Selected ion flow drift tube studies of the reactions of Si+(2P) with HCI, H2O, H2S, and NH3: Reactions which produce atomic hydrogen

Article abstract of DOI:10.1063/1.470375

The reaction rate coefficients, k, for the reactions of ground-state Si⁺(2P) with HCl, H2O, H2S, and NH3, have been measured as a function of reactant ion/reactant neutral center-of-mass kinetic energy, KE_CM, in a selected ion flow drift tube (SIFDT) apparatus, operated with helium at a temperature 298+/-2 K.The values k of the studied reactions have very pronounced, negative energy dependencies; the rate coefficients decrease by about 1 order of magnitude as KE_CM increase from near thermal values to ca. 2 eV.The results are interpreted in terms of a simple model assuming the reactions to proceed via the formation of long-lived complexes.These intermediate complexes decompose back to reactants or forward to products, the unimolecular decomposition rate coefficients for these reactions being k₁ and k₂, respectively.It is found that a power law of the form k_-1/k₂=const(KE_CM)^m closely describes each reaction.

Full text of DOI:10.1063/1.470375

Selected ion flow drift tube studies of the reactions of Si+(2P) with HCl, H2O, H2S, and
NH3: Reactions which produce atomic hydrogen
J. Glosík, P. Zakouřil, and W. Lindinger
Citation: The Journal of Chemical Physics 103, 6490 (1995); doi: 10.1063/1.470375
View online: http://dx.doi.org/10.1063/1.470375
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Selected ion flow drift tube studies of the reactions of Si؉(2P) with HCl,
H2O, H2S, and NH3: Reactions which produce atomic hydrogen
´
ˇ
J. Glosık and P. Zakouril
¨
¨
Institut fur Ionenphysik, Leopold Franzes Universitat, Technikerstrasse 25, A-6020 Innsbruck, Austria and
Department of Electronics and Vacuum Physics, Mathematics and Physics Faculty, Charles University,
V Holesovickach 2, Prague 8, Czech Republic
ˇ
ˇ ´
W. Lindinger
¨
¨
Institut fur Ionenphysik, Leopold Franzes Universitat, Technikerstrasse 25, A-6020 Innsbruck, Austria
͑Received 17 January 1995; accepted 12 July 1995͒
The reaction rate coefficients, k, for the reactions of ground-state Siϩ͑2P͒ with HCl, H2O, H2S, and
NH3, have been measured as a function of reactant ion/reactant neutral center-of-mass kinetic
energy, KECM , in a selected ion flow drift tube ͑SIFDT͒ apparatus, operated with helium at a
temperature 298Ϯ2 K. The values k of the studied reactions have very pronounced, negative energy
dependencies; the rate coefficients decrease by about 1 order of magnitude as KECM increase from
near thermal values to ϳ2 eV. The results are interpreted in terms of a simple model assuming the
reactions to proceed via the formation of long-lived complexes. These intermediate complexes
decompose back to reactants or forward to products, the unimolecular decomposition rate
coefficients for these reactions being k1 and k2, respectively. It is found that a power law of the form
m
k
Ϫ1/k2ϭconst͑KECM
͒
closely describes each reaction. © 1995 American Institute of Physics.
I. INTRODUCTION
Charge transfer or dissociative charge transfer ͑e.g., frag-
mentation of hydrocarbons in reactions with ions of rare
gases43͒ are essentially excluded when Siϩ ions, having a
low recombination energy of only 8.15 eV are reacting at
near thermal energies with any small molecules. The reac-
tions usually proceed by incorporation of Siϩ into the mo-
lecular product ions ͑see compilation by Anicich44 and re-
views by Bohme16,17͒. This requires a rearrangement of
existing bonds within the reactant molecule and the forma-
tion of new bonds. Such processes can take place only when
a long lived intermediate complex is formed. The mechanism
of such a reaction is reflected in its kinetics. They typically
show pronounced energy dependencies of their reaction rate
coefficients. In the case of association reactions the energy
dependence of the reaction rate coefficient is rationalized as
a consequence of the lifetime of the intermediate complex
towards dissociation back to the reactants ͑see, e.g., discus-
sion in Ref. 65͒. In the case of a binary reaction proceeding
via formation of an intermediate complex the overall reac-
tion rate coefficient can be rationalized in terms of the energy
dependence of the lifetime of this complex against dissocia-
tion backward to reactants and forward to products.
