Simultaneous thermal and plasma chemical activation of conversions in HI-Iz-HI mixtures

Article abstract of DOI:10.1021/jp982196j

Chemical quasi-equilibria represent the product composition of stable components at the outlet of a nonisothermal plasma chemical reactor under operating conditions of very high or vanishing electric power input. The properties of these quasi-equilibria in relation to the thermodynamic equilibrium are discussed first of all using an instructive kinetic model. The investigations show that for the formation of the quasiequilibria the existence of two time scales for the chemical conversions in the system is necessary. The quasi-equilibrium states are formed on a short time scale by fast relaxation and deactivation processes of unstable components. After that the system passes into the thermodynamic equilibrium for very long times. The transition from a chemical quasi-equilibrium state into the thermodynamic equilibrium was detected in the H₂-I₂-HI system experimentally, too. The analysis of a detailed microphysical model for this system shows that the transition into the thermodynamic equilibrium is caused by the increasing thermal production of unstable components (e.g. iodine atoms) at higher gas temperatures. Under these conditions the electronic production of atoms is only a small correction of the thermal degree of dissociation, and the thermodynamic equilibrium is the only stationary state for the system.

Full text of DOI:10.1021/jp982196j

2024
J. Phys. Chem. A 1999, 103, 2024-2030
Simultaneous Thermal and Plasma Chemical Activation of Conversions in H2-I2-HI
Mixtures
Frank Miethke,* Hans-Erich Wagner, Alfred Rutscher, and Siegfried Gundermann
Institute of Physics, Greifswald UniVersity, Domstrasse 10a, 17489 Greifswald, FRG
ReceiVed: May 12, 1998; In Final Form: August 27, 1998
Chemical quasi-equilibria represent the product composition of stable components at the outlet of a
nonisothermal plasma chemical reactor under operating conditions of very high or vanishing electric power
input. The properties of these quasi-equilibria in relation to the thermodynamic equilibrium are discussed
first of all using an instructive kinetic model. The investigations show that for the formation of the quasi-
equilibria the existence of two time scales for the chemical conversions in the system is necessary. The
quasi-equilibrium states are formed on a short time scale by fast relaxation and deactivation processes of
unstable components. After that the system passes into the thermodynamic equilibrium for very long times.
The transition from a chemical quasi-equilibrium state into the thermodynamic equilibrium was detected in
the H2-I2-HI system experimentally, too. The analysis of a detailed microphysical model for this system
shows that the transition into the thermodynamic equilibrium is caused by the increasing thermal production
of unstable components (e.g. iodine atoms) at higher gas temperatures. Under these conditions the electronic
production of atoms is only a small correction of the thermal degree of dissociation, and the thermodynamic
equilibrium is the only stationary state for the system.
Introduction and Motivation
In this paper experimental investigations on the formation
of chemical quasi-equilibrium states in the model system H2-
I2-HI as well as on the transition to the thermodynamic
equilibrium (TE) are presented. The transition was realized by
the common thermal and plasma activation of chemical reac-
tions. The kinetic background is studied in detail on the basis
of a microscopic reaction scheme. In a first step the general
situation of quasi-equilibrium states and the transition to the
thermodynamic equilibrium are analyzed for a simply con-
structed reaction system containing thermal and electron initiated
reactions.
Nonisothermal plasma chemical reactors are systems of high
complexity. Examples of these are the different types of gas
discharges (glow discharge, microwave discharge, corona
discharge, dielectric barrier discharge) operating in reactive gas
mixtures. Here the plasma components (electrons, ions, and
neutrals) are far from thermodynamic equilibrium. Therefore,
the description of chemical reactions requires a detailed kinetic
modeling under these conditions (e.g. ref 1). Usually, many of
the elementary data (e.g. dependence of electronic cross sections
on energy, rate coefficients of radical reactions) are not well-
known. To bypass the enormous difficulties of microscopic
kinetics, the description of plasma chemical reactions by the
methods of statistical physics and thermodynamics has been
attempted (e.g. refs 1 and 2). However, this concept is restricted
to simple processes. A very useful alternative is the so-called
method of macroscopic kinetics.3,4 This method correlates the
chemical conversions in nonisothermal plasma chemical reactors
directly to the operation parameters of the reactor (e.g. power
input, flow rate). The method allows the calculation of the
composition of the stable reaction products at the reactor outlet
depending on the reactor operation parameters starting from
reversible gross reactions for these components. The essential
basis for this concept consists of chemical quasi-equilibrium
states reflecting the basic role of reversible gross reactions for
the overall behavior of gas discharge reactors. These quasi-
equilibria characterize the limit situations of the reactor operation
at low power input (in the closed system) and high power input,
which includes the limits ne f 0 and ne f ∞, respectively (ne
is the concentration of plasma electrons). They were qualified
as chemical equilibrium of electronic catalysis (CEEC) and
chemical equilibrium of complete decomposition (CECD).
