored even under highly
diluted conditions.
The ARAS technique in conjunction with the shock tube
has made it possible for evaluating the rate coef®cients for
the primary decomposition steps and subsequent oxidation
steps, of small hydrocarbon molecules like CH4, HCN, C2H4
and C2H6 [37]. As a typical case study, the thermal decomposition and oxidation of CH4 will be discussed. For low
initial concentration of CH4 (5±200 ppm) in argon behind
re¯ected shock wave, the time dependent H atom concentration was directly measured using ARAS. The rate coef®cient for the initial decomposition reaction
CH4 1 M ! CH3 1 H 1 M
…8†
has been determined from the measured variation in H atom
concentration. For a low initial CH4 concentration of 5±
10 ppm, the experiment showed an immediate linear
increase of H concentration with time. The rate of
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
169
Fig. 14. Arrhenius plot of the rate coef®cient for CH4 1 M ! CH3 1 H 1 M.
production of H divided by the initial CH4 and argon
concentrations yields k8. Arrhenius plot of the rate coef®cient k8 for different CH4 1 Ar mixtures is shown in Fig.
14 from which the following expression can be deduced:
kg ˆ 7:85 £ 1027 exp…246;800=T† cm3 s21 molecule21 …9†
At higher initial CH4 concentrations of 50 and 200 ppm
and temperature T , 2000 K, the measured H atom pro®les
are curved and after some 100 ms, a quasi-stationary value
could be observed. The measured reciprocal steady state H
atom concentration multiplied by the total density is plotted
against reciprocal temperature in Fig. 15. The least squares
line through the data is
‰MŠ
ˆ 15:4 £ 1023 exp…139;210=T†
‰HŠ
…10†
The experimental evidence indicates that the ®rst pyrolytic decomposition step of CH4 is followed by reactions
of the products with methane. Very important is the reaction
of H atoms with CH4 [166]. Because of the low CH4 concentrations, further reactions could be neglected
H 1 CH4 ! H2 1 CH3
…11†
With the steady condition for H atoms, the observed
concentration [M]/[H]stat must be interpreted as the ratio of
k11/k8
k11 ˆ 1:2 £ 1029 exp…27580=T† cm3 s21 molecule21 …12†
Fig. 16 shows measured rate coef®cient k11 [167±170]
and a computation of Clark and Dove [171], where the
non-Arrhenius behavior of the reaction is clear.
Study of pyrolysis of hydrocarbons from the point of soot
formation has been carried out very extensively. Frenklach
et al. [172] have investigated soot formation in shock tube
during the pyrolysis of acetylene, allene and 1,3-butadiene.
Similarly Wagner et al. [173] have used the shock tube to
study soot formation during the high temperature pyrolysis
of benzene/acetylene and acetylene/hydrogen mixtures. A
170
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
Fig. 15. Arrhenius plot of measured steady state H-atom concentration and kinetic interpretation.
large volume of published information is available on soot
formation involving high temperature pyrolysis of hydrocarbons. Roth et al. [11] have recently used the LII technique for sizing the soot particles produced during the
pyrolysis of acetylene behind shock waves.
The pyrolysis of acetylene has received most attention in
recent years (see Ref. [174]) and the experimental results
obtained in a variety of kinetic studies were summarized by
Tanzawa and Gardiner [175,176] in a kinetic model that
suggests the sequences
C2 H2 ! C4 H3 ! C4 H2 ! C6 H2 ! C8 H2 !
…13†
for acetylene pyrolysis. The model also predicts establishment of equilibrium among the smaller acetylenes and
acetylenic radicals prior to soot formation. Frenklach and
co-worker [172] in their systematic study of soot formation
characteristics in shock tube pyrolysis of acetylene, have
analyzed in detail the in¯uence of temperature, pressure,
and initial concentrations. The results obtained by them is
discussed below:
The conversion of hydrocarbon to soot was monitored by
laser light extinction measurements conducted in visible
(632.8 nm) and infrared (3.39 mm) regions.
The induction time, de®ned as the maximum curvature in
the extinction signal, was extracted from the recorded
signals. The soot yields were calculated based on Graham's
model but are subject to the ambiguity in the value of the
refractive index assigned to the soot particles. The important
Fig. 16. Temperature dependence of the rate coef®cient k11 for the
reaction H 1 CH4 ! H2 1 CH3.
conclusions based on their observations are:
(i) Increase in acetylene concentration shortens the induction period for soot appearance at 3.39 mm, whereas it has
no effect at 632.8 nm.
(ii) The temperature dependence is approximately the
same at both wave lengths.
(iii) The induction periods were longer in the infrared
than in the visible region. This difference in induction
times supports the suggestion of consecutive rather than
explosive nature of the soot formation process.
A more informative analysis of experimental results on
soot formation can be achieved by comparing soot yield
dependence on temperature, pressure and concentration.
The results indicate the existence of a maximum in soot
yield with temperature at higher concentrations of acetylene
as shown in Fig. 17. The bell-shaped dependence of soot
yield on temperature has been observed in pyrolysis of a
variety of hydrocarbons. The existence of the soot-yield
maximum and its shift with a signi®cant increase in value
to higher temperatures at low pressures can be explained by
the following conceptual model [172]:
C2 H2 ! X
…14†
X!A
…15†
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
171
Fig. 17. Soot yield curves during acetylene pyrolysis. Ref. [172]. 120%C2H2, T ˆ 1748 2 2802 K; p ˆ 0:28 2 0:49 bar: W 4.65% C2H2, T ˆ
168723123 K; p ˆ 1:27 2 2:33 bar:
A1M!X
…16†
A1X!S
…17†
where X ˆ …X1 ; X2 ; ¼† collection of non-aromatic species
including acetylene, A ˆ …A1 ; A2 ; ¼† collection of aromatic
species, S ˆ …S1 ; S2 ; ¼† collection of light absorbing
species including soot, M ˆ …M1 ; M2 ; ¼† collection of collision partners.
The products of acetylene pyrolysis, X, interact among
themselves, eventually forming the aromatic species A.