In recent SIFDT studies in our laboratory we have stud-
ied a number of reactions, the reaction rate coefficients of
which decrease strongly when KECM ͑indicating the reactant
ion/reactant molecule average center-of-mass collisional en-
ergy͒ increases, starting from collisional limiting values at
room temperature.45–48 Also the presently reported reactions
of Siϩ have similar dependencies on KECM . We will show
that such reactions appear to proceed via the formation of
long-lived complexes, the rate coefficient for the decompo-
sition of which ͑back to reactants or forward to products͒
depends on the interaction energy in a power-law fashion.
The first step of any of the reactions studied, namely, the
formation of the ion–molecule collision complex is limited
by the capture rate coefficient kC . The values kC , for reac-
A large number of reactions of the silicon ion Siϩ have
been studied by Lampe and co-workers using a tandem mass
spectrometer1–6 ͑see also a review by Lampe7 and references
therein͒. A selected ion flow tube ͑SIFT͒ study on the reac-
tions of Siϩ with H2O, O2, H2, and NO ͑at 300 K͒ has been
carried out by Ferguson et al.8 Bohme, Wlodek, and co-
workers have made systematic studies of the reactions of
atomic Siϩ͑2P͒ ions focused on the kinetics, energetics, and
the mechanism of these reactions leading to the chemical
bonding of silicon with hydrogen, carbon, nitrogen, oxygen,
and sulfur,9–15 ͑see also reviews by Bohme16,17 and refer-
ences therein͒. These studies have been carried out using a
selected ion flow tube ͑SIFT͒ apparatus at 298 K and a he-
lium buffer gas pressure of 0.35 Torr. A guided ion beam
apparatus has been used by Armentrout and his co-workers
to study cross sections, mechanisms, and thermochemical as-
pects of several reactions of Siϩ͑2P͒ ions at kinetic energies
ranging from thermal to ϳ10 eV18–24 ͑see also reviews by
Armentrout25,26͒. In a selected ion flow drift tube ͑SIFDT͒
study carried out by Fahey et al.,27 the mobility of Siϩ in He
has been measured, and the influence of the speed distribu-
tion of the Siϩ ions drifting in He on the measured reaction
rate coefficients has been discussed.
Recently the structure, thermochemistry, and the reac-
tions of many silicon-bearing ions with neutral molecules
have been the subject of theoretical ͑see, e.g., Refs. 28–36͒
and various experimental studies ͑see, e.g., photoionization
mass spectrometric studies,37,38 a review by Bohme,16 and
references therein͒.
The reactions of atomic silicon ions are important for the
chemistry of interstellar clouds,39–42 and of the earth’s
ionosphere.8 These reactions also could be of interest to the
theoretical chemist because of fundamental aspects of the
chemical bonding of atoms to silicon.
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´
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Glosık, Zakouril, and Lindinger: Reactions of Si ( P)
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tions of ions with nonpolar molecules are, according to
simple Langevin theory, expected to be temperature indepen-
dent ͓kCLϭ2␲e(␣/␮r)1/2, in c.g.s. units, where ␣ is the po-
larizability of the neutral reactant molecule, ␮ is the reduced
r
mass of the reactant ion/reactant neutral molecule, and e is
the charge of the ion͔. The slightly temperature dependent
rate coefficients for reactions involving polar molecules
are often calculated according to the ADO theory
k
CϪADO(T) ϭ kCL ϩ 2Ce␮d(2␲/␮rkBT)1/2, where ␮d is the
͓
permanent dipole moment of the reactant molecule, kB is
Boltzmann’s constant, and C is a dipole locking constant
1/2
which, at a given temperature, is a function of ͑␮d/␣͒
only49,50͔. A more recent approach to the calculation of col-
lisional rate coefficients is done by using parametrization of
the results of trajectory calculations due to Su and
Chesnavich.51 When collisional rate coefficients have to be
calculated for temperatures below 300 K, an adiabatic cap-
ture theory ͑see review by Clary52͒ or statistical capture
theories53,54 are used. In all the following the capture rate
coefficients are indicated by kC , whether they represent
Langevin limiting values, kCL , or values calculated accord-
ing to the above mentioned ADO theory or the more recent
models of Su and Chesnavich.51
In drift tubes KECM can be increased to values up to a
few eV where theories which predict thermal energy capture
rate coefficients no longer apply. Reaction rate coefficients
measured in drift tubes at elevated energies are often ob-
served to exceed kC calculated for 300 K. This phenomenon
has been discussed in several recent papers55 ͑see also dis-
FIG. 1. The empirical correction factor ␤ ͑solid line͒ obtained from the
measured rate coefficients for the fast ion–molecule reactions ͑Ref. 47͒. ␤ is
the average value of k͑KECM͒/k0 , where k0 is the limiting value of k for
KECM→thermal value. For demonstration k͑KECM͒/k͑KECMϭ0.038 eV͒ vs
KECM for the reactions of Cϩ with H2S ͑symbol ᭿͒ and Cϩ with NH3
͑symbol ᮀ͒, as were measured in present experiment, are also plotted.
