High temperature rate coefficient measurements of H + O2 chain-branching and chain-terminating reaction

Article abstract of DOI:10.1016/j.cplett.2005.03.140

Rate coefficients for H + O₂ → OH + O (R₁) and H + O₂ + M → HO₂ + M (R₉) were measured via OH absorption behind reflected shock waves, being: k₁ = 6.73 × 10¹⁵ T^-0.50 e

Full text of DOI:10.1016/j.cplett.2005.03.140

Chemical Physics Letters 408 (2005) 107–111
www.elsevier.com/locate/cplett
High temperature rate coefficient measurements of H + O2
chain-branching and chain-terminating reaction
a
S.M. Hwang , Si-Ok Ryu , K.J. De Witt , M.J. Rabinowitz
b
a
c,
*
a
Department of Chemical Engineering, University of Toledo, Toledo, OH 43606, United States
b
Department of Chemical Engineering, Yeungnam University, Dae Gu, South Korea
c
NASA, Glenn Research Center at Lewis Field, Research and Technology Directorate, Mail Stop 5-10, Brook Park, OH 44135-3191, United States
Received 15 March 2005; in final form 30 March 2005
Available online 26 April 2005
Abstract
Rate coefficients for H + O2 ! OH + O (R1) and H + O2 + M ! HO2 + M (R9) were measured via OH absorption behind
reflected shock waves, being: k1 = 6.73 · 1015 Tꢀ0.50 exp(ꢀ8390 K/T) cm3 molꢀ1 sꢀ1 at T = 950–3100 K and k9, 0/[Ar] =
5.55 · 1018
T
ꢀ1.15 cm6 molꢀ2 sꢀ1 at T = 950–1200 K. Our experimental results for k1 strongly support recent ab initio calculations
showing temperature curvature due to back dissociation, HO2 ! O + OH following O + OH ! HO2 if the reaction is considered
from the reverse direction.
Published by Elsevier B.V.
1. Introduction
velop the reaction mechanism for H2/O2 system: static
bulb measurements of the three explosion limits of stoi-
chiometric H2/O2 mixtures at T = 670–840 K [1], shock
tube measurements of diluted H2/O2 mixtures at higher
temperatures and densities [2], and high temperature
flow tube experiments [3]. Over fifty years of experimen-
tal and theoretical studies have been performed to ob-
tain the rate coefficients of R1 (H + O2 ! OH + O)
and R9 (H + O2 + M ! HO2 + M); although steady
progress has been made, significant disagreement still
exists in their determination.
For R1, the primary obstacle has been the difficulty in
performing experiments at relatively low temperatures.
This has prohibited any single group from obtaining con-
sistent results over a sufficiently wide temperature range.
Instead, many groups have added Pirraglia et al.Õs [4] low
temperature k1 values (T = 960–1200 K) to their own
high temperature measurements in order to develop k1
expressions that cover the range of importance to com-
bustion applications (some groups have used SemenovÕs
evaluation [5] below 800 K, see references therein). This
The overall reaction H + O2 ! products has been
intensively studied due to both its practical and theoret-
ical importance. Nearly, all reaction characteristics
(flame speeds, ignition behavior, extinction, etc.) in
hydrogen and hydrocarbon combustion are controlled
by the balance between chain-branching and chain-
termination in the overall reaction. Theoretically, under-
standing the delicate interplay between complex
stability, energy barriers and entrance/exit channels for
the overall reaction has remained a major challenge.
The extent of back reaction and the relative contribu-
tions from statistical and non-statistical processes, and
thus curvature in the rate expression, has been exten-
sively debated. Experimental studies have also been
inconsistent as to the extent or existence of curvature.
Historically, three sources of data have been used to de-
*
Corresponding author. Fax: +1 216 433 5802.
E-mail address: martin.j.rabinowitz@nasa.gov (M.J. Rabinowitz).
0009-2614/$ - see front matter. Published by Elsevier B.V.
doi:10.1016/j.cplett.2005.03.140

