Electron attachment on HI and DI in a uniform supersonic flow: Thermalization of the electrons

Article abstract of DOI:10.1063/1.1763832

The attachment of electron on HI and DI was studied in the 48-170 K range using the CRESU (Cinetique de Reaction en Ecoulement Supersonic Uniforme) technique. The attachment to HI was found to be exothermic and was expected to be fast and to proceed at a rate closed to the capture limit. The attachment to DI was found to be endothermic, where a positive temperature dependence was expected to occur if the electrons were thermal. A model, based on electron heating by superelastic collisions with the buffer gas was proposed.

Full text of DOI:10.1063/1.1763832

Electron attachment on HI and DI in a uniform supersonic flow: Thermalization of the
electrons
F. Goulay, C. Rebrion-Rowe, S. Carles, J. L. Le Garrec, and B. R. Rowe
Citation: The Journal of Chemical Physics 121, 1303 (2004); doi: 10.1063/1.1763832
View online: http://dx.doi.org/10.1063/1.1763832
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 121, NUMBER 3
15 JULY 2004
Electron attachment on HI and DI in a uniform supersonic flow:
Thermalization of the electrons
F. Goulay, C. Rebrion-Rowe, S. Carles, J. L. Le Garrec, and B. R. Rowe
´
´
Laboratoire Physique des Atomes, Lasers, Molecules et Surfaces, UMR 6627 du CNRS, Universite de
Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France
͑Received 30 March 2004; accepted 28 April 2004͒
´
´
In order to check the electron thermalization in the CRESU technique ͑Cinetique de Reaction en
Ecoulement Supersonique Uniforme, e.g., ‘‘reaction kinetics in a uniform supersonic flow’’͒,
electron attachment on HI and DI has been studied in the 48–170 K range. Attachment to HI is
exothermic and the reaction is expected to be fast and to proceed at a rate close to the capture limit.
On the contrary, attachment to DI is slightly endothermic, and a strong positive temperature
dependence of the measured rate coefficient is expected if the electrons are thermal. This
dependence is not observed, and we conclude that the electrons are not in thermal equilibrium with
the neutrals in the afterglow. A model, based on electron heating by superelastic collisions with the
buffer gas, is proposed to explain this fact and implications for previously published results are
discussed. © 2004 American Institute of Physics. ͓DOI: 10.1063/1.1763832͔
I. INTRODUCTION
on dissociative electron attachment on CH3I ͑Ref. 19͒ were
found in clear discrepancy with those of Schramm et al.20
who used a laser photoionization attachment technique com-
bined with free jet cooling of CH3I.
The process of electron-molecule attachment can depend
strongly on the temperature, either through the electron ki-
netic energy or the internal state populations of the neutral
molecules. A variety of techniques have been described in
several review papers,1–9 which allow electron attachment
study at very low electron energy. Most of them, however, do
not permit one to vary the temperature of the molecular spe-
cies from room temperature. For practical applications and
especially for the chemistry of dense interstellar clouds, it is
essential to obtain rate coefficient data in conditions of true
local thermodynamic equilibrium.
Whether the temperatures of the electrons and the neu-
tral molecules are the same within the CRESU jet was al-
ways a matter of concern for us, as direct measurements of
electron temperature are not reliable in this temperature
range. Equilibrium was, however, expected because experi-
ments were performed either in a nitrogen or a helium buffer
gas: both gases relax efficiently electrons, nitrogen by rota-
tional transfer and helium by translational transfer.14 In ad-
dition, the excellent agreement with previous FALP data in
the temperature range common to both experiments, some-
times showing a similar strong temperature dependence, was
another argument in favor of true thermal conditions in the
CRESU.
The suggestion10,11 that the carriers of negative charges
in interstellar matter, when shielded from harsh UV radia-
tion, could be partly anions, probably formed from polycy-
clic aromatic hydrocarbons, has not yet received a definitive
answer due to the lack of relevant laboratory data. Our
present models of interstellar physics and chemistry, which
assume that electrons are the carriers of negative charge,
could be drastically changed by new experiments in this
field.