Which means the reactions of a nascent aromatic species
A comprise two parallel routes, Eq. (16) the pressure dependent high-activation-energy fragmentation of an aromatic
ring and Eq. (17) a low-activation-energy radical molecule
interaction of an aromatic ring with aliphatic fragments
leading to soot.
There is a difference, however, between the aromatic and
nonaromatic cases. In pyrolysis of aromatic hydrocarbons,
fragmentation via reaction (14) is the main source of X but,
at the same time, the aromatic rings are being destroyed. The
competition between supply of X and removal of A is
responsible for the appearance of the maximum in the soot
yield. In acetylene pyrolysis, the nonaromatic species X are
primarily formed from acetylene itself, whereas the contribution from the decomposition of the nascent aromatic
species is expected to be small. Therefore, the main role
of fragmentation is removal of the soot precursors. The
occurrence of the soot-yield maximum for acetylene can
be explained by the competition between the formation of
aromatic molecules A and their destruction via reaction
(16).
4.3. Oxidation reactions
High temperature oxidation or combustion of hydrocarbons is very complicated as it is governed by energy
and mass transfer as well as chemical kinetics and thermodynamics. The chief contribution to the understanding of
combustion by shock tube research has been in the area of
kinetics. The number of chemical reactions involved in
combustion is very large and the kinetic data obtained
from shock tube studies cover only the initial steps. Skinner
et al. [33] in their review article on hydrocarbon oxidation
have highlighted the contributions made by several
researchers who all used the shock tube. The kinetic
mechanism of the combustion process occurs largely
through reactions involving free radicals such as H, O,
OH, CH3, C2H5, C3H7, and HCO which are formed during
combustion and they in turn react to sustain the process.
Though the concentrations of these radicals may be small,
the rate constants of the reactions in which they participate
are large.
Homogeneous combustion of hydrocarbons is strongly
believed to proceed ®rst by pyrolysis to ethylene, acetylene,
methane and hydrogen followed by oxidation of these
172
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
substances to CO, CO2, and H2O. There may be some overlap of the stages but they can be ordinarily distinguished.
Therefore, the combustion of a complex hydrocarbon molecule can be explained by assembling the oxidation mechanisms of all the involved sub-molecules. The shock tube
investigations have so far been dealing only with the oxidation of simple molecules like CH4, C2H2, C2H4, C2H6, and
C6H6. Accurate rate coef®cient data for all the elementary
reactions involved in the oxidation of the above-mentioned
simple molecules is a must for detailed modeling of
complex combustion reactions.
4.3.1. Initial oxidation steps in O 1 CH4 reaction
An example is the oxidation of CH4 by O atoms. In ®ve
different gas mixtures 10/5, 20/10, 25/25, 15/100 and 15/
150 ppm CH4/N2O highly diluted in argon, measurements
of O and H atom absorptions were monitored using ARAS
[177]. Two types of O atom absorption signals were
obtained. At high temperatures and low N2O concentrations,
the production of O atoms from N2O begins immediately
after shock arrival and the absorption increases. The
produced atoms react with CH4 and the absorption signal
reaches a maximum. It subsequently decreases because of
the consumption of N2O and the resulting decrease in O
atom production as can be seen in Fig. 18. The production
of H atoms increases rapidly due to the thermal decomposition of CH4 and the subsequent reaction between
CH3 and O.
At lower temperatures (above 1500 K), high N2O concentrations of 100 ppm are needed to produce suf®cient O
atoms. After shock arrival, a discontinuity can be observed
because of the quasi-continuous absorption of N2O at
130.5 nm. It is followed by the resonance absorption of O
atoms that reach a maximum value. Under these conditions
the concentration of N2O remains nearly constant. The
whole kinetic mechanism is basically determined by the
competition of the reactions
N2 O 1 M ! N2 1 O 1 M
…18†
CH4 1 O ! CH3 1 OH
…19†
The measured H atom concentrations indicate that further
reactions of the radicals CH3 and OH take place according to
CH3 1 O ! CH2 O 1 H
…20†
CH4 1 OH ! CH3 1 H2 O
…21†
At temperatures above 1900 K, the in¯uence of the
known pyrolytic decomposition of CH4 cannot be neglected.
A differential equation system comprising of reactions
(8), (11), (18)±(21) can be solved to yield concentration
pro®les of the species involved. From parametric studies,
it can be seen how important reactions (18) and (19) are with
respect to the O atom pro®les. From the H atom measurements, one can estimate the in¯uence of reaction (20) with a
rate coef®cient
k20 ˆ 1:5 £ 10210 exp…21000=T† cm3 s21 molecule21 …22†
which is a factor 1.5 smaller than the value reported by
Peeters and Mahnen [178].
With this value for k20, matching of the measured and
computed H atom pro®les was found better. With the values
of k8, k11, and k20 ®xed at the above mentioned values, and
taking the value of the unimportant k21 as reported in
literature, one can adjust the computed O atom pro®les to
the measured pro®les by varying the values of k8 and k11.
The value determined for k8 is very similar to the earlier
experimental value of Olschewski et al. [179]. The results
obtained for the chain branching reaction (20) is shown in
Fig. 18. Measured H and O atom pro®les and ®tted curves: 10/5 ppm CH4/N2O/Ar, T ˆ 2055 K; p ˆ 2:09 bar:
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
173
Fig. 19. Temperature dependence of the rate coef®cient for the reaction O 1 CH4 ! OH 1 CH3.
Fig. 19. The least squares ®t through the data gives
k19 ˆ 6:8 £ 10210 exp…27030=T† cm23 s21 molecule21
…23†
The activation temperature of reaction (19) is much
higher than the values of the low temperature experiments
of Wong and Potter [180] and Westenberg and de Haas
[181]. The measured coef®cient k18 is very similar to the
value of Brabbs and Brokaw [182]. The non-Arrhenius
behavior of k19 is obvious from the comparison of low
temperature and high temperature data. In the entire
temperature range 300±2200 K, one can describe k19 by
the equation
k19 ˆ 1:94 £ 10217 T 2:075 exp…23840=T† cm3 s21 molecule21
…24†
Thus, it is possible, as in the case of CH4 1 O to
determine from shock tube measurements accurate rate
coef®cient data for the initial decomposition and oxidation
steps of other simple hydrocarbons also.