Various experimental and theoretical investigations in different
systems have shown the real existence of these states.5,6
The system H2-I2-HI was chosen, because the thermal
mechanism of the HI formation is relatively well-known.7,8
Furthermore, the thermal equilibrium is already arrived at within
a moderate reaction time scale (τ e 103 s) for temperatures
below 600 °C. The particle number densities of the stable
components nH , nI , and nHI have the same order of magnitude.
2
2
After the plasma chemical synthesis of HI, these molecules could
be fully decomposed again into H2 and I2 by the UV radiation
of a mercury lamp. So it was possible to generate a reversible
overall chemical process. Therefore, this system is especially
suitable for investigating these problems. The main interest was
aimed at the question of how the level of the CEEC is influenced
by thermally initiated reactions.
Plasma Chemical Quasi-Equilibria
Concept and Definitions. Contrary to the usual chemical
equilibrium, the quasi-equilibrium states are related to the special
operation conditions of the plasma chemical reactors. It is
indispensable to consider the double structure of every plasma
chemical reactor, which implies the combination of an active
zone with a passive zone in flow systems, separated in space,
or an active phase combined with a passive one in closed
systems, separated in time.3 Figure 1 shows the schematic
10.1021/jp982196j CCC: $18.00 © 1999 American Chemical Society
Published on Web 03/13/1999

Activation of Conversions in H2-I2-HI Mixtures
J. Phys. Chem. A, Vol. 103, No. 13, 1999 2025
Figure 1. Occurrence of chemical quasi-equilibria in a closed system
(illustration for the gross reaction H2 + I2 + e h 2HI + e).
Figure 2. Example of different equilibrium states of the closed reactor
operation of a closed reactor system. During the active phase
of the reactor the gas mixture of only stable components is
activated by collisions with highly energetic plasma electrons.
A variety of reactive unstable components are produced by these
processes (radicals, metastable atoms/molecules, ions, etc.).
After the discharge interruption the unstable species are
deactivated by relaxation and recombination processes. So the
gas mixture at the end of a long enough passive phase also
contains only stable products, including the input species as well
as new components. This product composition which is
established after the successive action of both phases in closed
systems (at the reactor outlet in flow systems) represents a
chemical quasi-equilibrium. Therefore, unstable components are
not included. For the limit situation of very high or vanishing
electric power input into the active phase (zone) of the reactor
the following two quasi-equilibrium states exist:9
for the reaction mechanism given in Table 1 (k1 ) k2 ) 10-10 cm3 s-1
,
k3 ) 12 s-1, k4 ) 6 s-1, k5 ) 10-17 cm3 s-1, k6 ) 10-17 cm3 s-1; solid
line: k+ ) k- ) 0; dashed line: k+ ) 10-7 s-1, k- ) 10-6 s-1).
1. CECD: chemical quasi-equilibrium of complete electronic
decomposition. Large concentrations of hot electrons (high
power input P f ∞, followed by ne f ∞) result in the nearly
complete decomposition of the reactants within the active phase
(zone) of the reactor. In the passive phase (zone) the unstable
components recombine into stable products, which are detected
at the end of the passive phase (zone). This product composition
is determined only by the conditions in the passive phase (zone).
2. CEEC: chemical quasi-equilibrium of electronic catalysis.
Generally, a finite degree of conversion at the limit of vanishing
concentration of hot electrons is produced, representing a kind
of electronic catalysis (i.e. P f 0, ne f 0 at τ f ∞; τ is the
duration time of the active phase (residence time in the active
zone)).