The CRESU technique uses a uniform supersonic flow
as a very cold chemical reactor. This technique is now well
established in the fields of ion-molecule or radical-molecule
kinetics.12,13 More recently, this technique has also been used
by our group to study electron attachment to cold neutral
molecules. Several studies have indeed demonstrated the
strong influence on the attachment rate of the temperature of
the molecule14 as well as of the presence of neutral
aggregates.15,16 These experiments displayed excellent agree-
ment with data obtained by another thermal technique, the
FALP ͑flowing afterglow Langmuir probe͒.17,18 The first sur-
prising results concerned the rate of electron attachment on
anthracene. The CRESU measurement of this rate constant
did not show any temperature dependence, although it was
much lower than the capture limit. More recently, our results
Unfortunately, as discussed in a relevant paper,15 most of
these first results concerned reactions which are rather insen-
sitive to electron temperature but strongly dependent on the
internal states of the molecule, and therefore cannot be taken
as a probe for electron temperature. The fact that electron
relaxation is very fast toward the cold rotation/translation
bath is not a definitive proof of equilibrium in our experi-
ment: if an efficient heating process competes with the cool-
ing process, electrons will be maintained in a steady state at
some intermediate temperature. In our search for possible
electron heating sources, we have investigated the role of the
electric fields present in the experiment. We have demon-
strated that this heating process was inefficient in the
CRESU.21
A definitive answer to the question whether our electrons
are thermal or not, needed to be given. The idea was to find
an attachment reaction which is predicted to be strongly de-
pendent of the electron energy, even at low temperature, that
is, a slightly endothermic reaction. In order to simplify the
0021-9606/2004/121(3)/1303/6/$22.00
1303
© 2004 American Institute of Physics
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1304
J. Chem. Phys., Vol. 121, No. 3, 15 July 2004
Goulay et al.
analysis of the results, molecules with low-lying vibrational
states have been avoided. Our test reaction is therefore the
dissociative electron attachment of deuterium iodide ͑DI͒.
Only the ground vibrational state is populated in the condi-
tions of our experiments, the attachment reaction is endoer-
gic for the low-lying rotational states, and becomes exoergic
for levels greater than 9. A strong positive temperature de-
pendence is therefore expected, provided the electrons are
thermalized. By contrast, electron attachment on HI is exo-
thermic. In the 23–300 K range, however, the measured rate
coefficients for DI do not exhibit the expected temperature
dependence. This can be taken as a proof that in the CRESU
flow, when an electron beam is used as a plasma source, the
electron temperature is not the same as the neutral one. A
model is presented which shows that vibrational excitation of
the nitrogen buffer gas in the electron source could heat the
electrons at some intermediate temperature. Our previous re-
sults are discussed in light of this finding.
FIG. 1. Schematic view of the experiment.
The measurements are made downstream of the electron
beam where it is expected that the electron temperature has
reached a steady value, as relaxation times are short. A Lang-
muir probe is used to measure the electron density and the
nature of the product anions is determined by mass spec-
trometry. Both the Langmuir probe and the quadrupole mass
spectrometer can be moved along the axis of the jet and it is
therefore possible to measure the electron and ion densities
downstream of the plasma source. As the flow is uniform, the
electron density depends on the density of the attaching gas
A and on the distance x between the Langmuir probe and the
source according to the equation
II. THE EXPERIMENT
Deuterium iodide is not commercially available in Eu-
rope, and therefore had to be synthesized in the laboratory.
The operating modes for the synthesis of DI and HI are the
same, and the following description concerns HI, unless oth-
erwise noted.
␤ A x
͓ ͔
eϪ ϭ eϪ exp Ϫ
,
͑1͒
͓
͔
͓
͔
0
ͩ
ͪ
v
A stainless steel reactor was filled with H2 and I2 in ratio
H2 /I2 of 6:1, at an initial pressure of 1.7 bar in presence of a
platinum sponge catalyst. This reactor was maintained at 673
K for 4 h. At this temperature, the chemical equilibrium H2
ϩI2⇔2HI is displaced in favor of hydrogen iodide. After
this time, the reaction product was separated from remaining
reactants: I2 together with the HI vapor were first trapped at
77 K to pump excess H2 ; in a second step the I2 /HI mixture
was distilled at 243 K, and HI trapped at 77 K. Finally, the
solid deposit of HI was slowly reheated to ambient tempera-
ture, then distilled again. It was stored in a stainless steel
tank, where it was diluted in H2 (D2 in the case of DI͒.