108
S.M. Hwang et al. / Chemical Physics Letters 408 (2005) 107–111
work is the first by a single group covering the entire
range of interest above 950 K. Considering the impor-
tance of R1, the discrepancies among the results are
still large, a factor of 1.3 at 1050 K [4,6]. For R9,
although a consensus rate coefficient value has been
established at room temperature [7], the scatter of the
data is also quite large at T > 750 K – a factor of 3 at
T = 1000 K (see Fig. 3b).
3. Results
The rate coefficients of R1 and R9 were obtained via
direct computer simulations of experimental absorption
profiles (not parameterizations as used in the sensitivity
analysis). For R1, 360 profiles were used (including the
previous high temperature results of eight rich mixtures
[6]) and for R9, 118 profiles were used. In the simulation,
only the rate coefficient of either R1 or R9 was varied.
The matches between experimental and simulated pre-
peak absorption profiles were excellent over the full
range of T and /. Post-peak profile matching, while
good, could be improved by varying k3 (OH + H2 !
H2O + H) for R1 and k14 (OH + HO2 ! H2O + O2)
for R9. Nevertheless, the resultant changes in k1 or
k9, 0/[Ar] were insignificant.
2. Experimental conditions and computer simulation
The experimental apparatus, operation and tempera-
ture correction methodology are described in detail else-
where [6,8]. H2/O2/Ar mixtures were prepared
manometrically and allowed to stand for at least 48 h
before use. Gases were used as delivered: H2,
99.9995% (MG Industries, Scientific Grade); O2,
99.999% (MG Industries, Scientific Grade); and, Ar,
99.9999% (MG Industries, UHP Grade).
Typical experimental and simulated absorption pro-
files are shown in Fig. 1 and the resultant k1 values
and their deviations from the least squares fit expression
are plotted in Fig. 2a,b. The least squares fit to the data
gives,
Our trial reaction mechanism is based upon our pre-
vious H2/O2 mechanism [6] with the following revisions:
k2 (O + H2 ! OH + H) from Sutherland et al. [9]; k10
(HO2 + H ! OH + OH) from GRI 3.0 [G.P. Smith,
et al., GRI-Mech, http://www.me.berkeley.edu/gri_mech/];
k15(HO2 + HO2 ! H2O2 + O2) and k20(H2O2 + OH !
H2O + HO2) from Baulch et al. [7] NASA thermodata
[10], employing the recent OH bond dissociation energy
of D0298.15ðHOHÞ ¼ 118.81 ꢁ 0.07 kcal molꢀ1 [11], has
been used throughout this study. Post reflected shock
conditions were corrected for boundary layer/reflected
shock interaction using the methodology described in
Hwang et al. [8]. As we have previously demonstrated
[6,8,12], the effect of O2 vibrational relaxation time on
our rate coefficient measurement was insignificant.
An extensive sensitivity study, using profile parame-
terization, was performed to select optimal experimental
conditions. For the low temperature k1 determination,
the parameter chosen was NSm = max (ꢀ[dI/I0]/dt)/Am,
where Am = (1 ꢀ I/I0)max (see figure 3 of [6]). A series
of mixture compositions, given by percent H2 and equiv-
alence ratio (/), was selected, namely: 1.0% H2, / = 1.0;
10.0% H2, / = 2.5; 6.0% H2, / = 3.0; 15.0% H2, / = 3.0.
For the determination of R9, the parameters chosen
were s75 (time to reach 75% of Am) and NSm. As ex-
pected, the sensitivity of R9 increases with increasing q
and with decreasing / and T; thus, very lean mixtures
were chosen: 0.5% H2, / = 0.025; 0.25% H2, / = 0.025;
0.25% H2, / = 0.0125. The experiments were designed
to vary q (·2 or ·3) in the same mixture composition
(0.25% H2, / = 0.0125) or to vary q by a factor of ꢂ2,
while keeping the initial aftershock [H2] and [O2] con-
stant in the / = 0.025 mixtures. Extreme time scale
and absorption level for our apparatus and sensitivities
restricted our T-ranges to T = 950–3100 K for R1 and
950–1200 K for R9.
k1 ¼ 6.73 ꢃ 1015 T ꢀ0.50 expðꢀ8390 K=TÞ cm3 molꢀ1 sꢀ1
;
for T ¼ 950–3100 K with r ¼ ꢁ7%.
For R9, we determined the collision–efficiency-
corrected k9, 0/[M] values for M = Ar; i.e., optimized k9, 0
values were scaled with [M] = q · [1 + x(O2)(e(O2) ꢀ 1) +
x(H2)(e(H2) ꢀ 1) + x(H2O)(e(H2O) ꢀ 1)], where the
collision efficiencies are: e(H2O) = 21.3, e(H2) = 3.33,
e(O2) = 1.33, and e (other species including Ar) = 1.0.
Because of the rather narrow temperature range of this
0.20
0.15
0.10
0.05
0.00
-0.05
0.0
0.5
1.0
1.5
2.0
2.5
Time/ms
Fig. 1. Experimental (black solid) and simulated (open circles) OH
absorption profiles. Profiles from the left are: 4% H2, / = 2.0, 1243 K,
2.46 atm, sm = 0.22 ms, A = Aactual/5; 5% H2, / = 5.0, 1243 K, 0.80 atm,
s
m = 0.97 ms, A = Aactual; 15% H2, / = 3.0, 999 K, 1.11 atm, sm =
1.32 ms, A = Aactual/4; 4% H2, / = 2.0, 999 K, 1.53 atm, sm = 2.27 ms,
A = Aactual/2.

