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

Article abstract of DOI:10.1063/1.476506

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:10.1063/1.476506

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, 3959 (1998); doi: 10.1063/1.476506
View online: http://dx.doi.org/10.1063/1.476506
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 109, NUMBER 10
8 SEPTEMBER 1998
The following article was originally published in The Journal of Chemical Physics 109, 531 (1998). It is reprinted here in its entirety due to the inadvertent
replacement of Figs. 7 and 9 during the production process.
Electron and anion mobility in low density hydrogen cyanide gas.
I. Dipole-bound electron ground states
Th. Klahn and P. Krebsa)
¨
¨
Institut fur Physikalische Chemie und Elektrochemie, Lehrstuhl fur molekulare physikalische Chemie,
¨
Universitat 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.
Experiments were performed at 294 and 333 K in the gas number density range 1.23ϫ1017рn
р3.61ϫ1018 cmϪ3. 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
nonsaturated CH3CN gas (Dϭ3.925 D͒ shows a density behavior similar to that in HCN. © 1998
American Institute of Physics. ͓S0021-9606͑98͒01626-2͔
an extensive orbital, described by a diffuse wave function.6
I. INTRODUCTION
The consideration of rotational degrees of freedom in real
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
DϾDc is reduced to a finite number as it was shown by
Garrett.7 However, the minimum dipole moment necessary
to support at least one bound state is increased by 10% to
30% in comparison with that of a dipole fixed in space. In
this case Dc depends on the effective dipole length, the ro-
tational state, and the moments of inertia of the polar
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
drift mobility measurements. For example, such a dipole-
bound anion in water, i.e., (H2O)Ϫ2 was prepared by Haber-
land and co-workers in a beam experiment and detected by
mass spectroscopy.9 The vertical detachment energy of the
water dimer anion of 42 meV was determined by photoelec-
tron experiments by Bowen and co-workers.10
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
interaction.1 For polar gases with a dipole moment DϷ3 D
the number density n at which the de Broglie wavelength
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-
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.
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
and Teller2 who first established the critical permanent elec-
tric dipole moment Dcϭ1.625 D required to bind an elec-
tron. Crawford and Delgarno,3 Crawford and Garrett,4 and
Garrett5 have shown that the electric dipole field of a station-
ary molecule can bind an electron in an infinite number of
bound states if D is greater than Dc . The electron exists in
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
a͒
Author to whom correspondence should be addressed.
0021-9606/98/109(10)/3959/12/$15.00
3959
© 1998 American Institute of Physics
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3960
J. Chem. Phys., Vol. 109, No. 10, 8 September 1998
Th. Klahn and P. Krebs
extensive electron mobility measurements in sub- and super-
and in subcritical H2O12,13 gas as a function
11,12
critical NH3
of gas density and temperature up to very high densities in
order to study this transition in a disordered medium of di-
pole scatterers. We continued these studies on electrons in
sub- and supercritical CH3OH gas14–16 and in subcritical
CH3CN17 gas also at much lower densities to study different
multiple scattering effects on the electron mobility. From
preliminary and not very accurate results on the electron mo-
bility in low density saturated CH3CN vapor (Dϭ3.925 D͒
we suggested that we have found dipole-bound electron
ground states in thermal equilibrium ͑we prefer to use the
formula eϪ¯CH CN instead of CH CNϪ to point out the
͓
͔
3
3
weakly bound electron͒ which are involved in the transport
process.14 In the meantime we have performed electron mo-
bility measurements in low density CH3CN gas with much
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
Schermann and coworkers19 showing that Compton’s
method20 for the production of dipole-supported
eϪ¯CH CN could be used as a general way to get ground
FIG. 1. Swarm drift velocity
as a function of the electric field strength E
vd
for electrons in low density HCN gas (Tϭ294 K, nϭ1.73ϫ1018 cmϪ3).
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.
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
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.