Samples were analyzed by mass spectrometry. The spectra
showed that impurities represented an amount less than 2%
in molar concentration, which is of no consequence for this
work.
To avoid destruction of hydrogen iodide in the injection
device, both lines and Tylan flow controllers were passivated
for several hours before the experiment ran. In addition,
when DI was used, deuterated water vapor D2O was flushed
through the lines to reduce isotopic transfer between ad-
sorbed water and DI.
Concerning the measurement of the attachment rate, the
CRESU technique has been described extensively else-
where13 and details concerning attachment measurements
can be found in a seminal paper.14 In this paper, only the
essential features and details specific to the present measure-
ments will be given. The apparatus is represented in Fig. 1.
The isentropic expansion of a buffer gas ͑mainly nitrogen for
electron attachment experiments͒ through a Laval nozzle
generates a uniform supersonic jet at very low temperature,
which is used as a flow reactor. For electron attachment stud-
ies, a weakly ionized plasma (108 –109 ions cmϪ3) is created
by a crossed beam of energetic electrons ͑12 keV, 10 ␮A͒.
where eϪ and eϪ are, respectively, the electron density
at a distance x, and at a position situated upstream and taken
͓
͔
͓
͔
0
as the origin. is the velocity of the flow, ͓A͔ the attaching
v
gas density, and ␤ the attachment rate coefficient. The value
of ␤ is obtained from the measurements by plotting the elec-
tron density as a function of ͓A͔ for different x values.
III. EXPERIMENTAL RESULTS
A. Rate coefficients
The rate coefficients obtained in the present work are
related to the dissociative attachment reaction HI(DI)ϩe
→H(D)ϩIϪ and are summarized in Table I and Figs. 2 and
3, together with numerical calculations. A rather large scat-
tering of the results is observed, which is presumably linked
to the line passivation, which makes the determination of the
HI ͑DI͒ flow rate within the experiment less precise. There-
fore the accuracy of the present measurements is somewhat
less than the usual Ϯ30%. The other experimental results are
obtained by FALP,17 threshold photoionization,22 and Ryd-
berg electron transfer.23
Our results concerning HI show apparently a good
agreement with the other studies, but it should be noted that
the conditions prevailing for each particular result are quite
different: the FALP is truly thermal at 300 K, in the threshold
photoionization method22 only the electron energy is varied
as the neutrals are kept at room temperature, and in the Ry-
dberg electron transfer method, the authors gather informa-
tion on the influence of electron energy on jet cooled HI in
low-lying rotational states.
Results on DI have been obtained experimentally with
the threshold photoionization method22 and theoretically.24
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J. Chem. Phys., Vol. 121, No. 3, 15 July 2004
Electron attachment on HI and DI
1305
TABLE I. Flow parameters ͑temperature, gas density, and hydrodynamic time͒ and measured rate coefficients
for electron attachment on HI and DI.
Measured rate coefficient
͑cm3 sϪ1
Flow
temperature
͒
Gas density
Hydrodynamic
time ͑␮s͒
Buffer gas
͑K͒
(1016 cmϪ3
)
HI
DI
N2
N2
N2
N2
N2
N2
169.7
145.4
84.6
74.5
71.5
47.7
0.572
9.23
1.66
1.67
5.79
2.74
980
412
167
190
762
700
2.38ϫ10Ϫ7
2.04ϫ10Ϫ7
4.94ϫ10Ϫ7
3.28ϫ10Ϫ7
3.05ϫ10Ϫ7
2.46ϫ10Ϫ7
3.06ϫ10Ϫ7
2.03ϫ10Ϫ7
3.40ϫ10Ϫ7
3.60ϫ10Ϫ7
2.26ϫ10Ϫ7
4.42ϫ10Ϫ7
Among the hydrogen halides HI is unique in that the
electron affinity25 of I ͑3.059 eV͒ is greater than the disso-
ciation energy26 of HI ͑3.054 eV͒. Both the electron affinity
and the dissociation energy have been determined by spec-
troscopic methods of great accuracy. As a consequence, dis-
sociative electron attachment is exothermic by 0.005 eV. All
experimental results agree to show that electron attachment
is then extremely fast under a variety of conditions and close
to the capture limit (kcapϭ2.6ϫ10Ϫ7 cm3 sϪ1 at 300 K͒.