ϩ
*
of the excited intermediate complex ͑AB ͒ , and kϪ1 and k2
are unimolecular rate coefficients for dissociation of the ex-
cited intermediate complexes into the primary ion/neutral re-
actant and the product ion/product neutral, respectively. We
assume that the excited intermediate complex is formed at
the capture rate, kC . Such an assumption is very common
͑e.g., in discussion of vibrational quenching by Ferguson57͒.
We want to stress the fact, that in the following we use the
specific values k1 ϭ kC ϭ ␤ • kC . By applying simple
0
reaction kinetics and using the steady-state approximation to
cussion in Ref. 56͒, where the capture rate coefficient is pre-
ϩ
0.5
dicted to increase as T0.5 ͓i.e., as ͑KECM
͒ ͔ at suprathermal
*
͑AB ͒ , the following relationship is obtained for the overall
rate coefficient k of reaction ͑1͒:
energies typical to those acquired in drift tube experiments.
In a recent paper47 we introduced an empirical correction
function ␤ ͑dependent only on KECM͒ derived from many
experimental data. This function is equal to unity at near
thermal energy and increases with increasing KECM , and has
a value of approximately ϳ2 at KECMϭ2 eV. We assume,
that the actual capture rate coefficient kC ϭ ␤kC , where kC
k2
1
kϭk1
ϭ␤•kC
.
͑2͒
0
k
Ϫ1ϩk2
kϪ1
1ϩ
k2
From this relation it is evident that the ratio (kϪ1/k2) and its
dependence on KECM is governing the energy dependence of
the overall reaction rate coefficient k, as long as the assump-
tion that the complex is formed at the capture rate is valid,
and as long as the capture rate has only a weak or no depen-
dence on KECM . Note at this point that for the same conclu-
sion ͑concerning dependence of k on kϪ1/k2͒ it will be suf-
ficient to assume, that the rate of formation of an
intermediate complex is nearly constant, but not necessarily
equal to the capture rate coefficient.
0
0
is the capture rate coefficient for a particular reaction at low
KECM ͑limiting value for KECM approaching thermal en-
ergy͒. In Fig. 1 the correction factor ␤ used for the present
work is plotted and for demonstration experimental data
kexp/k0exp ͑equivalent to kC /kC , if a reaction is proceeding at
0
the capture rate͒ as obtained for the fast reactions of Cϩ with
H2S and Cϩ with NH3 are included. In the following, when
energy dependencies of reactions are discussed, the term
‘‘capture rate coefficient, kC’’ always refers to the value
On the basis of statistical arguments,58 in analogy with
the ideas widely discussed for three-body association
reactions59,60 and on the basis of our studies of many ion–
molecule reactions proceeding via formation of long lived
intermediate complexes,45–48,61–63 we assume here that the
ratio (kϪ1/k2) will vary with KECM in a power law fashion:
(kϪ1/k2)ϰ͑KECM͒m. Expression ͑2͒ can then be rewritten as
␤kC
.
0
In order to describe the kinetics of the presently investi-
gated ion–molecule reactions we consider that the reactions
proceed via the formation of long-lived excited intermediate
complexes which subsequently decompose back to reactants
or forward to products. Thus the following reaction scheme
is appropriate:
1
kϭ␤•kC
•
,
͑3͒
m
0
KECM
k
k
2
1
1ϩ
ͩ
ͪ
ϩ
ϩ
ϩ
*
A ϩB ꢀ AB ͒ →C ϩD,
͑1͒
͑
KECM1
k
Ϫ1
where m and KECM1 are constants ͑KECM1 is the value of
KECM at which k has decreased to 1/2 of its maximum value
where k1 is the bimolecular rate coefficient for the formation
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´ ˇ
Glosık, Zakouril, and Lindinger: Reactions of Si ( P)
6492
and hence for which kϪ1ϭk2͒. The parameters kC , KECM1
,
0
and m can be obtained from the fit of the experimental
data.46,47 In order to visualize the dependence of kϪ1/k2 on
KECM , kϪ1/k2 can be expressed explicitly by using formulas
͑2͒ and ͑3͒ as
m
␤kC
kϪ1
k2
KECM
ϭ
0Ϫ1 ϭ
.
