Electron and anion mobility in low density hydrogen cyanide gas. I. Dipole-bound electron ground states

Article abstract of DOI:10.1063/1.476969

We measured the mobility of excess electrons in the polar hydrogen cyanide gas (D=2.985 D) at low densities as a function of density and temperature by the so-called pulsed Townsend method. Experiments were performed at 294 and 333 K in the gas number density range 1.23×10¹⁷≤n≤3.61×10¹⁸ cm^-3. We found a strong density dependence of the zero-field density-normalized mobility (μn). Only about 10% of the observed density variation can be qualitatively explained by coherent and incoherent multiple scattering effects. With increasing gas density an increasing number of linear HCN dimers is formed which due to the high dipole moment (D=6.552 D) represent much stronger electron scatterers than the HCN monomers. It was found that the dimers may be only in part responsible for the observed density effect. Therefore, we consider a transport process where short-lived dipole-bound electron ground states (lifetime ≥12 ps) as quasilocalized states are involved. For comparison the electron mobility in saturated 2-aminoethanol vapor with a dipole moment of similar size (D=3.05 D) does not show any anomalous density behavior in the temperature range 298≤T≤435 K. In contrast to this the electron mobility in saturated but also in nonsaturated CH₃CN gas (D=3.925 D) shows a density behavior similar to that in HCN.

Full text of DOI:10.1063/1.476969

Electron and anion mobility in low density hydrogen cyanide gas. I. Dipole-bound
electron ground states
Th. Klahn and P. Krebs
Citation: The Journal of Chemical Physics 109, 531 (1998); doi: 10.1063/1.476969
View online: http://dx.doi.org/10.1063/1.476969
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 109, NUMBER 2
8 JULY 1998
Electron and anion mobility in low density hydrogen cyanide gas.
I. Dipole-bound electron ground states
a)
Th. Klahn and P. Krebs
Institut f u¨ r Physikalische Chemie und Elektrochemie, Lehrstuhl f u¨ r molekulare physikalische Chemie,
Universit a¨ t Karlsruhe, Kaiserstrasse 12, D-76128 Karlsruhe, Federal Republic of Germany
͑
Received 3 September 1997; accepted 31 March 1998͒
We measured the mobility of excess electrons in the polar hydrogen cyanide gas (Dϭ2.985 D͒ at
low densities as a function of density and temperature by the so-called pulsed Townsend method.
17
Experiments were performed at 294 and 333 K in the gas number density range 1.23ϫ10 рn
р3.61ϫ1018 cm . We found a strong density dependence of the ‘‘zero-field’’ density-normalized
mobility (␮n). Only about 10% of the observed density variation can be qualitatively explained by
coherent and incoherent multiple scattering effects. With increasing gas density an increasing
number of linear HCN dimers is formed which due to the high dipole moment (Dϭ6.552 D͒
represent much stronger electron scatterers than the HCN monomers. It was found that the dimers
may be only in part responsible for the observed density effect. Therefore, we consider a transport
process where short-lived dipole-bound electron ground states ͑lifetime у12 ps͒ as quasilocalized
states are involved. For comparison the electron mobility in saturated 2-aminoethanol vapor with a
dipole moment of similar size (Dϭ3.05 D͒ does not show any anomalous density behavior in the
temperature range 298рTр435 K. In contrast to this the electron mobility in saturated but also in
Ϫ3
nonsaturated CH CN gas (Dϭ3.925 D͒ shows a density behavior similar to that in HCN. © 1998
3
American Institute of Physics. ͓S0021-9606͑98͒01626-2͔
I. INTRODUCTION
molecular systems has a rather strong effect on the critical
binding properties of polar molecules: The number of bound
states of the electron in the dipolar field of a molecule with
Slow electrons drifting under the influence of an external
electric field E in polar gases undergo strong scattering due
to the long-range anisotropic electron/electric dipole
DϾD is reduced to a finite number as it was shown by
c
7
1
Garrett. However, the minimum dipole moment necessary
interaction. For polar gases with a dipole moment DϷ3 D
to support at least one bound state is increased by 10% to
the number density n at which the de Broglie wavelength
3
0% in comparison with that of a dipole fixed in space. In
just exceeds the mean free path of the electron is low, i.e., in
the order of some 1019 cmϪ3 at Tϭ300 K. Therefore, mul-
this case D depends on the effective dipole length, the ro-
c
tational state, and the moments of inertia of the polar
tiple scattering has to be considered already at much lower
densities. In addition, it cannot be excluded at all that the
electron is temporarily or permanently captured by the dipole
molecules forming molecular negative ions. The probability
of such a process increases with n. Therefore, the electron
mobility in polar gases may show a large dependence on n
and T at such low gas densities.
molecules.8
The binding energies of dipole-bound electron states
may be extremely small at least in cases where the dipole
moment is near the critical value. Thus one could expect that
the formation of the dipole-supported anion might be diffi-
cult to observe since the very diffuse and weakly bound elec-
tron would be subject to stripping by thermal collisional pro-
cesses within a gas sample and/or by the electric fields to
which they are subjected in the process of mass analysis or in
Molecular negative ions formed by electron addition to
closed shell neutral molecules are frequently unstable rela-
tive to autodetachment. However, if the electric dipole mo-
ment of the molecule is sufficiently large then an electron
may be captured in the electrostatic dipole field of the mol-
ecule to form a so-called dipole-bound anion. It were Fermi
drift mobility measurements. For example, such a dipole-
Ϫ
bound anion in water, i.e., (H O)2 was prepared by Haber-
2
land and co-workers in a beam experiment and detected by
2
9
and Teller who first established the critical permanent elec-
mass spectroscopy. The vertical detachment energy of the
tric dipole moment D ϭ1.625 D required to bind an elec-
c
water dimer anion of 42 meV was determined by photoelec-
3
4
tron experiments by Bowen and co-workers.10
tron. Crawford and Delgarno, Crawford and Garrett, and
5
Garrett have shown that the electric dipole field of a station-
We are concerned with the electron transport processes
in polar gases, especially in the transition from the quasifree
to the localized electron state. In the past we have performed
extensive electron mobility measurements in sub- and super-
ary molecule can bind an electron in an infinite number of
bound states if D is greater than D . The electron exists in
c
6
an extensive orbital, described by a diffuse wave function.
The consideration of rotational degrees of freedom in real
11,12
12,13
critical NH3
and in subcritical H O
gas as a function
2
of gas density and temperature up to very high densities in
order to study this transition in a disordered medium of di-
a͒Author to whom correspondence should be addressed.