Concerning DI, zero point energy considerations27 show that
the same process is endothermic. The endoergicity is ⌬H
ϭ0.035 eV for the ground rovibrational state of DI, and the
reaction becomes exoergic for Jу8. A very strong tempera-
ture dependence is therefore expected for the rate coefficient
under conditions of thermal ͑thermodynamic͒ equilibrium,
just as for reactions with an activation barrier on the reaction
path leading from the reagents to products.28
culations are the following: let EJ be the energy of the J
rotational level relative to the ground vibrational state, and
nJ /n its relative ͑Boltzmann͒ population at temperature T.
Dissociative electron attachment on hydrogen halides can be
considered as acidobasic reactions, as a proton is transferred
to the electron. These reactions usually have no activation
barrier, and hence a positive temperature dependence is as-
cribed to the endothermicity of the reaction. If EJ is greater
than the endothermicity ⌬H, then the reaction is exoergic
and proceeds at the capture rate ␤cap(J,T). When this energy
is lower, the attachment rate for level J follows an Arrhenius
law where ␤cap(J,T) is the preexponential factor, and the
energy gap ⌬HϪEJ , the energy barrier
⌬HϪEJ
␤ J,T͒ϭ␤ J,T͒exp Ϫ
for JϽ8,
͑2͒
͑3͒
͑
͑
ͩ
ͪ
cap
kT
␤ J,T͒ϭ␤ J,T͒ for Jу9.
͑
͑
cap
A capture rate coefficient is usually appropriate for a
reaction without activation barrier. This condition is fulfilled
here, as the reaction does not proceed through an activation
complex. In the case of a reaction between a charged species
and a neutral molecule without dipole moment, the capture
rate is not dependent on the rotational state or on the tem-
perature and is called the Langevin rate. When the neutral
molecule has a dipole moment, it is known that the reaction
B. Numerical simulation of the expected attachment
rate on DI
The goal of the simulation is to predict the variation of
the rate constant according to the temperature. The spacing
of the vibrational levels of DI is such (␻ϭ2309.5 cmϪ1
)
that only the ground vibrational state is populated under our
experimental conditions.29 The hypotheses made for the cal-
FIG. 2. Rate coefficient for dissociative attachment for HI, vs neutral tem-
perature for CRESU measurements ͑᭹͒, FALP ͑᭡͒, and Rydberg electron
transfer ͑᭿͒ for nϾ23. The curve represents the expected rate constant for
FIG. 3. Rate coefficient for dissociative attachment for DI vs neutral tem-
perature for CRESU measurements ͑᭹͒, and Kr photoionization method
TeϭTneutral
.
͑᭡͒. The curve represents the expected rate constant for TeϭTneutral .
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1306
J. Chem. Phys., Vol. 121, No. 3, 15 July 2004
Goulay et al.
keelastic
N
͔
2
rate increases when the temperature decreases, and that the
capture rates for the individual J states, k(J), increase when
J decreases.30,31 In this paper, the individual ␤cap(J,T) have
been calculated by adapting the results of Clary et al.31 to the
reaction DIϩe. The calculations have been performed with a
polarizability ␣ϭ6.85 Å, a dipole moment ␮Dϭ0.42 D and
a rotational constant Bϭ3.30 cmϪ1 for the DI molecule. The
thermal attachment rate is then obtained by
͓
dEe
dt
3
2
Eeelasticϭ
˙
ϭ2 e m
͓ ͔
kB TϪT ͒.