͑4͒
ͩ
ͪ ͩ
ͪ
k
KECM1
Using the measured values k͑KECM͒, the function
log(␤(kC /k) Ϫ 1) vs log͑KECM͒ can be plotted. If
0
͑KECM/KECM1͒ӷ1, then Eq. ͑3͒ can be written in form
Ϫm
KECM
kЏ␤•kC0
•
.
͑5͒
ͩ
ͪ
FIG. 2. The variation of the reaction rate coefficient with KECM for the
reaction of Siϩ͑2P͒ with HCl ͑kCLϭ9.56ϫ10Ϫ10 cm3 sϪ1͒. Different buffer
gas pressures are indicated by different symbols.
KECM1
This form of the dependence of a rate coefficient on energy
͑temperature͒ has been observed many times for three-body
association reactions ͑e.g., Refs. 64–68͒ where the value of
m was coupled to the number of rotational degrees of free-
dom in the reactants and products. We will use the parameter
m to characterize the energy dependencies of the studied
reactions.
III. RESULTS AND DISCUSSION
The reaction rate coefficients and product ion distribu-
tions were determined for the reactions of Siϩ͑2P͒ ions with
the small 2, 3, and 4 atoms containing inorganic molecules
HCl, H2O, H2S, and NH3 over the energy range of KECM
from thermal ͑Ϸ0.04 eV͒ to about 2 eV. All these reactions
are fast ͑with rate coefficients of a few times 10Ϫ10 to 10Ϫ9
cm3 sϪ1͒ at near thermal energies and their rate coefficients
have a very pronounced negative energy dependence. The
main neutral product in all these reactions is atomic hydro-
gen. We estimated standard reaction entropies for all the
studied reactions and it is worth noting that mainly because
of the production of H in these reactions, the standard reac-
tion entropies in the studied reactions are all negative.
II. EXPERIMENT
The experiments were performed using the Innsbruck
selected ion flow drift tube ͑SIFDT͒ of conventional
design.69,70 The reactant ions Siϩ were produced from SiH4
in a high pressure electron-impact ion source, Ar was added
to the ion source in order to enhance the production of Siϩ
ions and to decrease the contamination of the ion source
caused by the presence of SiH4. The ions were subsequently
mass selected in a quadrupole mass filter and injected into
the flow tube via a venturi-type inlet. In the upstream part of
the drift tube, prior to the reaction region, low E/N was used
͑E is the electric field strength in this part of the drift tube
and N is the buffer/carrier gas number density͒. In this ‘‘ther-
malization’’ part of the drift tube the average collision energy
of the ions with the buffer gas atoms was kept below 0.1 eV.
The reactant and product ions were monitored down-
stream with a second quadrupole mass filter as a function of
the flow rate of the added neutral reactant. Established meth-
ods of analysis were used to derive reaction rate constants
and product distributions.71,72
A. The reaction of Si؉(2P) with HCl
The energy dependence of the reaction rate coefficient,
k, of the title reaction
SiϩϩHCl→SiClϩϩH
͑6͒
is shown in Fig. 2. To our knowledge there exists no previous
study of this reaction. The values of k have a minimum at
KECMЏ0.4 eV. SiClϩ was the only observed product ion
over the whole KECM range covered. A possible association
product SiClHϩ was observed only in traces ͑Ͻ0.5% of the
total ion signal͒ and we did not observe any pressure depen-
dence of the measured rate coefficients for helium buffer gas
pressures ranging from 0.177 to 0.344 Torr. Before further
treatment of the data, the measured rate coefficients were
divided by the factor ␤͑KECM͒, as has been discussed in the
Introduction. In the following, we will use the upper index ␤
in k␤ to indicate ‘‘␤ corrected’’ rate coefficients. The ob-
tained k␤ϭk/␤ is plotted vs KECM in a log–log plot in Fig.