S.M. Hwang et al. / Chemical Physics Letters 408 (2005) 107–111
109
15.8
(a)
13
12
11
10
(a)
15.6
15.4
15.2
15.0
14.8
0.5
0.8
1.0
1.3
1.5
3
5
7
9
11
1000 K/T
10000 K/T
16.2
16.0
15.8
15.6
15.4
15.2
15.0
14.8
(b)
75
45
(b)
15
-15
-45
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
1
3
5
7
9
11
1000 K/T
10000 K/T
Fig. 3. (a) Comparison of k9, 0/[Ar] at T > 667 K. Symbols and
references are: open diamond, [20]; open triangle up, [18]; open
square, [4]; filled circle, [19]; filled diamond, [21]; filled square, [22];
open circle, (this study). Lines are: dot dash, [7]; dash, [23]; gray long
dash, [24]; filled circle on solid line, [25]. The error bars represent 30%
of our k9, 0/[Ar]. (b) Comparison of k9, 0/[Ar] at entire temperature
range. Lines and symbols are as in Fig. 3a. Additional symbols and
references are: filled triangle, [26]; open circle with Ô · Õ inside, [27]; gray
filled square with Ô+Õ inside, [28]; star, room – T data (see table 3 in 24).
Fig. 2. (a) Non-Arrhenius plot of the experimental data for k1. The
solid line is the least squares fit to the data. The error bars represent
15% of the propagation uncertainty limit of the individual measure-
ments. (b) Comparison of the selected k1 values and expressions with
our expression. %Deviation = (k1, othersꢀ1) · 100/k1, this study. Symbols
and references are: open circle, [14]; open triangle, [4]; open diamond,
[13]. Lines and references are: dot dot dash, [4]; long dash, [7] and [13];
dash, [GRI 3.0, G.P. Smith, et al., GRI-Mech, http://www.me.berke-
ley.edu/gri-mech/]; dot dash, [17]; solid, (this study).
4. Discussion
study, we included the previously reported low temper-
ature data (T < 990 K) for the fit (see Fig. 3a,b). A
power law expression, k9, 0/[Ar] = ATnexp(ꢀH/T) with
H = 0 K yields
We examined the effect of flow disturbance by either
boundary layer interactions or contact surface or rare-
faction wave arrival. Fig. 1 shows the experimental
and simulated absorption profiles for experiments at
two temperatures, but having very different time to peak
absorption for each temperature. For a corrected tem-
perature of 1243 K (left two), the peak absorptions oc-
curred at 0.22 and 0.97 ms, while for a corrected
temperature of 999 K (right two) the peak absorptions
occurred at 1.32 and 2.27 ms. The k1 values from the
same corrected temperature (average temperature cor-
rections are l.4%) are in agreement within the uncer-
tainty limits. The observed peak absorption for a
10.0% H2, / = 2.5 mixture at T = 961 K occurred at
k
9;0=½Arꢄ ¼ 5.55 ꢃ 1018 Tꢀ1.15 cm6 molꢀ2 sꢀ1
;
for T ¼ 950–1200 K and ½Arꢄ ¼ 15 ꢀ 53 lmol cmꢀ3
.
Propagation-of-error analyses were performed for k1
and k9, 0/[Ar] using uncertainty contributions from the
transducers, mixture composition, shock velocity, P5
(used in the temperature correction) and cross-coupling
of other reactions in the computer simulation. The max-
imum uncertainties calculated using the formula
U ¼ ðRU2i Þ1=2, are 15% for k1 and 30% for k9, 0/[Ar].