4.4. Precursor initiated reactions
A complex reaction, after its initiation, is propagated
through the participation of several reactive radical species.
To be able to describe the rate at which the overall reaction
progresses, one needs precise information on the rate coef®cient data of radical±radical or radical±molecule reactions. A precursor molecule can be made to supply these
radicals of interest either by thermal decomposition due to
shock heating or by laser photolysis. After the test gas has
been `seeded' with the reactive radicals, the speci®c reaction
of interest can be monitored using, e.g. ARAS and its rate
coef®cient determined. It is of course obvious that the
radical formation reaction must be very fast compared to
the reaction under investigation.
4.4.1. Thermally initiated pre-cursors
The thermal method of producing radical species in a
shock tube involves use of a pre-cursor molecule which
readily decomposes by thermal reaction. If it is ensured
that the radical formation is very much faster than the reaction under investigation, then the complexity due to
coupling of the radical forming step with other simultaneous
pyrolysis reactions can be minimized. A good example for
this type of reaction is the reaction of Si atoms with CO
Si 1 CO ! SiO 1 C;
DR h ˆ 276:1 kJ mol21
…25†
The reaction was studied by Mick and Roth [183] in
mixtures containing 0.75±20 ppm SiH4 and 0.2±5% CO
diluted in argon at temperatures 2720±5190 K using Si
atom ARAS. A sample trace recorded for Si absorption in
mixtures without and with CO is shown in Fig. 20(a). Immediately behind the re¯ected shock wave, the precursor
SiH4 decomposes almost instantaneously to form Si atoms
and H2 at a constant level. In the mixture with CO, the
silicon atoms in turn react as per reaction (25) resulting in
a decrease in Si absorption.
The kinetic evaluation of the above type of absorption
signal is facilitated by the fact that the disappearance of Si
proceeds under ®rst order conditions, because the CO
concentration is practically constant
d ln‰SiŠ=dt ˆ 2k25 ‰COŠ0
…26†
The silicon atom concentration can be directly related
to the measured absorption via the modi®ed Lambert±
Beer Law with a concentration exponent n ˆ 0:8: The
above equation when rewritten, yields
d ln
{‰2ln…1 2 A†1=n Š
dy
ˆ
ˆ 2k23 ‰COŠ0
dt
dt
…27†
with A being the measured fractional Si absorption. Fig.
20(b) shows the property y as a function of reaction time.
174
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
Fig. 20. (a) Si atom absorption measured in mixtures of Ar and 1 ppm SiH4 without and with CO addition, T ˆ 3600 K; p ˆ 0:8 bar:
(b) Evaluation of the absorption signal by the ®rst order method.
The linear behavior of y con®rms the ®rst order assumption for reaction (25) and allows determination of the
rate coef®cient from the slope. A summary of the rate
coef®cients thus obtained is shown in the Arrhenius
diagram on Fig. 21. This also includes results of C
atom measurements. The standard deviation of the data
due to experimental scatter is very low at 110% Rate coef®cients of several silicon reactions obtained by Roth et al.
are summarized in Table 3.
4.4.2. Photolytically initiated radicals
The method of generating radical species by photolysis
and following their further reactions is an old and well
established technique in chemical kinetics, mostly used in
room temperature static cells. Earlier investigators have
used ¯ash lamps to photolyze precursor molecules in
shock-heated gases. With the availability of high intensity
pulsed UV lasers, which have a higher spectral intensity and
a greater monochromacity compared to ¯ash lamps, laser
photolysis has been preferred [81,184]. Compared to the
thermally (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 gas. An extension to lower temperatures is therefore un-problematic. A disadvantage is that the energy transfer or the absorption coef®cient during photolysis is not
known in detail, rendering prediction of the identity or the
energy states of the photofragments produced more dif®cult.
The following reaction belonging to this category was
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
175
Fig. 21. Rate coef®cient for the reaction Si 1 CO ! SiO 1 C.
investigated by Woiki and Roth [185]:
S 1 H2 ! HS 1 H;
DR h ˆ 80:3 kJ mol21
…28†
S atoms were photolytically produced by an excimer
laser pulse at 193 nm in mixtures of 25 or 30 ppm CS2
and 1000±4000 ppm H2, diluted in Ar. The laser was
coupled into the measurement plane of the shock tube
through an end plate made of quartz glass. The experimental arrangement is shown in Fig. 10. The original
rectangular beam was expanded by a cylindrical lense
allowing illumination of the whole ARAS diagnostic
path. The temperature range of the experiments was
1260±1840 K. Progress of the chemical reaction was
studied by ARAS monitoring of S( 3P) at 147.4 nm. A
typical absorption pro®le obtained is shown in Fig.
22(a). The arrival of the re¯ected shock, which is associated with a temperature discontinuity does not initiate any measurable S atom formation in the mixture.
Only the laser photolysis pulse of about 13 ns duration,
which was passed through the mixture 50 ms after the
arrival of the re¯ected shock wave, causes a step like
peak in S atom absorption. Subsequently the signal
decreases due to S consumption by its reaction with
H2. Data reduction could again be achieved by assuming
®rst-order decay of S. Results of all the experiments are
summarized in the Arrhenius plot of Fig. 22(b). The
data can be approximated by an Arrhenius expression
of the form
K
cm3 mol21 s21
k ˆ 6 £ 1014 exp 212;070
…29†
T
In Fig. 22(b) results obtained from another series of
experiments, where the S atoms were thermally initiated
by the pyrolysis of COS, are also included. Both the data
sets agree very well and this illustrates the high potential of
photolysis experiments at low temperatures and pyrolysis at
high temperatures for the initiation of radical±radical or
radical±molecule reactions.