3. We assume that two different reaction mechanisms are
involved at low and high energies KECM , respectively. In-
dexes I and II will be used to indicate the low and high
In order to determine the internal state of the Siϩ ions in
the reaction region of the drift tube in the present experi-
ment, D2 was added as a reactant gas. No production of SiDϩ
or any other reaction of Siϩ with D2 was observed. It is
known10,26 that the reaction of the ground-state Siϩ͑2P͒ with
D2 is endoergic and very slow ͑Ͻ2ϫ10Ϫ13 cm3 sϪ1͒ whereas
the reaction of the excited state Siϩ ͑probably P state͒ with
4
*
D2 is fast ͑7.7ϫ10Ϫ10 cm3 sϪ1͒ yielding the product SiDϩ.
We therefore concluded that the Siϩ ions are in their ground-
state Siϩ͑2P͒ in the present experiment.
KECM was derived by means of the Wannier
expression.73 The mobility of Siϩ ions in He was measured
in the present experiment and it agrees well with the mobility
data obtained by Fahey et al.27 The accuracy of the measured
rate coefficients is assumed to be Ϯ30% as is usual for
swarm experiments of the SIFDT type.
energy processes, respectively. The low energy segment of
Ϫm
the dependence of k␤ on KECM is of the form ͑KECM
͒
and
we assume that at high-energy the dependence on KECM is of
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FIG. 3. The variation of the ␤ corrected reaction rate coefficient, k␤, with
KECM for reaction of Siϩ͑2P͒ with HCl ͑solid symbols͒. Straight solid line
represents the best fit through the data in low energy region. The open
symbols correspond to reaction rate coefficient, kII , of the high energy pro-
cess obtained by substraction of the reaction rate coefficient, kI , of the low
energy process from k␤, kIIϭk␤ϪkI ͑see the text͒. Dashed line corresponds
to the best fit through the data in Arrhenius plot in Fig. 4. Dotted line is the
best fit curve according to Eq. ͑1͒. Different buffer gas pressures are indi-
cated by different symbols.
FIG. 5. The variation of the reaction rate coefficient k with KECM for the
reaction of Siϩ͑2P͒ ions with H2S. Different buffer gas pressures are indi-
cated by different symbols. Dotted line corresponds to the best fit of the high
energy segment of the data by function ␤•A•exp͑Ϫ3Ea/KECM͒, where
2
Eaϭ0.74 eV is given by endoergicity of the channel ͑8b͒ of the reaction. By
multiplication of the Arrhenius function by ␤, the ␤ correction is taken into
account. Dashed line corresponds to ␤ kI , where kI characterize low energy
segment of the data and is determined by the fit of the data in Fig. 7. The
best fit of the data according to Eq. ͑7͒ after inverse ␤ correction is indicated
by solid line.
an Arrhenius type, involving an activation energy, Ea . Over
the whole energy range covered k␤ can be approximated by
the expression
parameters kI ϭ 0.8 ϫ 10Ϫ9 cm3 sϪ1, mϭ1, kII ϭ 1.0
0
0
ϫ 10Ϫ10 cm3 sϪ1, and Eaϭ0.7 eV, obtained by a fit of both
the low and high energy sections, we obtain a fit of k␤ ͑dot-
ted line in Fig. 3͒ and k ͑dotted line in Fig. 2͒, which are in
good agreement with the data. Function ͑7͒ also was used
earlier to fit the data of our previous studies,46,47,61,62 on re-
actions of several small hydrocarbon ions with HCl, N2O,
CO2, NH3 and the ones of Viggiano et al.74 on the reaction
of Krϩ͑2P3/2͒ with HCl and the obtained parameters m were
discussed on the basis of internal degrees of freedom of the
reactants.
Ea
k␤ϭkIϩkIIϭkI KE
͒
ϪmϩkII exp Ϫ
,
͑
CM
0
0
2
ͩ ͪ
KECM
3
͑7͒
where kI is a ‘‘proportionality constant’’ and kII is the ‘‘lim-
0
0
iting value’’ of k␤ at high KECM . In order to calculate the
second term, kII , in Eq. ͑7͒ representing the Arrhenius de-
pendence, kII was expressed as kIIϭk␤ϪkI ͓kI was extrapo-
lated for that purpose from the low energy region by a
straight ͑solid͒ line as shown in Fig. 3͔. The calculated val-
ues kII are plotted in Fig. 3 ͑open symbols͒. Figure 4 shows
the Arrhenius plot of kII vs 1/KECM . From the Arrhenius plot
in Fig. 4 an activation energy Eaϭ0.7 eV was calculated.