͓
͔
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
field detached the dipole-bound electron from the produced
anion eϪ¯CH CN 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 HCN21 is much
smaller than that of CH3CN but far above Dc . Therefore,
HCN should form a dipole-bound electron state as predicted
theoretically by Garrett.6 Moreover, the influence of the
dipole-bound state should be more easily observed in elec-
tron mobility measurements in comparison with CH3CN be-
cause due to the lower dipole moment the contribution of
incoherent multiple scattering effects should be quite small.
However, in contrast to CH3CN some complications are to
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.22 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.
II. EXPERIMENT
A. Pulsed Townsend method
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
by a distance d. A thin slice of ne electrons is photoinjected
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 105 to 107
electrons drifts to the anode with the drift velocity
rise to an induced current iϭϪene d /d through a load re-
sistor RL , if dӶr. If electron attachment to the gas mol-
ecules can be neglected, ne and
giving
vd
v
are constant. In this
vd
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 td one obtains the
drift velocity dϭd/td . From the experimental linear rela-
v
tionship between
and E, the mobility ␮ is determined
vd
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-
lations on quantum multiple scattering corrections to the mo-
bility of the electrons.23,24 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-
from ␮ϭ d /E in the limit of zero field ͑see Fig. 1͒. In Fig.
v
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-
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J. Chem. Phys., Vol. 109, No. 10, 8 September 1998
Th. Klahn and P. Krebs
3961
B. Sample preparation25
1. Hydrogen cyanide
The production of HCN was performed according to a
method described in Ref. 26, however, the procedure was
stepwise improved in our laboratory. In the beginning about
24 g KCN were dried and degassed at 373 K at a vacuum
line ͑better than 10Ϫ6 mbar͒. After KCN was cooled down to
77 K about 10 ml of fourfold distilled water were condensed
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 H2SO4 ͑50 mass %͒
were prepared in a dropping funnel and were gently bubbled
with nitrogen ͑Messer Griesheim, 5.0͒ for at least 30 min to
remove O2 and other gases. Finally, the sulfuric acid was
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
filled with freshly prepared P2O5 .27 Thereafter, P2O5 was
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
P2O5 . It is well-known that small traces of water in HCN
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.
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; RL , load resistor; FAMP, fast amplifier
͑homebuilt͒; Nd:YAG laser, J.K. Lasers, System 2000; PD, photodiode for
triggering; Transient Recorder, Iwatsu DM 901; PC, personal computer;
ADC, analog/digital converter ͑see the text͒.
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
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.
2. 2-aminoethanol
C2H7NO was purified by us in the following manner:
2-aminoethanol ͑Aldrich, 99%͒ was gently bubbled with ar-
gon ͑Messer Griesheim, 5.0͒; thereafter with a small amount
of KBH4 ͑Fluka͒ it was refluxed for at least 3 h under re-
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
made free of electron scavengers such as O2 and CO2 by
several freeze–pump–thaw cycles. It should be pointed out
that all parts of the apparatus which came in contact with
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.
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3962
J. Chem. Phys., Vol. 109, No. 10, 8 September 1998
Th. Klahn and P. Krebs
HCN ͑or C2H7NO), in particular the drift cell, are cleaned
with several organic solvents and were finally rinsed with
overheated water vapor for at least 24 h.
At higher temperatures hydrogen cyanide shows autopo-
lymerisation: A black charcoal-like substance is produced
which is called ‘‘azulmin.’’28 To avoid this effect we have
tested many inhibitors mentioned in the literature.29 Very
effective was only cobaltoxalate (CoC2O4•2H2O, Aldrich͒.30
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 nϭ1.70ϫ1018 cmϪ3, Tϭ294K,
Eϭ1.533ϫ102 V cmϪ1; ͑b͒ nϭ2.70ϫ1018 cmϪ3, Tϭ333 K, Eϭ2.757
ϫ102 V cmϪ1
;
͑c͒ nϭ3.90ϫ1018 cmϪ3
,
Tϭ333 K, Eϭ6.126
ϫ102 V cmϪ1. The dashed lines in ͑b͒ and ͑c͒ are fitting time dependent
exponential functions demonstrating the electron capturing process ͓see Eq.