5. Dispersed systems
5.1. Heterogeneous±homogeneous systems
Certain reactive substances, originally in the form of
®nely dispersed powder, when subject to shock heating,
evaporate nearly instantaneously and within a short period
follow all the characteristics of a homogeneous system. A
typical example for this behaviour is the thermal decomposition of fullerene (C60). This material, which is known to be
a new carbon modi®cation, exists in the form of soot-like
black powder, at room temperatures. There is a growing
interest from industrial as well as scienti®c points of view,
to evaluate the thermal stability and chemical resistance of
this potential material at high temperatures.
Sommer et al. [186] have studied the thermal decomposition of C60 at temperatures above 2500 K behind re¯ected
shock waves and measured C2 emission using ring dye laser
diagnostic, shown in Fig. 23. The C60 powder was dispersed
in argon using the expansion wave driven aerosol generator
(Fig. 24) and ®lled into the shock tube where it was heated
by the shock wave. Time dependent C2 concentration in
the post-shock mixture was deduced from the intensity
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K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
Fig. 22. (a) S-atom ARAS signal after pyrolysis of a CS2/H2/Ar mixture, (b) rate coef®cient of reaction S 1 H2.
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
177
Fig. 23. Experimental arrangement for measurements with RDLS and infrared diode laser spectroscopy (IRDS).
difference between the incident and transmitted laser
light. One dif®culty with the data deduction was the
quantitative characterization of the amount of fullerene,
which was a dispersed powder in the pre-shock situation
and a vapour in the post-shock reacting mixture. This
problem was overcome by performing a separate set of
experiments under identical conditions with C60/Ar
mixtures enriched with 6% O2 and measuring the
products CO and CO2 with a tunable IR diode laser.
Assuming a complete oxidation of all carbonaceous material, which is justi®ed under the present high temperature
conditions, the post-shock C60 concentration was determined from the measured oxidation products.
Based on the C2 measurements, a simple C2 abstraction
step followed by other reactions was proposed:
C60 1 M ! C2 1 C58 1 M
…30†
An apparent activation energy for the above decomposition step was approximated by the expression
kapp ˆ 4:25 £ 1012 exp…2516 kJ mol21 =RT† s21
Fig. 24. Aerosol generator with particle analyzing system.
…31†
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Fig. 25. Schematic of droplet evaporation behind a stationary shock wave.
5.2. Heterogeneous reactions
Reactions involving ultra-®ne solid particles that are
homogeneously dispersed in a gas mixture at high temperature are of interest in many technical applications as in
pulverized fuel combustion, soot oxidation, dust explosions
or reduction of SO2 by limestone particles. The complexity
involved in analyzing such heterogeneous reactions is very
much higher than in the case of gas phase reactions. One
way of tackling the problem will be to consider the
dispersed system as a pseudo-homogeneous system (provided the system consists of only a dilute suspension of
ultra-®ne particles) and apply all the principles which are
valid for a gas. Under these conditions, the shock tube lends
itself as an ideal tool for investigating reactive aerosol
systems. The mixture containing ultra-®ne particles can be
heated by a shock wave, thus initiating chemical reactions,
which can be monitored by optical methods.
The combination of aerosol physics and shock wave technology, offers an ideal environment for the study of a variety
of problems including droplet evaporation at well de®ned
high temperature conditions. A shock wave running through
an aerosol disturbs the quasi-equilibrium of the gas particle
mixture and initiates relaxation processes. As an aerosol
is characterized by a very low particle volume fraction,
the mass, momentum and heat exchange processes are
relatively weak and do not affect the gas phase properties
signi®cantly.
The situation of a stationary shock wave in an aerosol
with low droplet volume concentration is shown schematically in Fig. 25 [187]. The shock front can be assumed as a
gas phase discontinuity. Because of the very low volume
fraction of the suspended droplets, the gas properties are
nearly independent of the droplet processes and can be
assumed to be constant. The behaviour of the particle
cloud going through the wave front is quite different and
more complex. The droplets are not directly in¯uenced by
the gas phase discontinuity. Their velocity decreases
because of the momentum transfer with the carrier gas,
the droplet temperature rises because of heat transfer from
the surrounding gas, and the droplet size decreases during
the subsequent evaporation processes.
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
The particle behaviour in the shock wave relaxation
zone is determined by three relaxing quantities namely,
the droplet velocity vp, the droplet temperature Tp
(assumed to be uniform for small Biot numbers), and
the droplet radius rp, all having different characteristic
relaxation lengths (or times). The experimental conditions are chosen in such a manner that the relaxation
length (time) for the evaporation process is much longer
than for other exchange processes. In this case, the
measured time dependent particle sizes behind shock
waves can easily be interpreted in terms of evaporation
rates. However, there are some limitations and special
problems in dealing with the study of dispersed systems
which are discussed below.
5.2.1. Preparation of the gas/particle mixture(aerosol) and
its homogeneous distribution in the test section of the shock
tube
The dispersibility of a powder in a gas depends on the
material, particle size, shape and moisture content. Hydrophobic materials such as talc are easier to disperse than are
hydrophilic materials like quartz and limestone. To fully
disperse a powder, it is necessary to supply suf®cient energy
to a small volume of the bulk material and to separate the
particles by overcoming van der Waals forces of attraction.
From theoretical considerations of inter-particle forces, it is
possible to conclude that the dispersibility of powdered
material increases with particle size. Particles of very
small sizes are more dif®cult to disperse than those of larger
sizes.
A practical method of dispersing ultra®ne powders homogeneously is to use a powder dispenser. A schematic of the
aerosol generator developed by Rajadurai et al. [188] is
shown in Fig. 24. It is basically a small glass shock tube
of 50 mm inner diameter connected to a spherical glass
vessel of 20 l volume to store the generated aerosol. The
powder to be dispersed is placed on a ¯at plate which is
inserted into the low pressure section near the diaphragm.
Either the incident shock or expansion wave can be used for
dispersing the powder based on the initial pressure ratio
across the diaphragm.