͑
e
ͯ
e
mN
elastic
2
͑6͒
͓e͔, ͓N2͔, me , mN are the electron ͑nitrogen͒ density and
2
mass, kB is the Boltzmann constant, and T the flow tempera-
ture. keelastic is the momentum transfer rate constant and is
given by34
8
4␲me
3kBTe
fe
nJ
n
⌬HϪEJ
M
v5e ve
keelastic
ϭ
␴
d
,
͑7͒
͵
e-N
␤ T͒ϭ
͑
␤
J,T͒exp Ϫ
͑
ͩ
ͪ
2
͚
cap
e
͓ ͔
kT
Jϭ0
M
e-N
where ␴
is the momentum transfer cross section,
the
ve
2
nJ
n
ϩ
␤
J,T͒.
͑4͒
͑
cap
electron velocity, and fe the Maxwell-Boltzmann electron
velocity distribution function. The present calculation has
been performed with the momentum transfer cross section
value of Engelhart et al.34,35 Equation ͑6͒ can also be written
as
͚
Jу9
These assumptions appear to be reasonable since the experi-
mental results from the other authors22,23 concerning HI
show that attachment occurs at the capture rate for all rota-
tional states.
1
elastic
e
3
2
Eeelasticϭ
e k TϪT ͒,
͓ ͔
͑8͒
˙
͑
B
e
The numerical evaluation of the rate constant is in good
agreement with the attachment rate obtained by Alajajian and
Chutjiian,22 for room temperature DI. At lower temperatures,
the expected attachment rate is up to two orders of magni-
tude lower than the values measured in the CRESU. This is
not due to a hypothetic exoergicity of the attachment reac-
tion, even for the lowest rotational levels, as the thermo-
chemistry data for this reaction are known with a good
accuracy.25,26 A possible conclusion is that the electrons are
not in complete thermal equilibrium with the neutrals in the
CRESU experiment. This will be discussed in the following
section.
␶
where 1/␶elasticϭ2keelastic N (m /m
)
N
2
is the relaxation
͓
͔
2
e
e
time. To simplify the evaluation of the vibrational relaxation
term, we shall assume that only the vibrational levels ϭ0
v
and ϭ1 of N are populated. Let k
(k1→0) be the rate
v
2
0→1
coefficients for excitation ͑deexcitation͒ according to the re-
action
N
2
ϭ0͒ϩeϪ→N ϭ1͒ϩeϪ.
͑v
If one assumes that the vibrational energy is converted into
electron kinetic energy only,
͑v
2
dEe
Eveibrationϭ
˙
ϭkB␪
vibration
k
N
͓
2
ϭ1͒ e
͑v ͔͓ ͔
͕
ͯ
v
1→0
dt
IV. ELECTRON TEMPERATURE MODEL
Ϫk0→1
N
2
ϭ0͒ e
͔͓ ͔
͖
͑9͒
͓
͑v
The only possible fast process for electron heating con-
sists in superelastic collisions with excited vibrational states
of N2 , since electric field heating has been excluded.21 The
electron energy Ee then follows a relaxation equation
and ␪vϭ3395 K for nitrogen atoms.29
Knowing the vibrational excitation cross section,35 the
excitation rate coefficient k0→1 can be calculated for a
Maxwell-Boltzmann distribution and the deexcitation coeffi-
cient k1→0 is then obtained from detailed balance.
Then
dEe
elastic
vibration
rotation
˙
˙
˙
ϭEe ϩEe
ϩEe
,
͑5͒
dt
EveibrationϭkB␪ e k
͓ ͔
N eϪ͑hc/k
͒
͑⌬G/T
͒
v
˙
B
elastic
vibration
rotation
͓ ͔
2
˙
˙
˙
v
1→0
͑hc/k ͒⌬G͓͑1/T ͒Ϫ͑1/T ͔͒
where Ee
, Ee
and Ee
are respectively the elas-
tic, vibrational, and rotational contributions of N2 molecules
to the energy transfer.