͑3͔͒.
1/2 Ϫ1
2p
4pB T͒
͑
nϷ
1ϩ 1ϩ
,
͑1͒
ͫ
ͬ
ͭ
ͮ
kBT
NAkBT
with the second virial coefficient B(T) taken from the
literature.31
5ϫ107 samples/s͒ which is connected via an IEEE-488 bus
interface to a personal computer. Signal accumulation was
performed.
Typical electronic wave forms u(t) are shown in Fig. 4
for increasing HCN number densities n . If a short bunch of
n0e excess electrons is photoinjected in the drift space, the
voltage drop u(t) decreases during the drift time. In the ideal
case it can be described by
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
(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
en0e
u t͒ϭϪR
exp Ϫt/␶
0рtрtd
͖
͑
͕
L
e
td
ϭ0 tϾtd ,
pressures at the measured temperatures ␪ in centigrades
T
were calculated from the Antoine equation
͑3͒
B0
C0Ϫ␪
log pϭA0Ϫ
,
͑2͒
where e is the elementary charge and ␶ is the mean lifetime
e
of the excess electrons in the low density HCN (k(1)ϭ1/␶ is
T
e
eff
with the parameters A0, B0, and C0 taken from the
the rate constant of disappearance of the electrons͒. In spite
of the strong decay of u(t) with time at nϭ2.7
ϫ1018 cmϪ3 the arrival of the electrons at the anode after
the time td can be still observed ͓see Fig. 4͑b͔͒. However, at
number densities nϾ3.6ϫ1018 cmϪ3 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
wave forms did not allow the determination of td due to the
fast reaction of the electrons.
literature.31
C. Signal wave forms
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
resistor RL which is amplified by a fast home-built amplifier.
The output is fed to a transient recorder ͑Iwatsu DM 901,
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J. Chem. Phys., Vol. 109, No. 10, 8 September 1998
Th. Klahn and P. Krebs
3963
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
demonstrates the proportionality k(e1ff)ϰn2. ͑b͒ Rate constant for reaction ͑4͒,
(1)
kϭk /n2, 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
density range 1.23ϫ1017рnр3.61ϫ1018 cmϪ3 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
eϪϩj HCN→AϪ.
͑4͒
AϪ 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-
cies AϪ. 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(e1ff) as a function of
n at 333 K. It follows from Figs. 5͑a͒ and 5͑b͒ that reaction
͑4͒ is second order with respect to HCN, i.e., jϭ2. Within
the margins of the experimental errors one obtains for the
rate constant kϭk(e1ff)/n2ϭ(8Ϯ2)ϫ10Ϫ32cm6 sϪ1. For a fur-
ther discussion of this result we refer to paper II of this
publication series.32
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3964
J. Chem. Phys., Vol. 109, No. 10, 8 September 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
by15,16
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
functions like (␮n)e0xp/(1ϩconst. n)]; the dashed lines represent the classical
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.
ͱ
8
␲
av
␮n͒Ϸ ␮ n͒ 1Ϫ
0.5␲Ϫ0.6͒⑄
␴
␧͒ n
͑
͑
͑
͑
͗
͘
ͭ
L
T
m
2B T͒
͑
ϩ
n . . . ,
͑5͒
ͮ
NA
where (␮Ln) is the classical density-normalized mobility in
the single collision approximation ͓Lorentz limit: see, e.g.,
Eq. ͑2͒ in Ref. 1͔. (␮Ln) does not depend on the gas density.