For expansion wave based dispersion, the pressure in
the low pressure section should be kept low (10 22 mbar)
and the dispersion gas (Ar) pressure in the driver
section increased until the diaphragm bursts. For shock
wave dispersion, the low pressure section is also ®lled
with argon up to a pressure of 500 mbar and the driver
section with the dispersion gas (Ar) up to about 2 bar.
After bursting of the diaphragm, the generated expansion or shock wave disperses the powder uniformly. The
glass vessel is ®nally ®lled to atmospheric pressure with
argon. The quality of particle dispersion is evaluated by
conventional sampling on nuclepore ®lters [189] or using
a scanning electron microscope (SEM) together with a
matched imaging system.
179
5.2.2. Gas dynamic problems associated with shock wave
heating of a two phase system
The non-homogeneity due to solid-gas mixture is
overcome to a large extent by choosing sub-micrometer
particle sizes with a low overall particle loading. By
this, the effect of particles on the physical properties
of the ¯uid will be minimum. This assumption enables
the temperature and pressure of the particle/gas mixture
to rise instantaneously behind the shock wave. Because
of the small size of the particles, the slip ¯ow effects
between the particle and gas are very short and therefore the
particles are also heated instantly to the same value as the
gas. The gas phase reactants initially present or formed
during a fast homogeneous process can react with equal
facility with the sub-micron particles as with other gas
phase reactants.
5.2.3. Determination of the reactive surface of the aerosol
system
The rate of a heterogeneous reaction depends, besides
other surface properties, on the size or the reaction area.
This requires the particles to be characterized with respect
to these properties. This can be done using either laser light
scattering, laser light extinction or LII techniques described
earlier.
5.2.4. Suitable optical diagnostic technique to measure gas
phase species in a particle loaded system
The problem of determining the progress of a heterogeneous reaction by measuring either the product
species formed or the reduction in reactant species
concentration can be achieved by using, e.g. tunable
IR-diode laser absorption spectroscopy. This is made
possible due to the fact that the actual interference by
the particles is small, as light extinction by small particles is weak in the infrared region. The optical
arrangement used by Brandt and Roth [190] is shown
in Fig. 23. 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 ®ltering
and a detection system. The laser is pulsed with a
frequency of 25 kHz 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 concentrations can be determined. It was recently shown that O atom ARAS can
be used to follow the heterogeneous reaction of O atoms
in gases containing dispersed soot particles. Because of
the high sensitivity of the spectroscopic technique, the
amount of dispersed particles can be very low. Nevertheless, the light extinction by the particles must be
taken into account.
5.3. Soot oxidation
A typical example of a thermally initiated reaction in a
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Fig. 26. (a) Example of a pulsed IR diode laser scans in a shock heated soot/N2 O/Ar mixture showing increasing CO spectral absorptions,
(b) corresponding CO concentration.
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 experiment using the shock tube was CO. The
oxidation proceeds mainly via the global heterogeneous
reaction
Cs 1 O ! CO
…32†
where Cs represents the solid carbon in the soot particles.
The O atoms were generated by the fast thermal decomposition of N2O that was present in the initial gas/particle
mixture. According to the above reaction, the rate of
formation of CO is
d‰coŠ
ˆ a0 Z0 ap
dt
…33†
where Z0 ˆ 1=4C 0 ‰OŠ:
In this equation, a0 ; 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 Z0 can be calculated from the
Hertz±Knudsen equation with C 0 being the mean thermal
velocity of O atoms. The required kinetic property not
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
181
Fig. 27. Reaction probabilities of soot oxidation by O, OH, and NO obtained from shock tube experiments.
known in the above equation is a0 ; which can be determined from the measured properties [CO] and ap for a
given [O].
A typical example of an individual shock tube experiment with a soot/N2O/Ar mixture at 2490 K is shown
in Fig. 26. The laser was tuned to 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
indicated on Fig. 26(a). In the traces on the lower
part of Fig. 26(a), selected scans of the same experiment are shown in more detail on an enlarged scale.
The strong absorption lines on scan A were caused by
spectral absorption of N2O under pre-shock conditions.
Beginning with the ®rst post-shock scans, sharp spectral
lines of CO appear showing 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 coef®cient
depends on the line strength and the line shape factor.
The latter was determined by ®tting a Voigt pro®le to
the measured absorption line. Taking this into account,
the sequence of absorptions obtained can be transformed
into a time dependent CO concentration, as illustrated in
Fig. 26(b). From the initial slope together with the
above equation, or from computer simulation of this
and other oxidation experiments, reaction probabilities
a 0 were determined. A summary of the results is
given in the Arrhenius diagram of Fig. 27, which also
contains results of soot oxidation by OH and NO. The
a 0 values obtained for O atom reaction are nearly
independent of temperature and can be approximated
by a mean value a0 ˆ 0:23: For more details see Ref.
[191].
6. Shock wave initiated material synthesis
Synthesis of nanoparticles is an essential part of nanotechnology, which is concerned with the development and
utilization of structures and devices scaling between individual molecules and features below 100 nm. Nanotechnology
is recognized like information technology and biotechnology as having a driving potential for the beginning
century with tremendous economic impact. Thin ®lms,
lateral structures and very small particles are examples
of nanotechnology having different geometrical dimension. These structures have novel properties compared
to the bulk materials due to size effects. Nanotechnology also encompasses the possibility of building
novel structures by controlled atomic and molecular
engineering.
Nanoparticles are nanostructures with reduced size in all
three dimensions, which is referred to as reduction from
3D to 0D. Because of the large surface to volume ratio,
boundary surface and quantum effects become dominant.
Nanoparticles therefore have interesting thermodynamic,
magnetic, optical, electronic, chemical, and mechanical
properties when compared to bulk materials. This is mainly
due to their limited size, where the number of atoms or
molecules on the partiale surface is comparable or larger
than those inside the particle.
Layers or folders of nanoparticles dispersed in a solid
matrix or consolidated are known as nanostructured, nanocrystalline, or nanophase materials. They are charecterized
by a large number of grain boundaries with a characteristic
nanometer length scale. These materials also show interesting novel properties such as alloying of normally immiscible materials, higher critical superconductor transition
temperature, ductile ceramics, super-magnetic or giant
magneto-resistance (GMR).