0021-9606/98/109(2)/531/12/$15.00
531
© 1998 American Institute of Physics
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1

532
J. Chem. Phys., Vol. 109, No. 2, 8 July 1998
Th. Klahn and P. Krebs
pole scatterers. We continued these studies on electrons in
1
4–16
sub- and supercritical CH OH gas
and in subcritical
3
1
7
CH CN gas also at much lower densities to study different
3
multiple scattering effects on the electron mobility. From
preliminary and not very accurate results on the electron mo-
bility in low density saturated CH CN vapor (Dϭ3.925 D͒
3
we suggested that we have found dipole-bound electron
ground states in thermal equilibrium ͑we prefer to use the
Ϫ
Ϫ
formula ͓e ¯CH CN͔ instead of CH CN to point out the
3
3
weakly bound electron͒ which are involved in the transport
process. In the meantime we have performed electron mo-
1
4
bility measurements in low density CH CN gas with much
3
higher accuracy which besides multiple scattering effects
demonstrate the existence of short-lived dipole-bound elec-
tron states with a mean lifetime of about 20 ps (303рT
р343 K͒ as precursors of the localized electron states.18 This
result is supported by recent beam experiments performed by
FIG. 1. Swarm drift velocity vd as a function of the electric field strength E
1
8
Ϫ3
for electrons in low density HCN gas (Tϭ294 K, nϭ1.73ϫ10
cm ).
19
The insets show the recorded electron current waveforms for different elec-
tric field strengths signed by the arrows. A part of the electrons is captured
during the drift by HCN forming anions. The dashed line demonstrates the
linear relationship between vd and E at low electric field strength.
Schermann and coworkers
showing that Compton’s
2
0
method
for the production of dipole-supported
Ϫ
͓
e ¯CH CN͔ could be used as a general way to get ground
3
state dipole-bound anions. With this method electrons are
attached to closed shell polar molecules from laser-excited
Rydberg atoms. Subsequently, Schermann and co-workers
event approximation. Finally, we consider an effective elec-
tron localization process involving the dipole-bound state to
take part in the electron transport. A summary is given in
Sec. IV.
field detached the dipole-bound electron from the produced
Ϫ
anion ͓e ¯CH CN͔ to ensure that it possessed in fact a
3
weakly bound diffuse electron as expected for the dipole-
bound species. Such it has become now possible to compare
qualitatively nonequilibrium results of beam experiments
with thermal equilibrium results of mobility measurements.
The dipole moment Dϭ2.985 D of HCN2 is much
II. EXPERIMENT
1
A. Pulsed Townsend method
smaller than that of CH CN but far above D . Therefore,
3
c
The pulsed Townsend method is a well-known and
widely used method to perform electron mobility measure-
ments. A constant potential difference U is applied between
two circular, plane, parallel electrodes of radius r, separated
HCN should form a dipole-bound electron state as predicted
6
theoretically by Garrett. Moreover, the influence of the
dipole-bound state should be more easily observed in elec-
tron mobility measurements in comparison with CH CN be-
3
by a distance d. A thin slice of n electrons is photoinjected
e
cause due to the lower dipole moment the contribution of
incoherent multiple scattering effects should be quite small.
from the cathode by means of a short UV laser pulse into the
medium under investigation. Under the influence of the ap-
plied electric field EϭU/d the swarm of about 10 to 10
5
7
However, in contrast to CH CN some complications are to
3
be expected due to orientational correlations among the HCN
molecules and/or due to HCN dimer formation. In a prelimi-
nary report we have given some hint to the formation of
dipole-bound electrons in low density HCN gas. In this
paper we present an extensive study of the mobility of elec-
trons in HCN gas. For comparison we present also results on
the electron mobility in 2-aminoethanol, a molecule with a
dipole moment similar to that of HCN but with larger mo-
ments of inertia.
electrons drifts to the anode with the drift velocity v giving
d
rise to an induced current iϭϪen v /d through a load re-
e
d
sistor R , if dӶr. If electron attachment to the gas mol-
L
22
ecules can be neglected, ne and vd are constant. In this
simple case the ͑constant͒ current drops to zero when all the
electrons are collected by the anode. With the experimentally
observed electron current pulse duration t one obtains the
d
drift velocity v ϭd/t . From the experimental linear rela-
d
d
tionship between v and E, the mobility ␮ is determined
d
In Sec. II we will give a description of our experiments.
The experimental results are presented and discussed in Sec.
III. There, we analyze the electron mobility observed in low
density HCN gas according to Polischuk’s theoretical calcu-
from ␮ϭv /E in the limit of zero field ͑see Fig. 1͒. In Fig.
d
2 we show the schematics of the experimental set-up for the
electron and ion mobility measurements in HCN gas. For the
electron mobility measurements in low density HCN gas we
have developed a new drift cell ͑see Fig. 3͒. This drift cell is
made out of Duran glass with quartz windows, and an elec-
trode assembly made out of stainless steel. The distance d
between the photocathode and the anode can be varied be-
tween 0.10 and 0.65Ϯ0.01 cm. This cell withstands pres-
sures up to 40 bar for temperatures Tр400 K. Different
pressure sensors ͑Hottinger Baldwin͒ can be coupled to the
drift cell to measure the gas pressure in the drift space with a
lations on quantum multiple scattering corrections to the mo-
bility of the electrons.2
3,24
It will be demonstrated, at least
qualitatively, that due to the real behavior of the dipolar gas
correlations in positions between the dipole molecules can-
not be neglected. These effects, however, do not describe the
observed density variation of the electron mobility. There-
fore, we estimate also the influence of HCN dimers in the
drift gas on the electron mobility in the single scattering
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J. Chem. Phys., Vol. 109, No. 2, 8 July 1998
Th. Klahn and P. Krebs
533
stepwise improved in our laboratory. In the beginning about
4 g KCN were dried and degassed at 373 K at a vacuum
2
Ϫ6
line ͑better than 10 mbar͒. After KCN was cooled down to
7 K about 10 ml of fourfold distilled water were condensed
7
on KCN. To avoid an undesired hydrolysis the KCN/water
mixture was kept frozen until starting the synthesis. Subse-
quently, 30 ml of an aqueous solution of H SO ͑50 mass %͒
2
4
were prepared in a dropping funnel and were gently bubbled
with nitrogen ͑Messer Griesheim, 5.0͒ for at least 30 min to
remove O and other gases. Finally, the sulfuric acid was
2
evacuated down to its own vapor pressure. Then the sulfuric
acid was dropped on the stirred KCN/water mixture at 283
K. Starting at about 12 mbar ͑water vapor pressure͒ the va-
por pressure increases due to the production of HCN gas. At
about 100 to 200 mbar a valve was opened and HCN ͑under
constant pressure conditions͒ was condensed in a trap cooled
down to 77 K. Drying of the raw HCN was performed by
trap-to-trap-sublimation at the vacuum line. Each trap was
FIG. 2. Schematics of the apparatus for the pulsed photoinjection swarm
experiments: Drift cell ͑see Fig. 3͒; P-TRANSD, different pressure trans-
ducers ͑Hottinger Baldwin͒; T-SENS, different temperature sensors; AMP
ϩDVM, amplifier and digital voltmeters; HVPS, high-voltage dc power
supply, Keithley Instruments 246; R , load resistor; FAMP, fast amplifier
L
27
͑homebuilt͒; Nd:YAG laser, J.K. Lasers, System 2000; PD, photodiode for
filled with freshly prepared P O . Thereafter, P O was
2 5 2 5
triggering; Transient Recorder, Iwatsu DM 901; PC, personal computer;
ADC, analog/digital converter ͑see the text͒.
added to hydrogen cyanide and it was refluxed for several
hours for further purification and drying. Finally, HCN was
fractionally distilled from the residues in a special glass ap-
paratus under a nitrogen atmosphere through a 30 cm Vi-
greux column. The middle fraction ͑about 30%͒ was col-
lected and kept in a reservoir attached to the vacuum line.