The first density correction on the right-hand side of Eq. ͑5͒
is due to quantum interference in multiple scattering which
has been calculated by Polischuk.23,24 This term is valid only
at sufficiently low gas densities where the de Broglie wave-
length ⑄Tϭប/(2mekBT)1/2 of the thermal electrons is much
smaller than their mean free path Lϭ1/ ␴av(␧) n. ␴av(␧)
is the thermal average of the theoretical momentum transfer
cross section, ␴amv(␧)ϭ(4␲/3)(De/ប)2me /␧, for dipole
molecules in the point-dipole limit averaged over the dipole
orientations (␧ϭ(បk)2/2me is the kinetic energy of the
where (␮n)0 is the experimental zero-field density-
normalized mobility in the limit of n→0. In this case (␮Ln)
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
lines represent the classical result. To obtain (␮n)e0xp we
have fitted the experimental points by a hyperbolic function
of the type (␮n)e0xp/(1ϩconst. n) ͑the theoretical justification
for this follows in Sec. III E͒. This was done also in Fig. 7.
The thermal averaged experimental scattering cross sections
͗
͘
͗
͘
m
m
34
electron͒
are ␴av(␧) expϭ2670Ϯ127Å2 (Tϭ294 K͒ and ␴av(␧)
͘
exp
͗
͘
͗
m
m
ϭ2341Ϯ135 Å2 (Tϭ333 K͒ which are distinctly smaller
av
␴
␧͒ theorϭAm /k T with Aϭ 8␲/3͒ De/ប͒2.
͑6͒
͑
͑
͑
͗
͘
e
B
m
than the corresponding theoretical values ␴av(␧)
theor
͗
͘
m
ϭ3473 Å2 and ␴av(␧) theorϭ3066Å2 obtained from Altshul-
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-
efficient in units of cm3 molϪ1. Polischuk proposed to use in
͗
͘
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
(␮n)0 . However, even at such low HCN gas densities of the
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
Eq. ͑5͒ the thermally averaged experimental cross section
␴av(␧)
obtained from measurements at very low
exp
͗
͘
m
density14,15
8e
av
m
1/2
Ϫ1
␴
␧͒ expϭ
2/␲mk T͒
␮n͒
͔
0
,
͑7͒
͑
͑
͓͑
͗
͘
B
3
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J. Chem. Phys., Vol. 109, No. 10, 8 September 1998
Th. Klahn and P. Krebs
3965
where pi and xi are the partial pressures and the mole frac-
tions of the monomers (M) and dimers (D), ptot is the sum
of the partial pressures, and p0ϭ1 bar. Higher oligomers
are neglected in the case when xM is replaced by (1ϪxD).
Giauque and Ruehrwein calculated Kp from the compression
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 (1ϩB (T)p); how-
Ј
ever, they employed the second virial coefficient of HCl
[B (T )ϭϪ0.0056 barϪ1, Tbϭ298.8 K is the boiling tem-
Ј
b
perature of HCN at 1 bar͔. The equilibrium constant for the
dimer formation at Tϭ303 K was obtained to be Kp
ϭϪB (303 K)p ϭ0.056. From the temperature depen-
Ј
0
dence of Kp they obtained the enthalpy of dimer formation
⌬H0DϭϪ13.73 kJ molϪ1, as well as the corresponding en-
tropy change ⌬SD0 ϭϪ69.04 J KϪ1 molϪ1. Neglecting the
formation of higher oligomers the mole fraction of the
dimers, xD , is a function of ptot , i.e.,
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
͑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
2
1/2
p0
2Kp T͒p
p0
2Kp T͒p
¯
͑Ref. 34͒ for DϷ3.0 D ͓Eq. ͑6͔͒.