Demonstration Example of Chemical Quasi-Equilibria
and the Thermodynamic Equilibrium. An instructive model
system was analyzed to illustrate the different states of equilibria.
The elementary processes are listed in Table 1. The conversion
of two species A and B proceeds via “normal” thermal reactions
(I) and via excited states marked by an asterisk (II, III, IV).
The excited species are produced by collisions with energetic
electrons. The rate coefficients were chosen similar to those in
the basic mechanism for the ozone synthesis given in ref 3.
The numerical computations were performed for a closed system
using an explicit Runge-Kutta formalism with step width
control.10 The total particle number density is n ) 3 × 1017
cm-3sas is typical for low-pressure gas discharge plasmas.
Neglecting thermal reactions (I), the quasi-equilibrium states
CEEC and CECD are found at low and high degrees of
ionization xe ) ne/n, as shown in Figure 2. The rate coefficients
lead to different states CEEC * CECD. Taking into account
the thermal reactions, the corresponding thermodynamic equi-
librium state predominates at very low xe. This state will be
changed dramatically at higher xe by the two electronic quasi-
Figure 3. Time required for the formation of the CEEC dependent on
the ionization degree (rate constants see Figure 2).
TABLE 1: Demonstration Example
k+
I. thermal reactions
A {k
\
} B
-
k1
A + e
98 A* + e
II. electron-initiated reactions
k2
B + e
98 B* + e
k3
98 B
A*
B*
III. modification via excited states
IV. modification via collision processes
k4
98 A
k6
A + B*
A* + B
98 B + B*
k5
98 A* + A
equilibrium states. So the transitions from one quasi-equilibrium
into the other as well as into the thermodynamic equilibrium
are well marked. Especially, it can be seen that the levels of
different equilibrium states are independent of xe. Identical
compositions of the stable products are performed starting from
both sides of the reversible gross reaction A + e h B + e. The
mole fraction xB in Figure 2 marks the conditions of the late
afterglow but is restricted to times which are small compared
with the relaxation time of the thermal reactions (t , τth
)
1/(k+ + k-)). These dynamic aspects are shown in more detail
in Figures 3-5. The time necessary for the formation of the
CEEC increases drastically for decreasing ionization degrees,
as shown in Figure 3. For ionization degrees xe e 10-11 this
time is comparable to that required for the formation of the
thermodynamic equilibrium. With an xe smaller than this value
the electronic excitation of the gas mixture is a negligible
disturbance only. The temporal situation for the formation as

2026 J. Phys. Chem. A, Vol. 103, No. 13, 1999
Miethke et al.
Figure 4. Temporal development of the CEEC as well as the transition
into the thermodynamic equilibrium (TE) (input values: xA ) xB
)
0
0
0.5, xe ) 10-8).
Figure 6. Experimental setup: (top) discharge tube, thermostat and
optical components; (bottom) microwave diagnostics device.
To summarize, the chemical quasi-equilibrium states are
characterized by the following properties:
1. Quasi-equilibria represent stationary product compositions
of only stable compounds after the combined action of the active
phase (zone) and the passive phase (zone) of a nonisothermal
plasma chemical reactor.
2. They are attainable from both sides of a reversible gross
reaction A + B + e h C + e of the stable components.
3. The product composition of the quasi-equilibria is inde-
pendent of the electron concentration (or power input) for several
orders of magnitude, the type of plasma zone, or the reactor
dead volume.5
4. These compositions only depend on the gas temperature.
If three-particle collisions are important, the quasi-equilibrium
states are influenced by the total particle number density too.5,6
A necessary condition for the existence of chemical quasi-
equilibrium states consists in the existence of two different time
scales for the chemical conversions: on a short time scale the
unstable components, generated by electron collision processes
in the active phase, recombine in the passive phase into an
altered mixture of stable compounds. The transition into the
thermodynamic equilibrium follows for large times caused by
thermally initiated conversions of the stable products. Therefore,
the quasi-equilibria may be interpreted as “kinetic frozen states”.