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K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
Nanoparticle synthesis techniques can be broadly classi®ed into two categories namely:
(a) colloidal systems where stabilization is used to
promote coagulation (wet methods);
(b) gas phase systems or aerosol synthesis where either
physical or chemical methods are used to to produce
nanoparticles.
Under physical methods, the solid is evaporated and
recondensed into particle form. Chemical methods, also
called reactive aerosol synthesis, is very similar to combustion. Depending on the precursor material, it can be
processed as spray pyrolysis,in which a reagent, dissolved
in a solvent is delivered to a reactor. The solvent evaporates
and the involatile precursor undergoes reaction to form
particles of the ®nal form. Alternatively, nanoparticle
formation can also proceed through a self sustaining or
pyrolysis type of reaction where the condensing vapours
nucleate and grow to form the ®nal nanoparticles.
The shock tube provides an excellent environment for
investigating nucleation and growth of nanoparticles from
the vapour phase at high temperatures. It provides nearly
instantaneous and uniform heating of reactants, rapid
quenching of products and importantly, the initial reaction
temperature, pressure and mixture composition can be
selected independently over wide ranges [192]. These
features make it possible, for instance, to isolate the effect
of reaction temperature on particle growth characteristics.
6.1. Pre-particle kinetics
High temperature gas phase synthesis of particles is very
much dependent on the homogeneous gas phase chemical
kinetics of the precursor reactions that precede particle
formation. Several silicon containing materials are used in
producing silicon precursor for chemical vapour deposition
(CVD) or for the generation of ceramic particles by gas
phase combustion synthesis. But lack of reliable thermochemical data and reaction rate coef®cients come in the
way of optimising the production processes. Systematic
investigation into the effects of temperature, pressure and
concentration of the pre-particle gas phase kinetics is essential to steer the particle production processes in a ¯uidized
¯ame reactor. As mentioned earlier, the shock tube as a high
temperature wave reactor coupled with highly sensitive
diagnostic techniques such as atomic resonance absorption,
ring dye-laser absorption and laser extinction enable study
of isolated reaction steps that play lead roles in the ®nal
particle formation.
Kunz and Roth [193] have studied the dissociation of
SiCl4 behind re¯ected shock waves by monitoring Cl and
Si atom concentrations using ARAS. Chlorinated silanes
like SiCl4 are widely used as precursors in high temperature
gas phase reactors for the synthesis of ceramic powders like
SIC, Si3N4 and SiO2. At temperatures of 2500 K and above,
thermal decomposition of SiCl4 is the predominant step
SiCl4 1 Ar ! SiCl3 1 Cl 1 Ar
…34†
Using the Cl-atom ARAS technique, an accurate rate
coef®cient value for the above reaction was determined. In
a second series of experiments they measured the Si formation directly and proposed a simpli®ed thermal decomposition mechanism for SiCl4, highly diluted in argon. The
results reported are of importance in the understanding
and modeling of ceramic material production via gas
phase synthesis.
Hydrogen is known to exhibit high reactivity towards
silane and its derivatives and therefore reactions involving
H atoms are of interest in silane chemistry. Hydrogen
abstraction from SiH4 via
SiH4 1 H $ SiH3 1 H2
…35†
was studied by Kunz et al. [194] using H-atom ARAS technique. Ethyliodide C2H5I was used as the source for H atoms
and the experiments covering the temperature range 998±
1273 K were performed behind the re¯ected shock. In addition to reporting a rate coef®cient for the abstraction reaction, they have also proposed a reaction mechanism for
C2H5I/SiH4 system highly diluted in argon. Simultaneous
measurement of H an Si atom concentrations were
performed to validate the proposed reaction mechanism.
Kinetic data pertaining to chlorinated silanes is not
readily available. Kunz et al. [195] studied reactions of H
atoms with the Si precursors SiHCl3 and SiCl4 behind
re¯ected shock waves in the temperature range 1000±
1730 K. The ARAS technique was used for monitoring H
and Si atom concentrations. Based on their experimental
results they have deduced rate coef®cients for the reactions
H 1 SiHCl3 $ products
…36†
H 1 SiCl4 $ SiCl3 1 HCl
…37†
The kinetic data reported is of great relevance as SiHCl3
is a widely used precursor gas in the deposition of silicon
®lms.
Tin dioxide SnO2 is an industrially important material as
it has a high electric conductivity and also transmissivity. It
is used extensively in photovoltaic cells an imaging devices.
Its use as an energy conserving coating on windows is
widely known. SnO2 is often produced in high temperature
gas phase processes as in CVD or ¯ow reactors. However,
optimum reaction conditions to control the gas phase
processes are still not known, due to lack ot relevant kinetic
data. Takahashi et al. [196] have investigated thermal
decomposition of Tin Tetrachloride which is an important
precursor in the gas phase synthesis of SnO2. ARAS technique was used for monitoring Cl and Sn atoms behind
re¯ected shock waves in the temperature range 1250±
1700 K (for Cl) and 2250±28,950 K (for Sn).
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
6.2. Synthesis of Si-nanoparticles
Homogeneous nucleation of silicon particles is an important phenomenon in several processes. Gas phase silicon
particle formation is the principal goal in the production of
sinterable ceramic powders. Control of particle size distribution and particle shape are among primary objectives in
the production of silicon powders [197,198]. Frenklach et al.
[10] carried out shock tube investigation of silicon particle
nucleation and growth in gas phase pyrolysis of silane and
proposed a reaction mechanism for the temperature range
900±2000 K. They used silane and di-silane diluted in argon
and hydrogen as test gas at pressures from 0.2 to 0.7 atm.