xDϷ1ϩ
Ϫ
1ϩ
Ϫ1 . ͑10͒
ͫ
ͩ
ͪ
ͬ
͑
͑
tot
tot
Hyde and Hornig39 were the first to show directly the exis-
tence of (HCN)2 by infrared measurements. Jones, Seel, and
Sheppard40 studied (HCN)2 by IR spectroscopy in the gas
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 r0(N¯C)
ϭ3.34Ϯ0.20 Å. The standard enthalpy of formation was de-
termined from the temperature dependent intensities of the
absorption bands of the monomer and dimer to be ⌬HD0
ϭϪ(23.85Ϯ2.10)kJ molϪ1 ͑see Table II.͒. In a further IR
absorption study concerning (HCN)2 in the gas phase at 300
K and a HCN gas pressure of up to 933 mbar Mettee41 tried
to verify spectroscopically the dimerization equilibrium con-
stant Kp of Giauque and Ruehrwein. From constant volume
measurements between 298 and 356 K ͑for pу933 mbar͒
they obtained the internal energy of dimerization ⌬UD0
ϭϪ15.90Ϯ0.67kJ molϪ1 and the corresponding dimeriza-
tion enthalpy ⌬H0DϭϪ(18.63Ϯ0.67)kJ molϪ1 and with
⌬S0D of Ref. 38 finally Kp ͑revised͒ ϭ 0.40 for 303 K. The
discrepancy between Kp ͑revised͒ ϭ 0.40 and Kp ͑Ref. 38͒
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.,
Kpϭ3.45. Of course, the strongly different dimerization
equilibrium constants of Mettee and Jones et al. lead to com-
pression factors which extremely differ from that of Giauque
and Ruehrwein.
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.
D. The influence of HCN dimer formation on the
electron mobility
1. The formation and properties of HCN dimers
Based on PVT-measurements performed on HCN in the
thirties and forties of this century dimers and higher oligo-
mers were postulated to exist in the gas phase.35–37 Giauque
and Ruehrwein38 determined from PVT-data the equilibrium
constant Kp for the dimerization reaction
K
p
2HCN↔ HCN͒ .
͑8͒
͑
2
The dimensionless equilibrium constant Kp is defined by
pD /p0
p0 xD
p0
xD
ptot 1Ϫx ͒
Kpϭ
2 ϭ
2 Ϸ
,
2
͑9͒
p
M /p0͒
ptot x ͒
͑
͑
͑
M
D
TABLE I. Zero-field density-normalized electron mobility (␮n)0 in HCN
gas, scattering cross section
av(␧) exp, and second virial coefficient B(T)
␴
͗
͘
m
of HCN as a function of T ͑see the text͒.
exp
(␮n)0 /
␴
av(⑀)
/
B(T)/
͗
͘
m
T/K
1021 cmϪ1 VϪ1 sϪ1a
10Ϫ13 cm2 b
cm3 molϪ1c
294
333
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%.
Concerning the structure and the dipole moment of
(HCN)2 we can rely on numerous experimental and theoret-
ical investigations. Legon, Millen, and Mjoberg42 have deter-
¨
bCalculated with Eq. ͑7͒.
cData from Ref. 31.
mined the rotational constant of the dimer in the gas phase
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3966
J. Chem. Phys., Vol. 109, No. 10, 8 September 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 Kp , rotational constant B0 , enthalpy of dimerization ⌬HD , and the equilibrium
bond length r0͑N¯C͒ of linear HCN dimers.
a
D
D /D
Kp
⌬HD /kJ molϪ1
r0(N¯C)/Å
B0 /MHz
Method
Ref.