Figure 5. Temporal development of the CECD as well as the transition
into the thermodynamic equilibrium (TE) (x/A ) 0.33, xB/ ) 0.66, xe
0
0
) 0).
well as the transition from the chemical quasi-equilibrium states
into the thermodynamic equilibrium is shown in Figures 4 and
5 for the CEEC and the CECD, respectively. It can be estab-
lished that the plateaus of the quasi-equilibrium states are formed
within a short time after the start of the passive phase. Then
the product composition is (nearly) stationary for several orders
of magnitude before the system passes into the thermodynamic
equilibrium at very large times. This behavior may be under-
stood by discussion of the reaction model given. As one can
see, the rate constants for the reactions including the unstable
components A* and B* are much greater than k+ and k- for
the thermal conversions of the products A and B. These con-
ditions are typical of nearly all nonisothermal reactive plas-
mas. The chemical conversions are initiated by the generation
of various very reactive unstable components, which are pro-
duced by collision processes of hot plasma electrons with the
neutral gas in the active phase. During a short period im-
mediately after the beginning of the passive phase the unstable
components generated react into stable products and only for
large times does the system pass into the thermodynamic
equilibrium caused by the thermally initiated reactions of the
stable compounds. For real systems the differences between
these two time scales amount to several orders of magnitude.
For example, in the case of the H2-I2-HI system the CEEC is
formed after a few minutes at T ) 300 K. But the thermody-
namic equilibrium would be generated after 1010 years under
the same conditions.
Investigations on the H2-I2-HI System
Experimental Setup and Detection Methods. The experi-
mental setup is shown in the parts of Figure 6. The discharges
operated in closed quartz tubes T, prepared under high-vacuum
conditions. The tubes were filled with well-defined mixtures
of iodine and hydrogen (some with admixture of an inert He
buffer gas). The discharge tube could be located within a
thermostat to perform measurements in the temperature range
from 300 to 800 K (Figure 6, top). Vanishing ionization degrees
were realized by the excitation of the mixture in a very faint
Tesla spark discharge using outer ring electrodes within a tube
of 20 mm diameter and 150 mm length. The electric power
input was varied, changing the primary voltage of the Tesla

Activation of Conversions in H2-I2-HI Mixtures
J. Phys. Chem. A, Vol. 103, No. 13, 1999 2027
transformer. Higher ionization degrees could be produced in
capacitively coupled rf discharges (frequency 450-650 kHz)
inside a further tube (diameter 9 mm, length 120 mm). In this
case the particle number density of electrons ne was determined
by the microwave cavity method (Figure 6, bottom). The
microwave signal from the generator M was coupled into the
resonator cavity R by the variable attenuator D, a slotted
waveguide W, and the inductive probe P. The adaptation of
the resonator to the measuring equipment was checked by the
slotted waveguide. The resonator was used as load element and
transmission element. The microwave signal, decoupled by the
inductive probe, was analyzed by the voltmeter V after its
rectification. The oscilloscope O was applied to check the time
dependence of the output signal. The interaction of the electric
hf field strength Ehf with the plasma produces a change ∆f of
the resonance frequency satisfying the following condition:11,12
Figure 7. Measured temperature dependence of the iodine concentra-
tion in comparison with the vapour pressure curve.16
Nhe
me
∞
2
3
ω
∂
∆f ) -
C
e2
U3/2 (U-1/2F(U)) dU (i)
∫
ν2(U) + ω2
0
∂U
where Nhe is the cross-sectional average value of the electron
density; e, and me charge and mass of the electron; C geometric
factor; ν(U) electron-neutral particle collision frequency; ω
circle frequency of the microwave signal; F(U) energy distribu-
tion function of the electrons; U volt equivalent of the electron
energy. The geometric factor
Ehf2 dV
∫
Vpl
C )
(ii)
Ehf2 dV
∫
Vr
(where Vpl is the plasma volume and Vr the resonator volume)
describes the degree of the coupling between the microwave
field and the resonator. The distribution function F(U) satisfies
the condition
Figure 8. Dependence of the relative iodine concentration on the
average concentration of plasma electrons: reactor diameter: 9 mm;
length: 120 mm; tube temperature: 360 K; (open square) Tesla spark
discharge (P < 0.1 W); (filled squares) rf discharge (450-610 kHz);
input mixture xI ) 0.61, xH ) 0.39; total particle number density:
∞F(U) dU ) 1
(iii)
0
2
2
0
∫
n ) 4.1 × 1016 cm-3
.