HCN was degassed by several ‘‘freeze–pump–thaw’’ cycles
and stored under its vapor pressure on twofold sublimated
maximum error of Ϯ0.6 mbar for the gas pressure range p
р200 mbar and of Ϯ2.5 mbar for p р 1 bar. The drift cell
is also provided with a reservoir for about 10 ml of the me-
dium under investigation.
B. Sample preparation25
P O . It is well-known that small traces of water in HCN
2 5
produce after some time brown and black condensates. How-
ever, hydrogen cyanide purified by our above mentioned
method does not change during months at room temperature.
1. Hydrogen cyanide
The production of HCN was performed according to a
method described in Ref. 26, however, the procedure was
2. 2-aminoethanol
C H NO was purified by us in the following manner:
2
7
2
-aminoethanol ͑Aldrich, 99%͒ was gently bubbled with ar-
gon ͑Messer Griesheim, 5.0͒; thereafter with a small amount
of KBH ͑Fluka͒ it was refluxed for at least 3 h under re-
4
duced pressure. Then it was fractionally distilled from the
residues through a 30 cm Vigreux column. The middle frac-
tion ͑about 30%͒ was collected and kept in a reservoir at-
tached to the vacuum line. The reservoir was protected
against irradiation of light.
3. Preparation of the sample in the drift cell
The drift cell was connected to the vacuum line in order
to fill its reservoir with the medium under investigation. In
the case of HCN the necessary amount of HCN was carefully
sublimated in the reservoir. During this process the tempera-
ture of the main storage vessel for HCN at the vacuum line
was held constant at 252 K. Before starting the mobility
measurements, HCN in the drift cell reservoir was again
FIG. 3. Drift cell ͑for gas pressures up to 40 bar for Tр400 K͒: 1, flange for
the connection to the vacuum line; 2, PTFE conical adapter for adjustment
of the drift cell in the steel tank; 3, quartz plate as optical window; 4, anode
covered with a light transparent stainless steel mesh; 5, PTFE-O-sealing; 6,
stainless steel flanges which hold together all the parts of the photocell; 7,
photocathode; 8, cell vessel made out of duran glass; 9, shielding against
electromagnetic irradiation; 10, PTFE centric adapter; 11, high vacuum
valve ͑Young͒; 12, flange for the pressure transducer; 13, reservoir for the
medium under investigation.
made free of electron scavengers such as O and CO by
2
2
several freeze–pump–thaw cycles. It should be pointed out
that all parts of the apparatus which came in contact with
HCN ͑or C H NO), in particular the drift cell, are cleaned
2
7
with several organic solvents and were finally rinsed with
overheated water vapor for at least 24 h.
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1

534
J. Chem. Phys., Vol. 109, No. 2, 8 July 1998
Th. Klahn and P. Krebs
At higher temperatures hydrogen cyanide shows autopo-
lymerisation: A black charcoal-like substance is produced
28
which is called ‘‘azulmin.’’ To avoid this effect we have
tested many inhibitors mentioned in the literature.29 Very
30
effective was only cobaltoxalate (CoC O •2H O, Aldrich͒.
2
4
2
Cobaltoxalate was ground and suspended in acetone ͑Merck,
p.a.͒. For the high temperature measurements the drift cell
was rinsed with this suspension. Then acetone was evapo-
rated at the vacuum line. A small amount of solid cobaltox-
alate was put also in the reservoir of the drift cell. Finally,
the drift cell was dried and baked at 473 K at the vacuum
line until there was formed a bluish colored coating on the
glass surface due to cobaltoxalate.
The filled drift cell was then transferred into a steel tank
filled with fine sand as a heat conducting medium. With an
electrical heating system with PID-controllers ͑Eurotherm͒
the chosen temperature in the cell could be held constant to
within Ϯ0.3 K. The temperature was measured by NiCr–Ni
thermocouples and by platinum thermoresistors Pt 100 which
were mounted on different positions at the drift cell. The gas
pressure in the drift cell could be adjusted by carefully open-
ing of a valve connected with the vacuum line or by con-
trolled filling of the drift cell. With the measured gas pres-
sure and temperature the number density n of HCN was
determined from the approximated virial equation of state
FIG. 4. Time dependent voltage wave forms of electrons in HCN gas as a
function of the gas number density: ͑a͒ nϭ1.70ϫ10 cm , Tϭ294K,
18
Ϫ3
2
p
4pB͑T͒ 1/2 Ϫ1
2
Ϫ1
18
Ϫ3
Eϭ1.533ϫ10 V cm ; ͑b͒ nϭ2.70ϫ10 cm , Tϭ333 K, Eϭ2.757
nϷ
1ϩ
ͫ
1ϩ
ͬ
,
͑1͒
ͭ
ͮ
ϫ102 V cm
Ϫ1
͑c͒ nϭ3.90ϫ10 cmϪ3
18
k T
B
N k T
A B
;
,
Tϭ333 K, Eϭ6.126
ϫ102 V cm . The dashed lines in ͑b͒ and ͑c͒ are fitting time dependent
exponential functions demonstrating the electron capturing process ͓see Eq.
͑3͔͒.
Ϫ1
with the second virial coefficient B(T) taken from the
3
1
literature.
In the case of aminoethanol we have not found any virial
coefficients in the literature. Therefore, we have estimated
the density of the saturated vapor from the ideal gas equa-
tion. In the pressure range 0рpр1 bar we have determined
a maximum error of 5% to 10% at the boiling temperature
Typical electronic wave forms u(t) are shown in Fig. 4
for increasing HCN number densities n . If a short bunch of
n excess electrons is photoinjected in the drift space, the
0
e
(
Tbϭ444 K͒. At higher temperatures aminoethanol corrodes
stainless steel. To avoid any additional complications con-
cerning the drift cell and to avoid the damaging of the pres-
sure sensors we have performed measurements only in the
saturated vapor without this equipment. Therefore, the vapor
pressures at the measured temperatures ␪T in centigrades
were calculated from the Antoine equation
voltage drop u(t) decreases during the drift time. In the ideal
case it can be described by
0
ene
u͑t͒ϭϪRL
exp
Ϫt/␶e 0рtрtd
͕ ͖
td
B0
ϭ0 tϾtd ,
͑3͒
0
log pϭA Ϫ
,
͑2͒
0
C Ϫ␪T
0
0
0
with the parameters A , B , and C taken from the
literature.
where e is the elementary charge and ␶e is the mean lifetime
3
1
(1)
of the excess electrons in the low density HCN (k ϭ1/␶e is
eff
the rate constant of disappearance of the electrons͒. In spite
of the strong decay of u(t) with time at nϭ2.7
ϫ1018 cm the arrival of the electrons at the anode after
C. Signal wave forms
Ϫ3
As the UV light source we used the fourth harmonic of a
Nd:YAG laser ͑J.K. Lasers, System 2000: ␭ϭ266 nm, pulse
duration Ͻ20 ns, pulse energy Ͻ20 mJ͒. The induced pho-
tocurrent i(t) produces a voltage drop u(t) across the load
the time t can be still observed ͓see Fig. 4͑b͔͒. However, at
d
18
Ϫ3
number densities nϾ3.6ϫ10 cm
almost all the elec-
trons are captured by HCN during the drift time ͓see, e.g.,
Fig. 4͑c͔͒. This is observed for 294 K as well as for 333 K.