¯
¯
¯
¯
0.056
0.40
3.45
¯
¯
Ϫ13.73
Ϫ18.63Ϯ0.67
¯
PVT
IR
IR
MW
MW
FTMW
ab initio
Pold
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
¯
6.0Ϯ0.5c
6.552Ϯ0.035c
6.57–7.37
¯
¯
¯
¯
¯
¯
¯
3.33–3.40
¯
6.53–6.67
¯
¯
¯
aCalculated for Tϭ303 K with ⌬SD0 ϭϪ69.04 J KϪ1 molϪ1 from Ref. 38.
bThis value was calculated by the authors of Ref. 42 using different data from the literature.
cStark-shift measurements.
dConsideration of mutual polarization of the monomers in the dimer.
xrDevϭ0.0824 obtained from the compression factor Z
(ptotϭ0.5 Torr, Tϭ200 K͒ to be B0ϭ1788.09 MHz. The
calculated bond length r0(N¯C)ϭ3.231 Å agrees quite well
with r0͑N¯C͒ϭ3.34Ϯ0.20 Å given by Jones et al. HCN
dimers have also been studied by microwave spectroscopy
by Brown et al.43 which yields B0ϭ1788.214 MHz. From
the observed Stark-shift it follows a dipole moment of the
dimer DDϭ6.0Ϯ1.5 D. Campbell and Kukolich44 have in-
vestigated the dimer (HC15N)2 in a molecular beam by the
method of Fourier transform microwave spectroscopy and
obtained DDϭ6.552Ϯ0.035 D.
*
ϭ0.9239. Defining a total number density n of this mixture
NMϩND Ntot ptot
*
n ϭ
ϭ
ϭ
,
͑11͒
V
V
kBT
*
one obtains from Eq. ͑10͒ the mole fraction xD of the dimers
in this artificial gas mixture as a function of ptot and T
p0
*
xDϭ1ϩ
rev
*
2n kBTK T͒
͑
p
Ab initio calculations on a linear HCN dimer done by
Kofranek et al.45,46 yield a dipole moment between 6.57 and
7.37 D. The equilibrium bond length r0͑N¯C͒ lies between
3.33 and 3.40 Å. The enthalpy of dimerization varies be-
tween Ϫ14.2 and Ϫ15.9 kJ molϪ1. Ruoff47 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
1/2
p0
Ϫ
1ϩ
Ϫ1
,
͑12͒
ͫ
ͩ
ͪ
ͬ
rev
*
2n kBTK T͒
͑
p
where Krpev(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
av
m
␧͒ mixϭAmixm /k Tϭ x A ϩx A ͒m /k T.
͑
͘
e B 1 1 2 2 e B
2. The influence of HCN dimers on the electron
mobility
␴
͑
͗
͑13͒
Because the scattering cross section depends approxi-
mately on the squared dipole moment it follows that the
scattering cross section of the dimer (HCN)2 should be by a
factor of almost 5 larger than that of the HCN monomer.
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
cross section ␴av(␧)
of HCN was determined by ex-
exp
Depending on the concentration of ͑HCN͒ the influence of
2
͗
͘
m
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 (ptotϭ1.01325 bar͒ is xDϭ0.0494.
trapolation of the density-normalized mobility (␮n) to n
→0. In this case it can be assumed that ␴av(␧)
repre-
exp
͗
͘
m
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,
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 ptotϭ1.01325 bar Giauque and Ruehrwein
have determined besides xD also xTϭ0.0089, and xQ
ϭ0.0016, etc.͒. Each of both components should behave like
an ideal gas. On the basis of the PVT data of Giauque and
Ruehrwein we obtain then a revised equilibrium constant
Krpevϭ0.098 at Tbϭ298.8 K (ptotϭ1.01325 bar͒ based on
*
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,
␴av(␧) exp, i.e.,
͗
͘
m
av
m
exp
av
m
2
exp
␴
␧͒ Ϸ D /D ͒
␴
␧͒
͘
.
͑14͒
͑
͑
͑
͗
͘
͗
D
M
D
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J. Chem. Phys., Vol. 109, No. 10, 8 September 1998
Th. Klahn and P. Krebs
3967
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.