0
The composition of the stable reaction products was deter-
of the CEEC. In Figure 8 the relative I2 concentration is shown
at different, very low, concentrations ne of plasma electrons in
the rf discharge at a constant gas temperature, starting from
identical input mixtures (for details see figure legend). Inde-
pendently of the average ionization degree, an identical com-
position of the stable reaction products is formed, representing
the plateau of the CEEC (Figure 8, full squares). This composi-
tion is far from the thermodynamic equilibrium at this temper-
ature. The same composition is produced by the excitation of
the mixture in a faint Tesla spark discharge (Figure 8, open
square). An example of the temporal development of the CEEC
is given in Figure 9, selecting the I2 component again. A large
particle number density of the chemically inert He buffer gas
was added to the H2-I2 (respectively H2-I2-HI) gas mixture.
The admixture of He gas enabled the relatively fast generation
of the thermodynamic equilibrium at gas temperatures T g 350
°C, because the time necessary for the formation of this state
depends exponentially on the total number density of the process
gas.17 In this way the transition from the CEEC to the
thermodynamic equilibrium could be investigated, too. The gas
mixture was excited only by the Tesla spark discharge. At a
defined gas temperature (here shown for T ) 100 °C) the
reactive mixture changes after a few minutes into the CEEC.
Starting from different initial compositions (at a constant total
number of H and I atoms) the curves converge into the same
quasi-equilibrium state. This result confirms that quasi-equilibria
mined by measuring the concentration nI of iodine with
2
absorption spectroscopy. The absorption coefficient of I2 at 480
nm is 1.24 × 10-18 cm2.13 Beer’s law of absorption was applied.
For the experiment a line of 480 nm emitted by Cd lamp L
(Figure 6) and detected by the photomultiplier tube S of a
monochromator (lock-in technique) was used. The detected I2
concentration in connection with the filling conditions allowed
the particle number densities of H2 and HI to be calculated in
the closed system. After the plasma chemical synthesis of HI,
these molecules could be fully decomposed into H2 and I2 again
by the UV radiation of a mercury lamp.14,15
As shown in Figure 7, the spectroscopically determined values
of the iodine particle number density are in good agreement
with those following from the vapor pressure curve in ref 16,
until all I2 is in the vapor form. Successive runs of the reversible
cycle lead to identical values, which represent the initial
concentration of I2. Irreversible processes were not of marked
influence inside the discharge tube and therefore the starting
conditions could be reproduced.
Results and Discussion
Experimental Investigations. In accordance with the defini-
tions of quasi-equilibrium states presented previously, the
formation of a finite conversion in a H2-I2 gas mixture at very
small ionization degrees takes place, reflecting the formation

2028 J. Phys. Chem. A, Vol. 103, No. 13, 1999
Miethke et al.
TABLE 2: Elementary Processes
species incorporated: e, H, I, I-, H2, I2, HI, H2I
rate coefficients: ki in cm3 s-1, γi in cm6 s-1, Ri in s-1
electronic processesb
ref
25
24
23
a
1.* H2 + e f H + H + e
2.* I2 + e f I + I-
k1 ) k1(E/n)(10-10
k2 ) k2(E/n)(10-10
)
)
3.* HI + e f H + I-
4. H2I + e f H2 + I + I
5. I- + e f I + e + e
5a. I- + M+ f I + M
k3 ) k3(E/n)(2 × 10-8
)
k4 ) k4(E/n)(10-10
)
)
k5 ) k5(E/n)(10-8
a
a
k5a ) k5a(E/n)(10-7
)
thermal processesb
ref
6. I- + M f I + M + e
k6 ) 10-14
a
a
a
26
7. I + I- + M f I2 + M + e γ7 ) 2.3 × 10-30 (M ) I2)
8.* I + wall f 1/2I2
9.* H + wall f 1/2H2
R8 ) ꢀVjI/(2r0), ꢀ ) 10-4
R9 ) ꢀVjH/(2r0), ꢀ ) 10-4
k10 ) 9.1 × 10-9T0.5e-18041/T
k-10 ) 6.6 × 10-10e-20/T
k11 ) 7.4 × 10-11e-290/T
k-11 ) 5.9 × 10-9T0.5e-16529/T