The apparent linear fit through the data in the Arrhenius plot
͑Fig. 4͒ is indicated by a dashed line in Fig. 3. When using
To our knowledge the heat of formation of SiClϩ is not
known, but from the fact that the reaction ͑6͒ is fast at low
KECM we assume that the reaction is exoergic or at least
thermoneutral. Using values ⌬Hf͑Siϩ͒ϭ295.8 kcal/mol,
⌬Hf͑HCl͒ϭϪ22.02 kcal/mol, and ⌬Hf͑H͒ϭ52.095
kcal/mol75 we obtain an upper limit ⌬Hf͑SiClϩ͒Շ221.7
kcal/mol.
B. Reaction of Si؉(2P) with H2S
The energy dependence of the rate coefficient, k, for the
reaction
SiϩϩH2S→͑SiSH͒ϩϩH
→SiHϩϩSH
͑8a͒
͑8b͒
is shown in Fig. 5. This reaction was used by Fox et al.13 to
produce ͑SiSHϩ͒, which then was used as a reactant ion for
further investigations, nevertheless the rate coefficient of re-
action ͑8͒ was not reported. The rate coefficient obtained is
independent of the pressure of the buffer gas and only traces
of adduct, SiSHϩ2 ions, created by association reactions, were
observed. The channel ͑8a͒ is exoergic, channel ͑8b͒ is en-
doergic by 0.74 eV ͑see Table I͒. The productions of both
isomers, the more energetic SSiHϩ and the less energetic
SiSHϩ ions are exoergic and may therefore occur ͑see dis-
FIG. 4. Arrhenius plot of the reaction rate coefficient kII corresponding to
the high energy process of the reaction of Siϩ͑2P͒ with HCl. Obtained
Arrhenius activation energy Eaϭ0.7 eV. Dashed line is the best apparent
linear fit. Different buffer gas pressures are indicated by different symbols.
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Glosık, Zakouril, and Lindinger: Reactions of Si ( P)
TABLE I. Summarized data for the reactions included in this study. The reaction energetics are indicated as
⌬E(ϭϪ⌬H), calculated using the thermochemical data given in Refs. 10, 13, 24, and 75. The values for the
rate coefficients are given in units of 10Ϫ9 cm3 sϪ1 and energies ⌬E and KECM1 in eV.
Product
ion
Product
neutral
Reaction
⌬E
kCL
k10
a
k10/kCL
m
KECM1
a
SiϩϩHCl
SiϩϩH2S
SiClϩ
H
H
H
SH
H
H
H
H
0.96
1.16
1.0
1.6
SiSHϩ
HSiSϩ
SiHϩ b
SiOHϩ
HSiOϩ
SiNHϩ2
HSiNH
0.78Ϯ0.2
0.25Ϯ0.2
Ϫ0.74
1.4Ϯ0.2
Ϫ1.2Ϯ0.2
0.74
0.79
0.68
0.12
SiϩϩH2O
SiϩϩNH3
0.85
1.07
0.29
0.77
0.34
0.72
2.9
2.0
0.104
0.13
Ϫ1.56
aFor reaction of Siϩ with HCl low energy limit was not yet reached at the near thermal energies accessible in
the present experiment.
bThe product observed for energies above ϳ0.8 eV.
cussion in Ref. 13͒ in parallel. We did not determine which
isomer actually is produced in the reaction. ͑SiSH͒ is the
͑channels͒ overlap kI has been calculated by subtraction of
kII from the experimental data, kIϭk␤ϪkII . The obtained
values kI are shown in Fig. 6.
ϩ
dominant product at low KECM . The signal of SiHϩ is in-
creasing at elevated KECM and is becoming the dominant
product above 0.8 eV. We cannot show the actual product
distribution because the masses of the product ions differ by
a factor of 2 and thus the mass discrimination of the quad-
rupole system may be substantial. The obtained relative
product distribution is in qualitative agreement with the ob-
tained values kI and kII as discussed below. As shown for the
reaction of Siϩ with HCl, also here the rate coefficient k␤ for
the overall reaction can be written in the form: k␤ϭkIϩkII ,
where kI and kII correspond to the channels ͑8a͒ and ͑8b͒,
respectively. We assume that the energy dependence of the
rate coefficient kII of the endoergic channel ͑8b͒ has an
Arrhenius form with an activation energy equal to the endo-
ergicity of the reaction, Eaϭ0.74 eV. Therefore, the high
energy segment of the data was fitted by the function
␤•A•exp͑Ϫ͑3/2͒Ea/KECM͒ with Eaϭ0.74 eV, and the param-
eter A was determined as shown by the dotted line in Fig. 5.