110
S.M. Hwang et al. / Chemical Physics Letters 408 (2005) 107–111
2.30 ms while the calculated contact surface arrival time
was 2.85 ms. Rarefaction waves never crossed contact
surface.
peratures, our extrapolated values have a general agree-
ment with the results of Pirraglia et al. [4] and Ashman
and Haynes [21]. There is particularly good agreement
between our values and those of Mueller et al. [22]. Also
displayed in Fig. 3a,b are the rate coefficient expressions
of Baulch et al. [7], Bates et al. [23], Michael et al. [24]
and Troe [25]. As seen, the extrapolation from the
expression of Michael et al. for M = Ar (4.57 ·
4.1. Chain-branching R1 (H + O2 ! OH + O)
Many k1 expressions are currently used
(cm3 molꢀ1 sꢀ1): Pirraglia et al. [4] (962–2577 K),
1.92 · 1014 exp(ꢀ8272 K/T); Du and Hessler [13] (960–
5300 K), and Baulch et al. [7] (300–5300 K),
9.76 · 1013 exp(ꢀ7474 K/T); GRI 3.0 (300–3000 K),
2.65 · 1016 Tꢀ0.6707 exp(ꢀ8575 K/T). These expressions
are fits to the combined results of many individual stud-
ies using different temperature ranges, compositions,
diagnostics and optimization schemes.
As shown in Fig. 2a,b, our rate coefficients are in
good agreement with the Pirraglia et al. experimental re-
sults (low temperatures), but not with the overall fit
(high temperatures are from the data of Frank and Just
[14]). In the range 950–2500 K, we are in good agree-
ment with the expressions of Baulch et al., Du and Hess-
ler and the GRI 3.0 optimization. Above 2500 K, the
absolute values of Du and Hessler and this study are
in within the combined error limits, but our T-depen-
dence of ꢀ0.50 separates from their non-T-dependent
expression.
1018
T
ꢀ1.12 cm6 molꢀ2 sꢀ1, T = 296–700 K) represents
our data equally well.
5. Conclusions
We present a consistent set of rate data in the wide
temperature range (T = 950–3100 K) for the chain-
branching reaction R1 (H + O2 ! OH + O). Our rate
coefficient measurements at low temperatures
(T < 1200 K) agree well with those of Pirraglia et al.
[4] and with the GRI expression over our entire temper-
ature range. Our data supports the negative temperature
coefficient of Troe and Ushakov [17] and is well repre-
sented by the following non-Arrhenius expression:
k1 ¼ 6.73 ꢃ 1015 T ꢀ0.50 expðꢀ8390 K=TÞ cm3 molꢀ1 sꢀ1
for T = 950–3100 K with propagated uncertainty limits
of 15%.
Three notable theoretical calculations for R1 are that
of Miller [15], Varandas et al. [16], and Troe and Usha-
kov [17]. Briefly, Miller obtains a negative curvature of
ꢀ0.816 due to dynamical effects involving the light H-
atom and Varandas et al. see no curvature of the rate
coefficient expression derived from calculations using
their DMBE IV potential energy surface. Detailed re-
views for these two works are given in [6,17]. Recently,
Troe and Ushakov performed classical trajectory calcu-
lations for Rꢀ1 (O + OH ! H + O2) using their new po-
tential energy surface (based upon the high precision ab
initio calculation along the MEP of HO2 ! H + O2 and
HO2 ! O + OH) that revealed the importance of the
both statistical and non-statistical back dissociation,
Our low pressure limit rate coefficients of the chain-
terminating reaction R9 (H + O2 + M ! HO2 + M) are
in the lower range of previous results. A power law
expression derived using the combined data of this work
and the previous low temperature studies gives:
k
9;0=½Arꢄ ¼ 5.55 ꢃ 1018 T ꢀ1.15 cm6 molꢀ2 sꢀ1
for T = 950–1200 K and [Ar] = 15–53 lmol cmꢀ3 with
propagated uncertainty limits of 30%.
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HO2 ! O + OH
following
O + OH ! HO2
at
T > 500 K (considered from the reverse direction). This
back reaction leads to a negative T-dependence of
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