γ12 ) 1.3 × 10-32
10.* HI + I {kk } H + I2
10
Figure 9. Temporal development of the CEEC (I2 component) in a
Tesla spark discharge at different gas temperatures and initial concen-
trations: (Full squares) T ) 373 K, nI20 ) 1.6 × 1017 cm-3, nH20 ) 2.1
× 1017 cm-3, nHI ) - cm-3, nHe ) 2 × 1019 cm-3; (full circles) T )
21, 22
-10
11.* HI + H {kk } I + H2
11
21, 22
-11
12. I + I + H2 {γ12 } H2I + I
373 K, nI ) 2.90 × 1016 cm-3, nH ) 6.3 × 1016 cm-3, nHI ) 2.6 ×
8
20
1017 cm-3, nHe ) 2 × 1019 cm-3; (2o0pen circles) T ) 773 K, 0nI20 ) 2.9
k-12 ) 4.3 × 10-10
k-12
13. H2I + I f 2HI
k13 ) 8.8 × 10-14
8
× 1016 cm-3, nH ) 6.3 × 1016 cm-3, nHI ) 2.6 × 1017 cm-3, nHe
)
14. I2 + M { k } I + I + M
20
2 × 1019 cm-3; (line) composition acc0ording the thermodynamic
k14 ) 5.3 × 10-4T-1.8e-17910/T
γ-14 ) 2.3 × 10-30 (M ) I2)
k15 ) 2.9 × 10-4T-1.5e-52007/T
γ-15 ) 3 × 10-32
14
21
γ-14
equilibrium (TE) for T ) 773 K.
15. H2 + M { k } H + H + M
15
21
γ-15
a Adapted. b M ) He if not specified.
collision dynamics of the hydrogen iodine exchange reaction
by Sims et al.8 There it was shown that the reaction
HI + HI f H2 + I2
is dynamically forbidden.
The Studied Reaction Mechanism. To understand the
background of the formation of chemical quasi-equilibrium
states as well as the transition to the thermal equilibrium, a
kinetic model was developed. The reaction channels considered
and the types of particles incorporated (electrons e, neutral atoms
H, I, molecules H2, I2, HI, reactive intermediates H2I, and
negative iodine ions I-) are summarized in Table 2. The
coefficients used for the electronic collision processes are given
in parentheses. The helium atoms were considered to act only
as inert collision bodies for the thermal dissociation of I2 and
H2 as well as for the recombination of I and H atoms by three-
particle collisions. These processes do not have marked influence
on the equilibrium composition. So for these reactions in each
case identical rate coefficients were used. If M is not specified,
the rate coefficient is given for M ) He. The neutralization
process of the negative iodine ions I- (channel 5a ) was taken
into account to ensure the required quasi-neutrality of the
plasma. The concentration of the positive ions is nearly that of
the negative ions, caused by the very strong electronegativity
of the H2-I2-HI system. The numerical computations were
performed using the program package CHEMKIN18 for a closed
system with constant gas temperature as well as constant total
particle number density. All numerical results refer to idealized
discharge conditions (no intermittances; continuous and homo-
geneous active phase). But the equilibrium values should be
correct also for the intermittent Tesla discharge because of the
great chemical time constants. The same is suitable for small
times (τ e 10-3 s) as shown e.g. in ref 19. The thermodynamic
data for the compounds including iodine were taken from ref
20.
Figure 10. Transition from the CEEC into the thermodynamic
equilibrium (TE) at common excitation by a Tesla spark discharge and
thermal activation (input mixture as in Figure 9, with xI + xH + xH
2
2
I
) 1).
are attainable from both sides of the reversible gross reaction
H2 + I2 + e h 2HI + e of the stable components. For a gas
temperature of T ) 500 °C, the thermodynamic equilibrium is
fulfilled. Then, in competition between the thermal and dis-
charge excitation, the velocity of the thermal reaction channels
dominates. This situation is illustrated in Figure 10 in more
detail. At lower temperatures the simultaneous excitation by
the spark discharge (with a constant power input) and the
thermal activation results in a nearly temperature-independent
CEEC. At higher temperatures (T g 350 °C) the situation is
controlled by thermal processes. The kinetic background of these
experimental results will be discussed in the next section.