K/10Ϫ20 cm3
exp
(␮n )0 /1021 cmϪ1 VϪ1 sϪ1 a
T/K
*
294
333
2.10Ϯ0.10
2.25Ϯ0.13
11.7Ϯ0.8
9.80Ϯ0.88
In the limit n →0 it follows that (␮n )e0xpϵ(␮n)0exp ͑see Table I͒.
a
*
*
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-
bility still more pronounced we have used instead of Krpev(T)
of Giauque and Ruehrwein also the very large equilibrium
constant Kpϭ0.40 of Mettee. The dashed-͑two͒-dotted lines
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
*
294 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
the revised equilibrium constant of Giauque and Ruehrwein Krpev(294 K)
ϭ0.107 and Krpev(333 K)ϭ0.055; dashed-͑two͒-dotted line: influence of
HCN dimers considering, however, the equilibrium constants of Mettee
Kp(294 K)ϭ0.502 and Kp(333 K)ϭ0.205 ͓Eq. ͑16͔͒; dotted line: dimer
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.
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.
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
8e
av
Similar to the case of multiple scattered electrons eϪf in
CH3CN gas18 we show that the anomalous density depen-
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.
1/2
exp
␮n ͒mixϭ
2 ␲m k T)
͓ ͑
␴
␧͒
͘
*
͑
͔
͑
͕
͗
e
B
m
3
2
Ϫ1
*
*
͔
͖
M
ϫ x D /D ͒ ϩx
͓
.
͑15͒
͑16͒
͑
D
M
D
*
*
With Eq. ͑7͒ and xMϭ1ϪxD one finally has
49–51
10͒
DD2
D2M
Ϫ1
␮n ͒mixϭ ␮n͒ 1ϩ
Ϫ1 x
,
2
*
*
͑
͑
ͫ
ͩ
ͪ
ͬ
0
*
*
␮lKn
D
␮fn
eff
*
␮ n ϭ
ϩ
͑17͒
*
*
1ϩKn
1ϩKn
*
where the mole fraction of the HCN dimer, xD , can be cal-
culated with Eq. ͑12͒.
with the constants K(T) given in Table III. The mobility of
the multiple scattered electrons, ␮f , has been determined by
Eq. ͑16͒. The experimental result of Eq. ͑17͒ is in accordance
with a dynamical electron attachment/detachment equilib-
rium
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.
10͒. However, it should be emphasized that according to Fig.
10 this effect is larger than the density correction due to
multiple scattering processes. It should be pointed out at this
K
eϪϩHCN↔ eϪ¯HCN
͑18͒
͓
͔
l
f
with the equilibrium constant K(T)ϭkfl /klf . The attach-
ment rate of the multiple scattered electron to HCN is given
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3968
J. Chem. Phys., Vol. 109, No. 10, 8 September 1998
Th. Klahn and P. Krebs
*
by kfln ϭ1/␶ and the electron detachment from the
is known to be about 2.6 D,55 and it binds an electron to form
the dipole supported anion ͓eϪ¯(H2O)2͔. From field de-
tachment experiments it follows an electron binding energy
close to Ϫ9 meV56 whereas photoelectron experiments mea-
sured the vertical detachment energy to be 42 meV.10
In the case of eϪ¯HCN the binding energy should be
fl
quasilocalized electron state eϪ¯HCN is determined by
͓
͔
l
the rate constant klfϭ1/␶ (␶ is the mean lifetime of the
lf
lf
quasilocalized electron state͒. The second term of Eq. ͑17͒
can be neglected in our case because for the quasilocalized
state one has ␮lӶ␮f . This equation is valid only if the drift
͓
͔
l
comparable to those limiting values. Jordan and Wendoloski
estimated E.A. Ϸ1 meV54 whereas Garrett studied the per-
manent and induced dipole requirements in ab initio calcu-
lations of the electron affinity of HCN within the limits 1
рE.A.р10 meV.6 From the temperature dependence of the
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
ϭϪ(1.52Ϯ0.98)NAkBT for Tϭ294 K.
time td is by many orders of magnitude larger than ␶ and
fl
49
␶ .
lf
We assert now that eϪ¯HCN represents a dipole-
͓
͔
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 ␶flϭ1/kfln . Mothes et al.