B
e
v
ϫ 1Ϫe
͑
͒,
͑10͒
where Tv is vibrational temperature, h the Planck constant, c
It is also assumed that the electron velocity distribution
is of Maxwell-Boltzmann type, i.e., an electron temperature
Te can be defined, due to fast relaxation in electron/electron
collisions. Owing to the very large Coulombic cross section,
29
the celerity of light, and ⌬Gϭ2330.7 cmϪ1
.
The rotational term of Eq. ͑5͒ is evaluated in the same
way except that now the whole manifold of rotational states
has to be considered (0рJр20).36 The cross sections for
rotational excitation and deexcitation are taken from Gerjuoy
and Stein,37 from which the rate coefficients for the direct
process
even with the plasma cutoff, this is
a reasonable
assumption32 as long as electron energy is not too high. This
is the case in the present CRESU experiment since previous
work15 with other monomers of hydrogen halides ͑HCl and
HBr͒ has shown that the attachment rate coefficient was too
low to be measured at 170 K. As the attachment on HBr is
endothermic by 0.4 eV, this result shows that the electron
energy is not greater than 0.4 eV in the attachment zone.
The elastic term can then be evaluated33 as
N J͒ϩeϪ→N Jϩ2͒ϩeϪ
͑
͑
2
2
and the reverse process can be evaluated.
The heating/cooling term in electron energy equation is
such that
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J. Chem. Phys., Vol. 121, No. 3, 15 July 2004
Electron attachment on HI and DI
1307
TABLE II. Thermalization delay for electrons in nitrogen at 169.70 K.
Temperature of the
buffer (N2)
Vibrational temperature
of N2
Initial temperature of the
electrons
T ͑K͒
Tv ͑K͒
Te0 ͑K͒
169.70 169.70 169.70
300
620a
0.56
300
1000
0.56
1500
1000
0.56
Density of N2
N
(1016 cmϪ3
)
͓
͔
2
Steady state value of the
temperature of the
electrons
Tϱ ͑K͒
169.72 169.72 572.66
Relaxation timeb
Relaxation timec
Hydrodynamic time
␶ ͑␮s͒
␶ ͑␮s͒
81.40
¯
97.90 219.40
75
¯
␶
͑␮s͒
980
980
980
hyd
aInitial temperature of photoelectrons produced by the ionization of tri-
methylamine at 153 nm.
bPresent work.
FIG. 4. Electron temperature evolution vs time. The vibrational temperature
is 300 K, the neutral temperature is 74.5 K. The electrons have an initial
temperature of 1000 K.
cReference 36.
V. DISCUSSION
The calculated electron relaxation times are small com-
pared to the hydrodynamic time, and the electron tempera-
ture reaches a steady state in the CRESU experiment. The
experimental results for electron attachment on DI, however,
cannot be explained if one does not assume that the electron
temperature is higher that the neutral one. This may be ex-
plained by vibrational excitation of nitrogen.
dEe
Ereotationϭ
˙
ͯ
dt
rotation
hc 2Jϩ1͒B
͑
ϭ e N k
͓ ͔͓
␪ k
J
͔
͚
2
B
J→Jϩ2 kB
T
J
ϫeϪ͑hc/k
1ϪeϪ␪ ͓͑1/T͒
͓͒BJ͑Jϩ1͒/T͔
͑1/T ͔͒
e
B
J
͓
͔
The vibrational states have very long relaxation times
toward equilibrium, and it is thus expected that as the reser-
͑11͒
voir of the nozzle is kept at room temperature, the ϭ1 state
v
with Bϭ2.010 cmϪ1 and ␪Jϭ(hc/kB)B(4Jϩ6) in K.29
Therefore the electron temperature evolves according to
the equation
of N2 is populated, even in the cold supersonic flow. In such
conditions, however, the calculations presented in Table II
show that electron temperature converges rapidly toward the
neutral temperature. If the vibrational temperature of N2 is
higher than 300 K, convergence occurs, but toward a value
that is higher than the neutral temperature. This could happen
if the vibrational states of nitrogen were excited, for instance,
by the electron beam source. This problem cannot be solved
by choosing helium as buffer gas, as metastable helium at-
oms are produced by the beam. These metastable atoms can
be destroyed by adding some argon to the flow, but this
quenching reaction forms metastable argon atoms, which un-
dTe
dt
1
2
͒Ϫ͑⌬G/T
͒
v
ϭϪ TϪT ͒ϩ ␪vk1→0 N eϪ͑hc/k
B
͑
͓
͔
2
e
␶
3
͒⌬G͓͑1/T ͒Ϫ͑1/T ͔͒
ϫ 1ϪeϪ͑hc/k
B
e
V
͓
͔
2
hc B
Ϫ
␪ k
J
N
2
2Jϩ1͒
͑
͓
͔
͚
J→Jϩ2
3
kB T
J
͓͒BJ͑Jϩ1͒/T͔
ϫeϪ͑hc/k
1ϪeϪ␪ ͓͑1/T͒Ϫ͑1/T ͔͒
.