Kinetic Modeling. For a long period the reaction
H2 + I2 h 2HI
(1)
was believed to be the prototype for a unimolecular elementary
reaction. But Sullivan was able to show by photochemical
experiments7 that the reaction 1 is not an elementary one. On
the contrary, reaction 1 is realized by a radical mechanism,
including reaction chains of H and I atoms, respectively. This
experimental result was confirmed by computations of the
At first it was verified that the mechanism used is suitable to
calculate the thermodynamic equilibrium. In Figure 11 the

Activation of Conversions in H2-I2-HI Mixtures
J. Phys. Chem. A, Vol. 103, No. 13, 1999 2029
Figure 11. Temporal development of the product composition of the
thermodynamic equilibrium calculated by the kinetic model (see Table
2) as well as by the gross reaction 1.17
Figure 12. Temperature dependence of the relative concentration of
the H atoms (a, left) and I atoms (b, right) at various ionization degress.
numerical results, according to the thermal reactions of the
mechanism given in Table 2, are compared with the product
composition calculated by the gross equation 1 according to
ref 17. The rate coefficients for (1) are given in ref 21. Both
computations excellently describe the product composition of
the thermodynamic equilibrium, but they differ in the time
dependence. This result is in accordance with that of Sims et
al.8 These authors showed in detail that reaction 1 is not suitable
to describe the dynamical behavior of the H2-I2-HI system.
Furthermore the kinetic model describes in a sufficient manner
the experimentally detectedsne independentsplateau of the
CEEC (see Figure 8). The detailed analytical analysis of the
system of balance equations for the proposed reaction mecha-
nism showed that the composition of the CEEC is estimated
by a small number of elementary processes, which are marked
by a * in Table 2. It can be emphasized that at the extreme
situation of the CEEC (i.e., ne f 0) all those reaction channels
have no influence which are of second order regarding the
unstable intermediate species. Within a factor of 2 the CEEC
can be calculated by the following simple relation
Figure 13. Temporal development of the gas composition at T ) 1000
K for a stoichiometric input mixture (xI ) xH ) 0.5).
20
20
x0H x0I
k3 k11
2
2
≈ 0.5
02
k1 k-10
x
HI
where the superscript zero denotes the case ne f 0.
Surprisingly, the formula has the form of a mass action law.
This formula shows that the CEEC is fixed by reaction channels
generating or consuming H atoms. In contrast to this situation
the thermal HI formation is dominated by I atoms (channels
14, -11, 12, 13). This will be discussed below.
Interpretation of the Experimental Results by the Kinetic
Model. As shown in Figure 10, the model calculations are in
good agreement with the experimental results for the dependence
of the CEEC on the gas temperature, too. At lower values (T <
600 K) the common excitation results in a nearly temperature-
independent CEEC. To the right of a sharp transition region
(600 K < T < 680 K) the product composition detected is
controlled by the thermodynamic equilibrium. At these tem-
peratures the weak excitation by electronic processes is not able
to alter the gas composition. The explanation for this behavior
can be taken from Figure 12a and Figure 12b. There the
calculated dependences of the concentrations of the H and the
I atoms on the gas temperature are plotted for different ionization
degrees xe. For low gas temperatures the dissociation into atoms
is determined only by the electronic processes (reactions 1 and
Figure 14. Temporal development of the gas composition at T ) 400
K for a stoichiometric input mixture (xI ) xH ) 0.5).
20
20
2 in Table 2). For increasing temperatures the importance of
the thermal dissociation processes (reactions 14 and 15 in Table
2) increases in relation to the electronic ones. Therefore, at high
gas temperatures the thermal dissociation dominates the creation
of the iodine atoms. Then the electronic excitation of the gas
mixture is only a small disturbance of the system. Under these
conditions the chemical quasi-equilibrium states do not exist

2030 J. Phys. Chem. A, Vol. 103, No. 13, 1999
Miethke et al.
Acknowledgment. The work was supported by the “Deut-
sche Forschungsgemeinschaft”, Sonderforschungsbereich 198
“Kinetics of partially ionized plasmas”.
References and Notes
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Figure 15. Calculated composition of the stable reaction products on
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,
20
20
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