In the low energy region the endoergic channel ͑kII͒ is neg-
ligible and kIЏk␤. In the energy region where both processes
In order to visualize the form of the dependence of kI on
KECM , ((kI /kI) Ϫ 1) vs KECM is plotted in Fig. 7. The
0
m
excellent linearity of the plot kϪ1/k2ϰ͑KECM
͒
justifies our
assumption that two parallel reaction channels occur, the
exoergic one ͑8a͒ resulting in the production SiSHϩ and the
endoergic one ͑8b͒ producing SiHϩ, predominantly at ener-
gies KECMу0.8 eV. Parameters of the fit are listed in Table I.
C. The reaction of Si؉(2P) with H2O
The reaction
SiϩϩH2O→SiOHϩϩH
͑9͒
has been studied only over the limited energy range, from
thermal up to 0.3 eV. At higher energies the flow of the H2O
vapor was too small to obtain a sufficiently strong decay of
the Siϩ signal allowing for an accurate calculation of the rate
coefficient of the reaction. The energy dependence of the
obtained rate coefficient is shown in Fig. 8. Thermal SIFT
data of Fahey et al.27 and Wlodek et al.10 are included, and
show very good agreement with the present data ͑low energy
limit͒. Note that at thermal energy the measured rate coeffi-
cient of reaction ͑9͒ is only 1/4 of the capture rate coefficient,
k
CLЏ8.5ϫ10Ϫ10 cm3 sϪ1. This observation disagrees with a
FIG. 6. The reaction rate coefficient, kI , corresponding to the low energy
process of the reaction of Siϩ͑2P͒ with H2S, kIϭk␤ϪkII , where kII is the
reaction rate coefficient corresponding to the endoergic production of SiHϩ,
obtained by fit of the high energy segment of the data ͑see text͒. Dotted line
corresponds to straight line in Fig. 7. Different buffer gas pressures are
indicated by different symbols.
FIG. 7. Dependence of (kI0 /kI Ϫ 1) vs KECM of the data plotted in Fig. 6.
Straight solid line is the best apparent linear fit of the data.
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6495
FIG. 10. The KECM dependence of the reaction rate coefficient of the reac-
FIG. 8. The variation of the reaction rate coefficient with KECM for the
tion of Siϩ͑2P͒ with NH . indicates SIFT data of Wlodek et al. ͑Ref. 77͒.
reaction of Siϩ͑2P͒ with H O. indicates SIFT data ͑Refs. 8, 10, 27͒. Dotted
*
3
*
2
Dotted line corresponds to best fit in Fig. 11. Different pressures are indi-
cated by different symbols.
line represents the data obtained by calculation of the reaction rate coeffi-
cient from reported reaction cross section obtained in guided beam study
͑Ref. 21͒. Dashed line corresponds to straight line fit in Fig. 9. Different
pressures are indicated by different symbols.
KECM as discussed in Sec. I. Because KECM did not exceed
0.3 eV, ␤Џ1, and the ‘‘␤ correction’’ is negligible.
guided ion beam study of this reaction,21 where cross sec-
tions equal to the collisional cross section have been reported
for energies from 0.02 up to 0.2 eV. Also the reported rela-
tive change of the cross section of the reaction ͑9͒ as depen-
dent on the collision energy is not in agreement with the
energy dependence of the reaction rate coefficients obtained
in the present study ͑dotted line in Fig. 8 represents the re-
action rate coefficients as calculated from the cross sections
reported in Ref. 21͒. There exist two isomers SiOHϩ and
HSiOϩ, but while the production of SiOHϩ in the reaction of
Siϩ with H2O is exoergic by 1.4 eV, the production of the
HSiOϩ isomer is endoergic by 1.2 eV ͑see Table I͒. Thus in
the present study the product ion can only be the SiOHϩ
isomer ͑see also discussion by Bohme76͒. The obtained en-
ergy dependence of the reaction rate coefficient ͑plot in Fig.