͔
͑12͒
B
J
e
͓
TABLE III. Thermalization delay for electrons in nitrogen at 74.5 K.
The function Te versus time was obtained for various initial
conditions using Matlab procedures. The steady state limit
Tϱ of electron temperature was calculated by setting the
right hand side of Eq. ͑12͒ to zero, and it has been verified
that it was indeed the asymptotic limit of the former function
Te(t). Like Mozumder,38 we define the relaxation time ␶
toward the steady state with the criterion 0.99TϱϽTe(␶)
Ͻ1.01Tϱ .
Temperature of the
buffer (N2)
Vibrational temperature
of N2
Initial temperature of the
electrons
T ͑K͒
Tv ͑K͒
Te0 ͑K͒
74.50
300
74.50
300
74.50
2000
1000
620a
1000
N
(1016 cmϪ3
)
Tϱ ͑K͒
Density of N2
1.67
74.5
1.67
74.5
1.67
1040
͓
͔
2
Steady state value of the
temperature of the
electrons
In Fig. 4, a typical electron temperature evolution is rep-
resented. Vibrational temperature Tv is linked to the relative
Relaxation timeb
Relaxation timec
Hydrodynamic time
␶ ͑␮s͒
␶ ͑␮s͒
27.0
¯
30.7
25
190
12.5
¯
population of the ϭ1 state since other states have not been
v
considered. The electron temperature obviously reaches a
steady value in a short time. Tables II and III summarize the
results obtained together with an estimation of relaxation
time by previous authors for some initial conditions.36 The
agreement is good.
␶
͑␮s͒
190
190
hyd
aInitial temperature for photoelectrons produced by the ionization of tri-
methylamine at 153 nm.
bPresent work.
cReference 36.
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1308
J. Chem. Phys., Vol. 121, No. 3, 15 July 2004
Goulay et al.
dergo superelastic collisions with electrons too. The work
performed with HBr ͑Ref. 15͒ together with the present work
show that electron temperature ranges between the neutral
temperature and 500 K. Buffer gas excitation will be avoided
in the future by the use of a photoionization laser source.
What are the consequences of the above finding on pre-
vious published works on electron attachment performed
with the CRESU experiment? In fact, several of the pub-
lished results highlight the strong effect of the cooling of the
internal states of the neutral molecules14 or of the presence of
neutral dimers and higher oligomers15 within the flow. These
conclusions are still valid. Conclusions drawn on the electron
temperature dependence have, however, to be invalidated in
these previous studies, namely: electron attachment on
anthracene39 and methyl iodide.19 In this latter case, the dis-
crepancy between our results and those of Schramm et al.20
is explained.
There is still a great interest in developing the CRESU
method for electron attachment. This technique allows one to
cool the neutral molecules down to very low temperatures in
conditions of true thermodynamic equilibrium. This is espe-
cially interesting for highly condensable species, like poly-
cyclic aromatic hydrocarbons, which represent an important
issue for interstellar chemistry and for which we have re-
cently built a dedicated chamber with heated reservoir and
nozzle. Our plan is to use photoionization by laser, recently
bought for this purpose, in order to create electrons without
exciting the nitrogen buffer. Near threshold photoionization
of trimethylamine by an excimer laser at 157 nm will pro-
duce electrons with an excess of energy well below the ex-
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