We have also tried to measure electron mobilities at T
ϭ373 K but under the present experimental conditions the
resistor R which is amplified by a fast home-built amplifier.
L
The output is fed to a transient recorder ͑Iwatsu DM 901,
7
5
ϫ10 samples/s͒ which is connected via an IEEE-488 bus
interface to a personal computer. Signal accumulation was
performed.
wave forms did not allow the determination of t due to the
fast reaction of the electrons.
d
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J. Chem. Phys., Vol. 109, No. 2, 8 July 1998
Th. Klahn and P. Krebs
535
FIG. 6. Electron and anion mobilities in gaseous HCN as a function of n
and T. Electron mobilities: ᭺, 294 K; ᭿, 333 K. Anion mobilities: ᮀ, 294
K; ᭹, 333 K; ᭝, 373 K. The dashed lines show the classical 1/n density
dependence.
(
1)
FIG. 5. ͑a͒ Rate constant k ͑of first order with respect to electrons͒ de-
eff
scribing the disappearance of the electrons during the drift as a function of
the HCN number density n for Tϭ333 K: ϫ, experiment; the dashed line
(
1)
2
demonstrates the proportionality k ϰn . ͑b͒ Rate constant for reaction ͑4͒,
eff
(1)
2
kϭk /n , as a function of n: ᭿, experiment; the dotted line shows the mean
eff
value of k.
B. Electron and anion mobility
The electron mobility ␮ has been measured in the gas
17
18
Ϫ3
density range 1.23ϫ10 рnр3.61ϫ10 cm for the tem-
peratures 294 and 333 K. To give a survey on the experi-
mental results of this investigation we present in Fig. 6 the
mobility isotherms of the electrons for 294 and 333 K to-
gether with those of the anions for 294, 333, and 373 K ͑see
also paper II of this publication series͒. Taking a first look on
the electron mobility isotherms in the logarithmic represen-
tation one notes a much stronger density dependence than the
classical 1/n behavior which was frequently assumed in the
past by condensed matter physicists for such low gas
densities.33 This effect is better visualized when the ‘‘zero-
field’’ density-normalized mobility (␮n) is shown as a func-
tion of n in a linear representation ͑Fig. 7͒. For comparison,
the classical behavior of the electron mobility is given for
Tϭ333 K by the horizontal dashed line. The overall experi-
mental uncertainties of (␮n) were estimated to be Ϯ5%.
Each mobility isotherm has been measured several times up
and down to show the reproducibility of these measurements.
It is generally noticed that the scatter of the very low density
data is relatively high ͑see also Fig. 7 with the maximum
calculated errors shown at some arbitrarily selected experi-
mental points͒. The origin for this is at present unknown.
The observed strong density variation of (␮n) will be
discussed in the following section according to Polischuk’s
theoretical calculations on quantum density corrections to the
mobility due to interference in multiple scattering and by
taking into account also the imperfect gas behavior.
III. RESULTS AND DISCUSSION
A. The kinetics of the reaction of electrons with HCN
We have analyzed the kinetics of the electron capturing
process by fitting of Eq. ͑3͒ to the experimentally observed
electronic wave forms. As can be seen from the fitting curves
in Figs. 4͑b͒ and 4͑c͒ the disappearance of the electrons can
be well described by an exponential function corresponding
to a reaction of first order with respect to the electrons, i.e.,
͑
1͒
k
eff
Ϫ
Ϫ
e ϩj HCN→A .
͑4͒
Ϫ
A
stands for some anionic species which is formed by the
reaction of the electrons. In this overall reaction j HCN mol-
ecules may participate in the formation of the unknown spe-
Ϫ
cies A . The rate constant determined by fitting of Eq. ͑3͒ to
the experimental induced current profiles depends on the
HCN gas density n. In Fig. 5͑a͒ we show k as a function of
n at 333 K. It follows from Figs. 5͑a͒ and 5͑b͒ that reaction
(
1)
eff
͑4͒ is second order with respect to HCN, i.e., jϭ2. Within
the margins of the experimental errors one obtains for the
(
1)
2
Ϫ32
6
Ϫ1
rate constant kϭk /n ϭ(8Ϯ2)ϫ10 cm s . For a fur-
eff
ther discussion of this result we refer to paper II of this
3
2
publication series.
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536
J. Chem. Phys., Vol. 109, No. 2, 8 July 1998
Th. Klahn and P. Krebs
FIG. 7. Density-normalized mobilities (␮n) of excess electrons in HCN gas
as a function of number density n for 294 and 333 K. The solid lines are for
the present guides for the eyes ͑see the text͒. The dashed line represents the
classical result for 333 K. The error bars show the maximum calculated
errors.
C. Multiple scattering corrections
The zero-field density-normalized mobility (␮n) of mul-
tiple scattered electrons in an imperfect polar gas is given
1
5,16
by
FIG. 8. Density-normalized mobility (␮n) of electrons in HCN gas at 294
K ͑a͒, and 333 K ͑b͒ as a function of n in comparison with the results
considering multiple scattering effects: solid lines connecting the experi-
mental points have for the present no theoretical significance ͓they represent
ͱ
8
␲
av
͑
␮n͒Ϸ͑␮ n͒
ͭ
1Ϫ
͗ ͘
͑0.5␲Ϫ0.6͒⑄T ␴ ͑␧͒ n
m
L
exp
2
B͑T͒
functions like (␮n)0 /(1ϩconst. n)]; the dashed lines represent the classical
ϩ
n . . .
ͮ
,
͑5͒
result; the dashed-dotted lines show the density correction due to interfer-
ence in multiple scattering ͓first correction term in Eq. ͑5͔͒; the dotted lines
take into account additionally coherent multiple scattering effects due to the
imperfect gas ͓complete Eq. ͑5͔͒.
NA
where (␮ n) is the classical density-normalized mobility in
L
the single collision approximation ͓Lorentz limit: see, e.g.,
Eq. ͑2͒ in Ref. 1͔. (␮ n) does not depend on the gas density.
The first density correction on the right-hand side of Eq. ͑5͒
L
where (␮n)0 is the experimental zero-field density-
normalized mobility in the limit of n→0. In this case (␮ n)
is due to quantum interference in multiple scattering which
L
has been calculated by Polischuk.2
3,24
This term is valid only
in Eq. ͑5͒ has to be replaced consequently by (␮n) .