52
*
have determined the low pressure attachment rate constant
kfl by the electron cyclotron resonance method, however, at
much lower HCN gas densities (nр1012 cmϪ3) in compari-
son with those of our swarm experiment. Without taking into
account the possible detachment reaction they obtained kfl
ϭ9.1ϫ10Ϫ11 cm3 sϪ1 at Tϭ290 K. With this value we get
from the equilibrium constant Kϭ11.7ϫ10Ϫ20 cm3 at T
ϭ294 K and n ϭ1ϫ10 cmϪ3 ␶lfϷ1.3 ns and ␶flϷ11 ns.
18
*
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
the autodetachment rate constant is also very high so that the
formation of stable eϪ¯HCN could not be directly ob-
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 ⑄TӶL. From this
interpretation it follows that the lifetime of eϪ¯HCN of
͓
͔
l
*
about 12 ps does not depend on n in the density range
under investigation. This can be true only if with increasing
͓
͔
l
*
density n ͑or n) the mean time interval between two mo-
served in swarm experiments. This was already suggested by
Stockdale et al. in the case of electrons in CH3CN.20 Scher-
mann and co-workers19 studied charge transfer collisions be-
tween laser excited xenon (nf, np) Rydberg atoms and ac-
etonitrile molecules and clusters. eϪ¯CH CN has been
lecular collisions is much larger than the lifetime of the
dipole-bound state. This time was estimated to be in the or-
der of 1 ns at the highest density of this investigation. There-
fore, the lifetime of eϪ¯HCN is obviously not controlled
͓
͔
l
͓
͔
l
3
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., kflϭ(1
Ϯ0.5)ϫ10Ϫ8 cm3 sϪ1. This result has to be compared with
the corresponding low pressure value kflϭ7.2
ϫ10Ϫ12 cm3 sϪ1 of Mothes et al.52 We use Schermann’s
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)ϫ10Ϫ20 cm3 obtained in our swarm experi-
F. Excess electrons in saturated aminoethanol vapor
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
that its dipole moment Dϭ3.05 D57 is similar to that of HCN
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
ment yield ␶lfу11.7 ps and ␶flу(1/n )ϫ10Ϫ10 s, where the
number density n has to be substituted in units of
*
*
1018 cmϪ3. 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 ␶ in the order of some tens picoseconds due to the
lf
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
was determined by Schermann and co-workers in the case of
eϪ¯CH CN by field detachment in the supersonic beam
of the mean momentum transfer cross section ␴av(␧)
exp
͗
͘
͘
m
Ϸ(2655Ϯ136) Å2 which agrees quite well with ␴av(␧)
exp
͗
m
ϭ2661 Å2 determined by Hamilton and Stockdale58 at 300
K ͑Fig. 9͒.
͓
͔
l
3
19,53
experiment. They obtained EbϭϪ11.5 meV.͒
For com-
parison, the electron affinity E.A. Ϸ0.5 meV for CH3CN was
determined by an ab initio calculation by Jordan and
Wendoloski.54 The dipole moment of the neutral water dimer
For comparison it should be mentioned that in contrast
to the results in aminoethanol the density-normalized mobil-
ity in saturated CH3CN vapor shows in spite of likewise
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J. Chem. Phys., Vol. 109, No. 10, 8 September 1998
Th. Klahn and P. Krebs
3969
ACKNOWLEDGMENTS
This work is dedicated to Professor U. Schindewolf on
the occasion of his 70th birthday. Support of this work by the
Deutsche Forschungsgemeinschaft and by the Fonds der
Chemischen Industrie is gratefully acknowledged.
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FIG. 11. Electron mobility in saturated aminoethanol vapor as a function of
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binding energy and the lifetime are comparable in both me-
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3970
J. Chem. Phys., Vol. 109, No. 10, 8 September 1998
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