8͒ has a form similar to the low energy parts ͑kI͒ of the
dependencies of the rate coefficients for the reactions of Siϩ
with HCl and H2S. Therefore Eq. ͑3͒ was used to fit the data
in Fig. 8, and the obtained fit is represented by a dashed line.
The obtained parameters of the fit are listed in Table I. Figure
9 shows the log–log plot of the function ((␤•k0)/(k)Ϫ1) vs
D. The reaction of Si؉(2P) with NH3
The reaction
SiϩϩNH3→SiNHϩ2 ϩH
͑10͒
is very fast at near thermal energies and its rate coefficient
decreases, with increasing KECM by nearly 2 orders of mag-
nitude, as is shown in Fig. 10. At low energy our data agree
well with the value obtained by Wlodek et al.77 Only one
product ion of mass 44 has been observed. Assuming the
product ion to be the isomer SiNHϩ2 , the reaction is exoergic
by 0.75 eV, the production of the isomer HSiNHϩ would be
endoergic by 1.57 eV, and is not possible over the whole
energy region covered ͑for energetics of the reaction see data
in Table I and for more details concerning energetic of the
reaction ͑10͒ see discussion in Ref. 77͒. Figure 11 represents
a log–log plot of the function ((␤•k0)/(k)Ϫ1) vs KECM
.
Note the extraordinary linearity of the plot indicating a very
high accuracy of the approximation of the ratio (kϪ1/k2) by
the power function, as it was discussed in Introduction. The
FIG. 9. Plot of ((␤•k0)/(k)Ϫ1) vs KECM of the reaction rate coefficient for
the reaction of Siϩ͑2P͒ with H2O. Solid straight line is the best apparent
linear fit. Different pressures are indicated by different symbols.
FIG. 11. Plot of ((␤•k0)/(k)Ϫ1) vs KECM of the reaction rate coefficient of
the reaction of Siϩ͑2P͒ with NH3 . Solid straight line indicates the best ap-
parent linear fit. Different pressures are indicated by different symbols.
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ϩ
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Glosık, Zakouril, and Lindinger: Reactions of Si ( P)
6496
data in Fig. 11 were fitted by the function given in Eq. ͑4͒,
parameters m and KECM1 of the fit are listed in Table I.
schaftlichen Forschung under Project No. 10014 and in part
by Grant Agency of The Czech Republic under Project No.
0446.
IV. CONCLUDING REMARKS
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76, 3321 ͑1972͒.
We have investigated the dependence of the reaction rate
coefficients k on the center-of-mass interaction energy KECM
for several reactions which proceed at near collisional rate
͑see Table I for k10/kCL͒ at low KECM ͑near thermal collision
energies͒ and for which the reaction rate coefficients de-
crease quite rapidly with increasing KECM . We showed that
for low KECM the energy dependence of all studied reactions
can be expressed by a power function of the type
2 T. M. H. Cheng, T. Y. Yu, and F. W. Lampe, J. Phys. Chem. 77, 2841
͑1973͒.
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1
kϰkC0
.
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m
1ϩ KECM /KECM1
͒
͑
These results can be interpreted on the assumption that the
reactions are proceeding via formation of long lived interme-
diate complexes, and in such cases the overall reaction rate
coefficients are governed by the ratio kϪ1/k2 ͓see Eq. ͑2͔͒ of
the unimolecular reaction rate coefficient for decomposition
of the complex to the reactants (kϪ1) and the rate coefficient
of the forward reaction (k2). By analogy with ideas used in
the interpretation of energy dependencies of the reaction rate
coefficients of the three body association processes it was
postulated that the ratio kϪ1/k2ϰ͑KECM/KECM1͒m. Using this
assumption an analytical function for energy dependences of
the reaction rate coefficients of the studied reactions was
derived ͓see Eqs. ͑3͒, ͑4͒, and ͑5͔͒. The high accuracy of the
fits supports our assumption about the nature of the reaction
processes.
All four reactions are exoergic ͑i.e., ⌬HϽ0͒ but not
strongly and the entropy changes in these reactions are nega-
tive ͑i.e., ⌬SϽ0͒. With increasing KECM ͑temperature͒ in
these reactions T•⌬S becomes increasingly negative, thus
the free energy change ⌬Gϭ⌬HϪT•⌬S becomes positive
and therefore unimolecular decomposition back to reactants
is favored. The parameter KECM1, characterizing the energy
where the negative energy dependence of the reaction rate
coefficient starts, may well coincide with the energy at which
⌬G becomes positive.
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¨
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