0
To compare the experimental results in HCN gas with
theory we display in Fig. 8 the zero-field density-normalized
mobility (␮n) vs n for Tϭ294 K and Tϭ333 K. The dashed
at sufficiently low gas densities where the de Broglie wave-
1/2
length ⑄ ϭប/(2m k T) of the thermal electrons is much
T
e B
av
av
smaller than their mean free path Lϭ1/
͗ ͘ ͗ ͘
␴ (␧) n. ␴ (␧)
m m
exp
lines represent the classical result. To obtain (␮n)0 we
is the thermal average of the theoretical momentum transfer
av
m
2
have fitted the experimental points by a hyperbolic function
cross section, ␴ (␧)ϭ(4␲/3)(De/ប) m /␧, for dipole
e
exp
of the type (␮n)0 /(1ϩconst. n) ͑the theoretical justification
molecules in the point-dipole limit averaged over the dipole
2
for this follows in Sec. III E͒. This was done also in Fig. 7.
orientations (␧ϭ(បk) /2m is the kinetic energy of the
electron͒
e
3
4
The thermal averaged experimental scattering cross sections
av
exp
2
av
exp
are
͗
␴ (␧)
͘
ϭ2670Ϯ127Å (Tϭ294 K͒ and
͗
␴ (␧)
͘
m
m
av
theor
2
2
͗
␴ ͑␧͒
͘
ϭAm /k T with Aϭ͑8␲/3͒͑De/ប͒ .
͑6͒
ϭ2341Ϯ135 Å (Tϭ333 K͒ which are distinctly smaller
than the corresponding theoretical values
ϭ3473 Å and
m
e
B
av
theor
͗ ͘
␴ (␧)
m
2
av
theor
2
The second term in Eq. ͑5͒ is a coherent multiple scattering
correction due to positional correlations among the dipole
scatterers in an imperfect gas. B(T) is the second virial co-
͗
␴ (␧)
͘
ϭ3066Å obtained from Altshul-
m
er’s Eq. ͑6͒ ͑see also Fig. 9͒. With the experimental scatter-
ing cross section one can calculate the first correction term in
Eq. ͑5͒. The result ͑dash–dotted lines in Fig. 8͒ shows that
this is only a relatively small correction to the classical
3
Ϫ1
efficient in units of cm mol . Polischuk proposed to use in
Eq. ͑5͒ the thermally averaged experimental cross section
av
exp
͗
␴ (␧)
͘
obtained from measurements at very low
(␮n) . However, even at such low HCN gas densities of the
m
0
1
4,15
density
present investigation correlations between the scatterers can-
not be neglected.15 With the virial coefficients B(T) of Table
I one obtains from the complete Eq. ͑5͒ the dotted lines pre-
sented in Fig. 8. That means that both density corrections in
8
e
av
expϭ
͑2/␲mk T͒1/2͓͑␮n͒0͔Ϫ1,
͗
␴ ͑␧͒
͘
͑7͒
m
B
3
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J. Chem. Phys., Vol. 109, No. 2, 8 July 1998
Th. Klahn and P. Krebs
537
where p and x are the partial pressures and the mole frac-
i
i
tions of the monomers (M) and dimers (D), p is the sum
tot
0
of the partial pressures, and p ϭ1 bar. Higher oligomers
are neglected in the case when xM is replaced by (1Ϫx ).
D
Giauque and Ruehrwein calculated K from the compression
p
factor ZϭpV/nRT of HCN gas based on measurements of
Sinosaki and Hara.35 Giauque and Ruehrwein used for p Ͻ
0
.3 bar ͑where the measurements are not sufficiently accu-
rate͒ the virial approximation pVϷRT (1ϩBЈ(T)p); how-
ever, they employed the second virial coefficient of HCl
Ϫ1
[
BЈ(T )ϭϪ0.0056 bar , T ϭ298.8 K is the boiling tem-
b
b
perature of HCN at 1 bar͔. The equilibrium constant for the
dimer formation at Tϭ303 K was obtained to be Kp
ϭϪBЈ(303 K)p ϭ0.056. From the temperature depen-
0
dence of K they obtained the enthalpy of dimer formation
p
0
Ϫ1
FIG. 9. Thermal averaged momentum transfer cross sections of polar mol-
ecules with respect to electrons vs the reciprocal temperature: ᭹, HCN (T
ϭ294 and 333 K͒, this work; ϫ, aminoethanol, Hamilton and Stockdale
⌬
H ϭϪ13.73 kJ mol , as well as the corresponding en-
D
0
Ϫ1
Ϫ1
tropy change ⌬S ϭϪ69.04 J K mol . Neglecting the
D
formation of higher oligomers the mole fraction of the
͑Ref. 58͒; ٌ, aminoethanol, this work (Tϭ300 K, see below͒. The dashed
line shows a possible 1/T dependence of the experimental momentum trans-
fer cross section. The solid line represents the theoretical result of Altshuler
dimers, x , is a function of p , i.e.,
D
tot
p0
p0
2
1/2
¯
͑
Ref. 34͒ for DϷ3.0 D ͓Eq. ͑6͔͒.
xDϷ1ϩ
Ϫ
ͫ
ͩ
1ϩ
ͪ
Ϫ1
ͬ
. ͑10͒
2
K ͑T͒p
2K ͑T͒p
p
tot
p
tot
Hyde and Hornig39 were the first to show directly the exis-
Eq. ͑5͒ are by far not sufficient to describe the density varia-
tion of (␮n) in HCN. Concerning the orientational correla-
tions in HCN gas we present in the following thermody-
namic and spectroscopic evidence for significant formation
of linear HCN dimers and their influence on the electron
mobility.
tence of (HCN) by infrared measurements. Jones, Seel, and
2
Sheppard40 studied (HCN) by IR spectroscopy in the gas
2
phase in more detail. The monomers are chain-like coupled
caused by the large dipole moment of HCN and by a com-
paratively weak hydrogen bond interaction leading to an
equilibrium N¯C distance of the HCN dimer of r (N¯C)
0
ϭ3.34Ϯ0.20 Å. The standard enthalpy of formation was de-
D. The influence of HCN dimer formation on the
electron mobility
termined from the temperature dependent intensities of the
0
absorption bands of the monomer and dimer to be ⌬H
D
Ϫ1
ϭϪ(23.85Ϯ2.10)kJ mol ͑see Table II.͒. In a further IR
1. The formation and properties of HCN dimers
absorption study concerning (HCN) in the gas phase at 300
2
Based on PVT-measurements performed on HCN in the
41
K and a HCN gas pressure of up to 933 mbar Mettee tried
to verify spectroscopically the dimerization equilibrium con-
thirties and forties of this century dimers and higher oligo-
3
5–37
mers were postulated to exist in the gas phase.
Giauque
stant K of Giauque and Ruehrwein. From constant volume
3
8
p
and Ruehrwein determined from PVT-data the equilibrium
measurements between 298 and 356 K ͑for pу933 mbar͒
constant K for the dimerization reaction
0
D
p
they obtained the internal energy of dimerization ⌬U
K
p
Ϫ1
ϭϪ15.90Ϯ0.67kJ mol
and the corresponding dimeriza-
0
Ϫ1
2
HCN↔͑HCN͒2 .