Formation of silicon particles was monitored by the attenuation of laser beams of two different wave lengths (light
extinction technique), thereby determining particle number
density and fractional yield.They observed that the conversion of silane and disilane into silicon particles exhibited a
pronounced maximum at about 1150 K and it was affected
by reaction pressure, initial reactant concentration, and addition of hydrogen. Selected silicon particle samples were
examined by electron microscopy and secondary ion mass
spectrometry. Their results indicated that the produced
particles were spherical, ranging from 10 to 40 nm in
diameter, loosely agglomerated, and contained about 15%
hydrogen on an atomic basis. Based on their experimental
results, they have proposed a detailed kinetic model which
describes gas phase pyrolysis of the parent molecule and
homogeneous nucleation of silicon partiales.
Bauer and co-workers [199,200] used the shock tube to
determine the critical silane pressure for the onset of silicon
condensation in 0.05±1.0% SiH4 in Ar mixtures. The particle condensation was detected by monitoring the turbidity
and the intensity of the light scattered at 908. The observations were made both behind incident and re¯ected shock
waves covering reaction temperatures from 1500 to 2800 K.
It was assumed that at these high temperatures, silane
decomposes to silicon atoms instantaneously upon
shock arrival and the produced silicon atoms undergo
condensation. The authors concluded that the observed
temperature dependence of the critical silane pressure
did not follow the prediction of the classical homogeneous
nucleation theory.
Another shock tube investigation on the production of
silicon particles was carried out by Steinwandel and coworkers [201]. They conducted experiments behind
re¯ected shock waves above 2500 K and low initial silane
concentrations Several molecular and atomic species (SiH2,
SiH, Si2, H2, Si and H) were identi®ed by monitoring the
emission spectrum and it was found that the concentration
ratio of Si2 to Si cannot be explained by the classical theory
of homogeneous nucleation if the condensation is assumed
to begin with Si atoms. Instead they proposed a simple
kinetic model with Si2 as the monomer species.
Non-oxide ceramic compounds, especially nitrides and
carbides, are of great technical interest because they are
183
extremely hard, partly chemically inert, refractory and resistant to high temperatures [202]. The gas phase synthesis
of non-oxide ceramics is a currently developing area
compared to the synthesis of oxide ceramics. Synthesis by
aerosol gas phase route allows production of nano-sized
particles which have several desirable properties like superplasticity, lower reaction sintering temperatures, higher
theoretical densities, higher fracture toughness and ductility
than materials sintered from larger particles.Most of these
properties are dependent on the availability of small,
uniform diameter, spherical particles of high purity. A
deep understanding of the gas phase kinetics and the particle
growth mechanisms are necessary to choose the appropriate
condition.
6.3. Gas phase synthesis of tin nanoparticles
Herzler et al. [4] have investigated the formation of both
TiN molecules and particles in TiCl4 /NH3/H2 systems
behind re¯ected shock waves at temperatures between
1400 and 2500 K and pressures 1±2.3 bar by applying
laser absorption spectroscopy. The above mixture was
chosen by the investigators because the same type of
mixture is used in industrial aerosol reactors to produce
TiN nano-particles. A brief description of the experimental
procedure and the diagnostic technique employed is given
below.
The shock tube set up and the optical arrangement used is
the same as shown in the upper part of Fig. 23. Details of the
vacuum system and gas mixture preparation can be obtained
from Roth et al. [4]. As TiCl4 and NH3 are known to form
TiCl4(NH3)x complexes at low pressures, they were not
mixed before ®lling into the shock tube. TiCl4/H2 and
NH3/H2 were ®lled simultaneously and the resulting
TiCl4(NH3)x complex heated by the incident shock produces
TiCl4 and NH3 instantaneously.
The laser spectrometer consisting of a cw ring dye laser
pumped by an Ar 1 laser was used to measure the relative
TiN molecule as well as TiN particle concentrations. The
laser beam was coupled into the measurement plane of the
shock tube via an optical ®ber and was split into probe and
preference beams prior to entering the shock tube. Two Si
photodetectors were used in differential technique to monitor the absorption. The relative TiN molecular absorption
was determined by ring dye laser light extinction at the two
TiN absorption wavelengths l ˆ 614:036 and 620.125 nm
as well as at another wavelength about 1.3 cm 21 away from
them. To corroborate the TiN particle formation, light
extinction measurements were also performed with a He
Ne laser (632.8 nm) and with a coherent Ar 1 laser at
514.5 nm.
The experiments on formation of molecular TiN were
performed in the temperature range 1700±2500 K on a
mixture containing 200 ppm TiCl4 and 200 ppm NH3
and 10% H2 in Ar. In a small temperature region of
1800±2000 K, the absorption at l ˆ 614:036 nm is
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K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
Fig. 28. TiN absorption pro®les in 200 ppm TiCl4/200 ppm NH3/10%H2/Ar mixtures. Full line: 1945 K, 2.09 bar, l ˆ 614:036 nm (line center),
dashed line: 1930 K, 2.06 bar, l ˆ 620:125 nm (line center), dotted line: 1975 K, 2.16 bar, l ˆ 613:987 nm (off line).
dominated by TiN molecule absorption which can be
seen in Fig. 28, where the absorption signal is compared
with that at l ˆ 613:987 nm; where no TiN absorption
exists. The pro®les show an induction time, a fast increase to a
maximum and then a consumption due to nucleation and
particle formation. The formation of TiN molecules could be
con®rmed by additional measurements on the absorption line
at l ˆ 620:125 nm: At temperatures .2000 K, no difference
between on-line and off-line absorption could be observed
(Fig. 29), which con®rms TiN particle formation. The
slightly faster increase of the signal is at l ˆ 614:036 nm
only due to the higher temperature of this experiment. At
temperature less than 1800 K, no absorption above the
detection limit of about 0.5% could be seen.
Fig. 29. TiN particle extinction in a mixture of 400 ppm TiCl4/2000 ppm, NH3/10%/H2/Ar. Full line: 1570 K, 2.04 bar, l ˆ 515:4 nm (off line),
dotted line: 1595 K, 2.11 bar, l ˆ 614:036 nm (16285.70 cm 21 line center), dashed line: 1617 K, 2.14 bar, l ˆ 632:8 nm (off line).