͑8͒
͑9͒
tion enthalpy ⌬H ϭϪ(18.63Ϯ0.67)kJ mol and with
S of Ref. 38 finally K ͑revised͒ ϭ 0.40 for 303 K. The
D
D
0
⌬
The dimensionless equilibrium constant K is defined by
p
p
discrepancy between K ͑revised͒ ϭ 0.40 and K ͑Ref. 38͒
p
p
0
p0 xD
p0
pD /p
xD
ϭ 0.056 was explained by Mettee to be due to an overesti-
mate of the contributions of trimers and higher oligomers by
Giauque and Ruehrwein by fitting the former vapor density
data. HCN trimers have not been determined spectroscopi-
cally, neither by Jones et al. nor by Mettee. Using now the
dimerization enthalpy of Jones et al. and the corresponding
entropy term of Giauque and Ruehrwein one obtains for 300
K a much higher value for the equilibrium constant, i.e.,
K ϭ
ϭ
0 2
Ϸ
,
p
ptot ͑x ͒2 ptot ͑1Ϫx ͒2
͑
p /p ͒
M
M D
TABLE I. Zero-field density-normalized electron mobility (␮n) in HCN
0
av
exp
gas, scattering cross section
͗
␴ (␧)
͘
, and second virial coefficient B(T)
m
of HCN as a function of T ͑see the text͒.
av
exp
(
␮n) /
͗
␴ (⑀)
10
͘
/
B(T)/
cm mol
0
m
1021 cm
Ϫ1
V
Ϫ1
sϪ1a
Ϫ13
cm
2 b
3
Ϫ1c
T/K
K ϭ3.45. Of course, the strongly different dimerization
p
equilibrium constants of Mettee and Jones et al. lead to com-
pression factors which extremely differ from that of Giauque
and Ruehrwein.
2
3
94
33
2.10 Ϯ 0.10
2.25Ϯ0.13
2.670Ϯ0.127
2.341Ϯ0.135
Ϫ1584.25
Ϫ913.92
aThe errors are the maximum calculated errors determined by the method of
error propagation. The standard deviation of the density normalized mobili-
ties from the mean is р0.6%.
Calculated with Eq. ͑7͒.
Data from Ref. 31.
Concerning the structure and the dipole moment of
(
HCN) we can rely on numerous experimental and theoret-
2
42
b
ical investigations. Legon, Millen, and Mj o¨ berg have deter-
c
mined the rotational constant of the dimer in the gas phase
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1

538
J. Chem. Phys., Vol. 109, No. 2, 8 July 1998
Th. Klahn and P. Krebs
TABLE II. Summary of the properties of HCN dimers taken from the literature: Dipole moment DD , equilib-
rium constant of dimerization K , rotational constant B , enthalpy of dimerization ⌬H , and the equilibrium
p
0
D
bond length r ͑N¯C͒ of linear HCN dimers.
0
DD /D
Kpa
B0 /MHz
⌬HD /kJ molϪ1
r0(N¯C)/Å
Method
Ref.
¯
¯
0.056
0.40
3.45
¯
¯
Ϫ13.73
Ϫ18.63Ϯ0.67
¯
PVT
IR
IR
MW
MW
38
41
40
42
43
44
45, 46
47
¯
1709Ϯ120
1788.09Ϯ0.10
1788.214
¯
¯
¯
Ϫ23.85Ϯ2.10
3.34Ϯ0.20
3.231
¯
¯
Ϫ14.8b
¯
c
6
.0Ϯ0.5
¯
c
6
.552Ϯ0.035
.57–7.37
.53–6.67
¯
¯
¯
FTMW
ab initio
6
6
¯
¯
¯
3.33–3.40
¯
d
¯
¯
¯
Pol
a
Calculated for Tϭ303 K with ⌬S ϭϪ69.04 J K molϪ1 from Ref. 38.
0
D
Ϫ1
b
c
This value was calculated by the authors of Ref. 42 using different data from the literature.
Stark-shift measurements.
Consideration of mutual polarization of the monomers in the dimer.
d
ϭ0.9239. Defining a total number density n* of this mixture
(
p ϭ0.5 Torr, Tϭ200 K͒ to be B ϭ1788.09 MHz. The
tot
0
calculated bond length r (N¯C)ϭ3.231 Å agrees quite well
0
M
N ϩND
Ntot
ptot
with r ͑N¯C͒ϭ3.34Ϯ0.20 Å given by Jones et al. HCN
0
n*ϭ
ϭ
ϭ
,
͑11͒
V
V
k T
B
dimers have also been studied by microwave spectroscopy
4
3
by Brown et al. which yields B ϭ1788.214 MHz. From
0
*
one obtains from Eq. ͑10͒ the mole fraction xD of the dimers
in this artificial gas mixture as a function of ptot and T
the observed Stark-shift it follows a dipole moment of the
4
4
dimer D ϭ6.0Ϯ1.5 D. Campbell and Kukolich have in-
D
15
p0
vestigated the dimer (HC N) in a molecular beam by the
2
x*Dϭ1ϩ
rev
method of Fourier transform microwave spectroscopy and
2
n*k TKp ͑T͒
B
obtained D ϭ6.552Ϯ0.035 D.
D
p0
2
1/2
Ab initio calculations on a linear HCN dimer done by
4
5,46
Ϫ
ͫ
ͩ
1ϩ
rev
ͪ
Ϫ1
ͬ
,
͑12͒
Kofranek et al.
yield a dipole moment between 6.57 and
2n*k TKp ͑T͒
B
7
3
.37 D. The equilibrium bond length r ͑N¯C͒ lies between
0
where K rp ev(T) can be calculated with the results of Giauque
and Ruehrwein. This artificial monomer/dimer gas mixture
behaves with respect to electrons like a mixture of differently
strong polar scatterers. In order to calculate the total scatter-
ing cross section of the mixture we can take into account an
ansatz of Christophorou et al.48 used for a mixture of the
nonpolar ethene and a polar gas
.33 and 3.40 Å. The enthalpy of dimerization varies be-
Ϫ1
47
tween Ϫ14.2 and Ϫ15.9 kJ mol . Ruoff has calculated
the dipole moment of the HCN dimer considering addition-
ally mutual polarization effects. He obtained values for DD
between 6.53 and 6.67 D. For a better survey we have col-
lected all these quantities in Table II.
2. The influence of HCN dimers on the electron
av
mixϭAmixm /k Tϭ͑x A ϩx A ͒m /k T.
mobility
͗
␴ ͑␧͒
͘
m
e
B
1
1
2
2
e
B
͑
13͒
Because the scattering cross section depends approxi-
mately on the squared dipole moment it follows that the
Assuming that there are only single scattering events ͑Lor-
entz approximation͒ between the electron and the monomer
or the dimer, respectively, we can apply Eq. ͑13͒ on our
‘‘mixture of two polar gases’’. The experimental scattering
scattering cross section of the dimer (HCN) should be by a
2
factor of almost 5 larger than that of the HCN monomer.
Depending on the concentration of ͑HCN͒ the influence of
2
av
exp
the dimers on the electron mobility might be quite consider-
able. For example, based on the analysis of Giauque and
Ruehrwein the mole fraction of the dimers at the boiling
point 298.8 K (p ϭ1.01325 bar͒ is x ϭ0.0494.
cross section ␴ (␧)
of HCN was determined by ex-
͗
͘
m
trapolation of the density-normalized mobility (␮n) to n
av
m
exp
→0. In this case it can be assumed that ␴ (␧)
͗
͘
repre-
tot
D
sents the thermally averaged cross section of the HCN mono-
mers with respect to electrons. As mentioned above any de-
viation of the compression factor Z from Zϭ1 has been
interpreted as being due to HCN dimer formation. Therefore,
the former number density n has to be replaced by n*.
Within the presented experimental density range the quanti-
ties n and n* differ by only 1%. With Eq. ͑6͒ the scattering
cross section of the dimer can be approximately calculated
from the scattering cross section of the monomer,
In order to estimate the effect of HCN dimers on the
electron mobility we ‘‘synthesize’’ a gas mixture consisting
of monomers and dimers neglecting the relatively large con-
tributions of all the higher oligomers of HCN ͑at Tb
ϭ298.8 K and p ϭ1.01325 bar Giauque and Ruehrwein
tot
have determined besides xD also x ϭ0.0089, and xQ
T
ϭ0.0016, etc.͒. Each of both components should behave like
an ideal gas. On the basis of the PVT data of Giauque and
av
exp
Ruehrwein we obtain then a revised equilibrium constant
͗
␴ (␧)
͘
, i.e.,
m
rev
K
x
ϭ0.098 at T ϭ298.8 K (p ϭ1.01325 bar͒ based on
p
b tot
av
exp
D
2
av
exp.
rev
͗
␴ ͑␧͒
͘
Ϸ͑D /D ͒
͗
␴ ͑␧͒
͘
͑14͒
ϭ0.0824 obtained from the compression factor Z
m
D
M
m
D
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1

J. Chem. Phys., Vol. 109, No. 2, 8 July 1998
Th. Klahn and P. Krebs
539
TABLE III. Experimental density-normalized electron mobilities,
exp
(
␮n*)0 , in the limit n*→0 and the electron attachment/detachment equi-
librium constant K as a function of temperature.
T/K
(␮n*) e0 xp/1021 cmϪ1 VϪ1 sϪ1 a
K/10Ϫ20 cm3
2
3
94
33
2.10Ϯ0.10
2.25Ϯ0.13
11.7Ϯ0.8
9.80Ϯ0.88
a
exp
exp
In the limit n*→0 it follows that (␮n*)0 ϵ(␮n)0 ͑see Table I͒.
stage that considering multiple scattering effects we took
into account only the incoherent correction ͑dotted line in
Fig. 10͒. By neglecting the coherent multiple scattering cor-
rection depending on B(T) we want to avoid that the effect
of B(T) leading to HCN dimers will be counted twice. To
demonstrate the influence of the dimers on the electron mo-
rev
bility still more pronounced we have used instead of Kp (T)
of Giauque and Ruehrwein also the very large equilibrium
constant K ϭ0.40 of Mettee. The dashed-͑two͒-dotted lines
p
in Fig. 10 show that the density effect due to dimers depends
very sensitively on the accuracy of the thermodynamic re-
sults on the HCN gas. The assumption that gaseous HCN at
Tϭ294 K consists only of monomers and dimers must be
considered as an approximation. A small amount of trimers
can have a nonnegligible influence on the electron mobility
since the molecular beam FTMW experiments have shown
linear trimers with a dipole moment of 10.61 D. However,
we do not consider the influence of trimers and higher oli-
gomers on the electron mobility due to the lack of suffi-
ciently accurate data.
FIG. 10. Density-normalized mobility (␮n*) of electrons in HCN gas at
2
94 K ͑a͒, and 333 K ͑b͒ as function of the total number density n* of the
monomer/dimer gas mixture ͑see the text͒. Dashed lines: classical result;
dashed-dotted lines: influence of HCN dimers ͓Eq. ͑16͔͒ taking into account
rev
the revised equilibrium constant of Giauque and Ruehrwein Kp (294 K)
rev
ϭ0.107 and Kp (333 K)ϭ0.055; dashed-͑two͒-dotted line: influence of
HCN dimers considering, however, the equilibrium constants of Mettee
From Fig. 10 it is concluded that there must exist an
additional density dependent scattering process or a localiza-
tion process which is more effective than the weak localiza-
tion due to interference in multiple scattering. In the follow-
ing section we give another explanation for the density
variation of the density-normalized mobility which is based
on the concept of the so-called dipole bound electron ground
state.
K (294 K)ϭ0.502 and K (333 K)ϭ0.205 ͓Eq. ͑16͔͒; dotted line: dimer
p
p
formation ͑Giauque and Ruehrwein͒ and density correction due to interfer-
ence in multiple scattering ͓Eqs. ͑5͒ and ͑16͔͒. Solid line: best fit of the
dipole-bound electron state model ͓Eq. ͑17͔͒ to the experimental points. The
density-normalized mobility of the quasi-free electrons in this model has
been calculated with the corresponding corrections due to incoherent mul-
tiple scattering and due to dimer formation.
Using Eq. ͑2͒ of Ref. 1 and Eqs. ͑13͒ and ͑14͒ one obtains
the density-normalized electron mobility in the monomer/
dimer gas mixture
E. The dipole-bound electron ground state as a
temporary localization center
8
e
Ϫ
f
␮n*͒mix
1/2
av
exp
Similar to the case of multiple scattered electrons e in
͑
ϭ
͕
͗ ͘
͓2͑␲m k T)͔ ␴ ͑␧͒
e B
m
18
3
CH CN gas we show that the anomalous density depen-
3
dence of the electron mobility in HCN can be described by
the first term on the r.h.s. of the following expression for an
oscillatory transport process ͑see the solid line in Fig.
2
Ϫ1.
ϫ͓x*͑D /D ͒ ϩx* ͔
͖
M
͑15͒
͑16͒
D
D
M
With Eq. ͑7͒ and x*ϭ1Ϫx* one finally has
M
D
49–51
1
0͒
2
D
Ϫ1
D
␮n*͒mixϭ͑␮n͒0 1ϩ
͑
ͩ
Ϫ1
ͪ
x*
,
␮ Kn*2
ͫ
2
M
D
ͬ
␮ n*
f
l
D
␮effn ϭ
*
ϩ
͑17͒
1
ϩKn* 1ϩKn*
where the mole fraction of the HCN dimer, x* , can be cal-
D
with the constants K(T) given in Table III. The mobility of
culated with Eq. ͑12͒.
the multiple scattered electrons, ␮ , has been determined by
At the highest number density of this investigation on
the electron mobilities the mole fraction of the HCN dimers
is about 0.015. It follows that the influence of the dimers on
the electron mobility at these low gas densities is relatively
small in spite of the large scattering cross section ͑see Fig.
f
Eq. ͑16͒. The experimental result of Eq. ͑17͒ is in accordance
with a dynamical electron attachment/detachment equilib-
rium
K
Ϫ
f
Ϫ
e ϩHCN↔͓e ¯HCN͔
͑18͒
1
1
0͒. However, it should be emphasized that according to Fig.
0 this effect is larger than the density correction due to
l
with the equilibrium constant K(T)ϭk /k . The attach-
fl lf
multiple scattering processes. It should be pointed out at this
ment rate of the multiple scattered electron to HCN is given
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540
J. Chem. Phys., Vol. 109, No. 2, 8 July 1998
Th. Klahn and P. Krebs
is known to be about 2.6 D,55 and it binds an electron to form
by k n*ϭ1/␶ and the electron detachment from the
fl
fl
Ϫ
Ϫ
quasilocalized electron state ͓e ¯HCN͔ is determined by
the dipole supported anion ͓e ¯(H O) ͔. From field de-
l
2
2
the rate constant k ϭ1/␶ (␶ is the mean lifetime of the
tachment experiments it follows an electron binding energy
lf
lf
lf
close to Ϫ9 meV56 whereas photoelectron experiments mea-
quasilocalized electron state͒. The second term of Eq. ͑17͒
can be neglected in our case because for the quasilocalized
state one has ␮ Ӷ␮ . This equation is valid only if the drift
1
0
sured the vertical detachment energy to be 42 meV.