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
At higher concentrations of TiCl4 and NH3 (100±400 ppm
TiCl4, 400±2000 ppm NH3 and 0±20% H2), no distinguishable difference between the on-line and off-line TiN absorption signals was noticed. This was because, under these
condition, the TiN molecules start nucleating and particles
start forming. This was con®rmed by measurements at
632.8 nm (He Ne laser) and 515.4 nm (Ar 1 laser). At all
wave lengths used, no difference between on-line and offline signals was observed. The signals always show an
induction time, which depends on the reaction condition
(especially the reaction temperature) and which is independent of the wave length. The He Ne laser extinction was
used to study the in¯uence of temperature, pressure, TiCl4,
NH3 and H2 concentrations on the induction time of particle
formation.
The temperature dependance of the induction time
of a mixture of 400 ppm TiCl4, 400 or 2000 ppm NH3
and 10% H2 is shown in Fig. 30. The Arrhenius
expression
K
ms
t ˆ 1020:98^0:3 £ exp 11; 840 ^ 1130
T
…38†
describes the various experimental points. The activation
energy is in very good agreement with the vale of about
100 kJ/mol, which was reported by Dekker et al. [203].
A dependance of the induction time on the H2 concentration in the range 1.4±20% was not to be found. This
is in accordance with the measurements of Buiting et al.
185
[204] and Pintchovski et al. [205] on CVD ®lm growth.
They found no in¯uence of the H2 concentration on the
®lm growth and concluded that no H2 is needed to
produce TiN ®lms in CVD reactors [206].
6.4. Production and sizing of soot nano-particles
In view of the great industrial demand for carbon
black, a new interest has been generated for ®nding
optimized methods of producing this material. Extremely
®ne soot particles of nano- meter size are of particular
interest in paint industries. As mentioned earlier, high
temperature pyrolysis of hydrocarbons is an expensive
way of producing nano-sized soot particles. A shock tube
can be conveniently used to carry out investigations to
optimize the controlling parameters such as mixture composition, temperature and pressure so that the soot particle
size and yield can be regulated.
Roth et al. [13] have started a series of shock tube
investigations into the formation and growth of soot
nano-particles from the pyrolysis of acetylene, benzene
and propane. Laser light extinction together with LII are
the diagnostic techniques used for measuring total
soot concentration and particle sizing, respectively. A
combination of these two in-situ measuring techniques
provides reliable and accurate data on soot nano-particle
formation.
Typical results obtained by them on a mixture of 5% C2H2
in Ar at 2059 K and 2.9 bar pressure is shown in Fig. 31. The
Fig. 30. Induction time of TiN particle formation in a mixture of 400 ppm, TiCl4/400 or 2000 ppm NH3/10%H2/Ar, Full circle: 2000 ppm NH3,
l ˆ 614:036 nm (on line), open circle: 2000 ppm NH3, l ˆ 613:987 nm (off line), full square: 400 ppm NH3, l ˆ 614:036 nm (on line), open
square: 400 ppm NH3, l ˆ 613:987 nm (off line), triangle: 2000 ppm NH3, l ˆ 632:80 nm (off line), star: 2000 ppm NH3, l ˆ 515:40 nm (off
line).
186
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
Fig. 31. cw-Laser extinction (upper part) and typical LII (lower part) abtained with 5%C2 H2 in Ar at T ˆ 2059 K; p ˆ 2:90 bar:
extinction caused by the formation of soot particles occurs
with an induction time of about 240 ms and increases during
the entire observation time. The trigger of the Nd/YAG laser
causes a short overshoot of the signal, which is a convenient
control of the delay for the LII measurement. The LII
signal(lower part) shows a small background level of
about 0.1 a.u. and a peak value of 0.85 a.u. within
15 ns and then a slower decrease back to the back-
ground level within the next 250 ns. As a measure for
the signal decay, the 50% decay time t 50% is also indicated in the diagram.
Fig. 32 shows the decay of LII signal and the corresponding calculated thermal radiation (explained earlier under LII
diagnostic technique). A least square ®t for a log normal
geometric standard deviation of 1.1 yields a particle mean
radius of 8.1 nm. The sensitivity of the method is also
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
187
Fig. 32. Fitting of a normalized LII decay signal, full line: best ®t for a particle mean diameter of a ˆ 8:1 nm; dashed line: variation by 1100%
at 250% of the best ®t.
demonstrated by the two dashed curves calculated with
assumed particle radii of 4 nm and 16.2 nm (250 and
1100%) which are clearly outside the uncertainty of measurements.
The transformation of LII signals into mean particle
radii is shown in Fig. 33 where the particle radius is plotted
against the reaction time. The smallest size of about 1.8 nm
was found at an early reaction time of about 200 ms. in the
2020 K temperature range. At later reaction times sizes up to
10 nm were found. The general behavior of increasing particle size with increasing reaction time is expected due to
agglomeration effects. The appearance of bigger particles
at higher temperatures is also reasonable due to the bellshaped soot yield curve reported by Frenklach et al. [172]
Fig. 33. Soot particle mean radius at different reaction times during the pyrolysis of C2H2.
188
K.A. Bhaskaran, P. Roth / Progress in Energy and Combustion Science 28 (2002) 151±192
for acetylene. The ®gure also shows how the induction times
reduce (dashed lines) with increase in temperature.
7. Conclusion
The versatility of the shock tube as a high temperature
wave reactor for kinetic studies in both homogeneous and
heterogeneous systems, as also for material synthesis has
been illustrated with several examples. The use of highly
sensitive laser based diagnostic techniques that enable study
of rate processes in very dilute systems (reactant concentration in the order of 1 ppm) has been explained. Recent
advances made in the ®eld of gas phase particle synthesis
using the shock tube as a wave reactor have been brought
out. The importance of pre-particle kinetic studies, it is
hoped, will continue to keep the shock tube as the most
important research tool in the area of high temperature
kinetics for many years to come.
Acknowledgements
The authors gratefully acknowledge the ®nancial support
provided by the German Science Foundation.
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