Ϫ
In the case of ͓e ¯HCN͔ the binding energy should be
l
f
l
time t is by many orders of magnitude larger than ␶ and
comparable to those limiting values. Jordan and Wendoloski
d
fl
4
9
54
␶lf
.
estimated E.A. Ϸ1 meV whereas Garrett studied the per-
Ϫ
We assert now that ͓e ¯HCN͔ represents a dipole-
manent and induced dipole requirements in ab initio calcu-
l
bound electron ground state. In the following we want to
support this suggestion. First we are looking for some infor-
mation on the time constant ␶ ϭ1/k n*. Mothes et al.
lations of the electron affinity of HCN within the limits 1
6
рE.A.р10 meV. From the temperature dependence of the
52
equilibrium constant K for the attachment/detachment equi-
librium ͑18͒ one can get a measure for the binding energy.
The relevant parameters are collected in Table III. From the
results for 294 and 333 K one can realize a decrease of K
with increasing temperature as it is expected. The van’t Hoff
equation ͑under the experimental condition Vϭconst.͒ leads
finally to an estimate of the internal energy change for the
electron attachment reaction ͑formation of the dipole-bound
state͒ ⌬UϭϪ(38Ϯ25)meV corresponding to ⌬U
fl
fl
have determined the low pressure attachment rate constant
kfl by the electron cyclotron resonance method, however, at
12
Ϫ3
much lower HCN gas densities (nр10 cm ) in compari-
son with those of our swarm experiment. Without taking into
account the possible detachment reaction they obtained k
fl
Ϫ11
3
Ϫ1
ϭ9.1ϫ10
cm s at Tϭ290 K. With this value we get
Ϫ20
3
from the equilibrium constant Kϭ11.7ϫ10
cm at T
ϭ294 K and n*ϭ1ϫ1018 cm ␶ Ϸ1.3 ns and ␶ Ϸ11 ns.
Ϫ3
lf
fl
ϭϪ(1.52Ϯ0.98)N k T for Tϭ294 K.
Both time constants seem to be not sufficiently small in com-
parison with the observed drift time of several hundred nano-
seconds to about 5 ␮s as required by the oscillatory model.
We conclude, therefore, that kfl may be by several orders of
magnitude larger than the above experimental estimate but
A B
The proposed electron transport process with the tempo-
rary nondissociative dipole-binding of an electron by HCN is
valid only in the gas density range where ⑄ ӶL. From this
T
Ϫ
interpretation it follows that the lifetime of ͓e ¯HCN͔ of
l
about 12 ps does not depend on n* in the density range
under investigation. This can be true only if with increasing
density n* ͑or n) the mean time interval between two mo-
lecular collisions is much larger than the lifetime of the
dipole-bound state. This time was estimated to be in the or-
the autodetachment rate constant is also very high so that the
Ϫ
formation of stable ͓e ¯HCN͔ could not be directly ob-
l
served in swarm experiments. This was already suggested by
20
Stockdale et al. in the case of electrons in CH CN. Scher-
3
mann and co-workers19 studied charge transfer collisions be-
der of 1 ns at the highest density of this investigation. There-
tween laser excited xenon (nf, np) Rydberg atoms and ac-
Ϫ
Ϫ
fore, the lifetime of ͓e ¯HCN͔ is obviously not controlled
etonitrile molecules and clusters. ͓e ¯CH CN͔ has been
l
3
l
by molecular collisions as it was feared in the introduction of
this paper.
observed in these supersonic expansion beam experiments
only in narrow ranges of Rydberg n values. The attachment
rate constant was found to be much higher, i.e., k ϭ(1
fl
Ϫ8
3
Ϫ1
Ϯ0.5)ϫ10
cm s . This result has to be compared with
F. Excess electrons in saturated aminoethanol vapor
the corresponding low pressure value kflϭ7.2
Ϫ12
3
Ϫ1
52
ϫ10
cm s
of Mothes et al. We use Schermann’s
Finally we present the results of the electron mobility
measurements in saturated aminoethanol vapor in the tem-
perature range 298рTр435 K ͑Fig. 11͒. Despite the fact
rate constant as an upper limit for the interpretation of our
results in HCN. This value and the equilibrium constant K
ϭ(11.7Ϯ0.10)ϫ10
Ϫ20
3
57
cm obtained in our swarm experi-
that its dipole moment Dϭ3.05 D is similar to that of HCN
Ϫ10
ment yield ␶ у11.7 ps and ␶ у(1/n*)ϫ10
s, where the
the density-normalized mobility does not show any anoma-
lies ͑see the inset in Fig. 11͒. It should be emphasized, how-
ever, that the errors of these experiments are for the follow-
ing reasons extremely large. On the one hand, temperature
fluctuations lead sometimes to condensation of aminoethanol
from the saturated gas phase on the photocathode surface
thus changing the mobility. On the other hand, the lack of a
useful equation of state for aminoethanol does not allow an
accurate determination of the vapor number density. The ex-
trapolation of the density-normalized mobility to n→0 ͑see
the dashed line in the insert of Fig. 11͒ leads to an estimate
lf
fl
number density n* has to be substituted in units of
1
8
Ϫ3
10
cm . The calculated lifetimes of the electron in the
different states are in fact much smaller than the experimen-
tally observed drift times between at least 400 ns and a few
microseconds in accordance with the conditions of the
model.
Such an oscillatory transport process with the short life-
time ␶lf in the order of some tens picoseconds due to the
detachment process is reasonable only if the binding energy
of the quasilocalized electron is small, i.e., it should be com-
parable to the thermal energy. The electron binding energy
av
exp
exp
of the mean momentum transfer cross section
͗
͗
␴ (␧)
͘
͘
m
2
av
was determined by Schermann and co-workers in the case of
Ϸ(2655Ϯ136) Å which agrees quite well with
␴ (␧)
m
Ϫ
2
58
͓
e ¯CH CN͔ by field detachment in the supersonic beam
ϭ2661 Å determined by Hamilton and Stockdale at 300
3
l
19,53
experiment. They obtained E ϭϪ11.5 meV.͒
For com-
K ͑Fig. 9͒.
b
parison, the electron affinity E.A. Ϸ0.5 meV for CH CN was
For comparison it should be mentioned that in contrast
to the results in aminoethanol the density-normalized mobil-
3
determined by an ab initio calculation by Jordan and
5
4
Wendoloski. The dipole moment of the neutral water dimer
ity in saturated CH CN vapor shows in spite of likewise
3
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J. Chem. Phys., Vol. 109, No. 2, 8 July 1998
Th. Klahn and P. Krebs
541
ACKNOWLEDGMENTS
This work is dedicated to Professor U. Schindewolf.
Support of this work by the Deutsche Forschungsgemein-
schaft and by the Fonds der Chemischen Industrie is grate-
fully acknowledged.
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FIG. 11. Electron mobility in saturated aminoethanol vapor as a function of
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21
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IV. SUMMARY
͑
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1