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JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS
doi:10.1088/0953-4075/46/6/065203
J. Phys. B: At. Mol. Opt. Phys. 46 (2013) 065203 (7pp)
Electron-scattering cross sections for
1-pentene, H2C=CH–(CH2)2CH3,
molecules
Czesław Szmytkowski, Paweł Możejko, Mateusz Zawadzki
and Elżbieta Ptasińska-Denga
Atomic Physics Division, Department of Atomic Physics and Luminescence, Faculty of Applied Physics
and Mathematics, Gdańsk University of Technology, 80-233 Gdańsk, Poland
E-mail: [email protected]
Received 12 December 2012, in final form 30 January 2013
Published 7 March 2013
Online at stacks.iop.org/JPhysB/46/065203
Abstract
Cross sections, both experimental and theoretical, are reported for electron scattering from
1-pentene (C5 H10 ) molecules. Absolute grand-total cross sections (TCSs) were measured at
electron impact energies ranging from 1 to 300 eV, using a linear electron-transmission
technique. The dominant behaviour of the experimental TCS energy function is a distinct
asymmetric enhancement with the maximum located around 6.5 eV. Discernible are also three
weak TCS structures: a small peak in the vicinity of 1.8 eV and two broad shoulders located
between 10 and 30 eV. The additivity rule was employed to calculate the elastic cross section
(ECS) from 20 to 3000 eV, while the binary-encounter-Bethe approach was used for the
computation of the ionization cross section (ICS), from the threshold up to 3000 eV. Within 30
and 300 eV, the sum of computed cross sections (ECS+ICS) quite reasonably reproduces the
experimental TCS values. Comparison is also made between the experimental TCS energy
curve for 1-pentene (H2 C=CH–(CH2 )2 CH3 ) and those measured for the ethylene (H2 C=CH2 )
molecule and its substituted derivatives: propene (H2 C=CH–CH3 ) and 1-butene
(H2 C=CH–CH2 CH3 ).
(Some figures may appear in colour only in the online journal)
1. Introduction
tests of the reliability of theoretical models and computational
procedures used in the electron-scattering calculations. In spite
of continuous interest in the electron-driven processes for
media containing hydrocarbons, the data for somewhat more
complex compounds still remain fragmentary (see Itikawa
2000–2003 and Raju 2012).
For 1-pentene molecules (see figure 1), the electronscattering results available in the literature are very scarce,
and absolute scattering intensities are entirely absent. The only
e− –1-C5 H10 experiment has been carried out very recently by
Aflatooni et al (2010) at low impact energies, within 1–5 eV.
They noted the resonant structure at around 1.8 eV in the
derivative with respect to the energy of the electron beam
current transmitted through 1-pentene in the gas phase.
In this paper, we present the absolute electron-scattering
grand -TCSs for 1-pentene molecules measured from 1 to
300 eV, and the total elastic cross section (ECS) and
Modelling and controlling electron-assisted processes in
various media is of great importance in many areas of science
and nowadays technology. For this purpose, the comprehensive
set of reliable electron-scattering cross sections and reaction
rates for atoms and their aggregates is required. The grand total cross section (TCS), the sum of integrated cross sections
for all scattering channels, is that scattering quantity which
can be determined with good accuracy, usually in absolute
scale, without any normalization procedures. Thanks to its
reliable absolute value, the experimental TCS can be used
as a calibration standard or upper limit reference for the
normalization of particular cross sections, which are usually
taken only in arbitrary units, as well as for the reasonable
estimation of scattering quantities difficult to obtain. The
TCS may also serve as one of the ranges of experimental
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J. Phys. B: At. Mol. Opt. Phys. 46 (2013) 065203
Cz Szmytkowski et al
and eventually detected by a Faraday cup. An intensity of the
ambient magnetic field along the electron trajectory is reduced
to less than 100 nT. This ensures that the trajectories of the
unscattered electrons are straight lines within the scattering
and the detector volumes.
The acquisition of data, necessary for the TCS derivation,
and their processing are under the control of a personal
computer. In our experiment, the quantities used in the BBL
formula are taken directly; therefore, the TCS values presented
in this work are in absolute scale. The statistical uncertainties
(one standard deviation of the weighted mean value) of the
TCS values are about 2% below 2 eV, while they do not
exceed 1% over the whole remaining range of the electronimpact energies applied.
Recent investigations show that in spite of a great care
declared in the transmission experiments, the TCSs values
obtained in different laboratories can differ even by a factor of
2 (see in Khakoo et al 2009). Therefore, for the reliability
of the experimental TCSs, it is very important to single
out, and if possible to reduce, these effects which may
systematically overcharge the measurements of particular
quantities necessary for the TCS determination (Bederson and
Kieffer 1971). A significant error in the transmission method
is connected with a fact that the electron detector does not
distinguish projectiles scattered elastically into small forward
angles from those not scattered. Due to this forward scattering
effect, the measured intensity of the transmitted electron
current, Ip (E ), is always overestimated leading to systematic
lowering of the measured TCS with respect to its exact value.
This effect can lead to significant changes in the magnitude
of the measured TCS and, as shown by Sullivan et al (2011),
also in the shape of the TCS energy dependence, especially at
low electron-impact energies. Based on the scattering region
geometry and the available differential cross section data for
molecules with the electric dipole moment similar to that of
1-pentene (cf table 3), we have estimated that the inability to
discriminate against electrons scattered elastically through the
small angles in the forward direction may lower our measured
TCSs between 5 and 50 eV by about 2%; below 2 eV the TCS
lowering may be as high as 4%. The reported TCS data are not
corrected for the forward scattering effect.
The inevitable effusion of target molecules through the
scattering cell orifices means that a notable number of
scattering events may also occur outside the reaction volume.
It is found, following the electron pathlength calculations
of Nelson and Colgate (1973), that the denominator pL in
the BBL formula is equal to, within 2%, the product of the
geometrical distance (= 30.5 mm) between the entrance and
exit cell apertures and the pressure measured in the centre of
the cell. The pressure of the sample in the scattering volume
was kept within 80–180 mPa; at these values no systematic
variation of measured TCSs with the target pressure was
observed.
The electron impact energy scale can be determined
against the 2.3 eV resonant structure in molecular nitrogen,
with an accuracy better than 0.1 eV. However, due to
growing contamination of the electron optics elements with the
1-pentene molecules, a drift in energy up to 0.1 eV has
Figure 1. Schematic geometry of 1-pentene, H2 C=CH–(CH2 )2 CH3 ,
molecule.
ionization cross section (ICS) calculated at intermediate and
high energies. The sum, ECS + ICS, of calculated cross
sections extends the electron-scattering data for 1-pentene
far beyond the experimental TCS energy range, up to several
keV. In addition, the measured and theoretical TCS values are
confronted with the TCS estimations, based on two different
empirical formulas developed for hydrocarbons by Floeder
et al (1985), Wickramarachchi et al (2009) and Ariyasinghe
and Villela (2010). Finally, we compare the experimental TCS
for 1-pentene with those measured earlier for smaller members
of straight-chain ethylenic series: ethylene, propene and 1butene. Some similarities and differences in the TCS energy
dependence for this series are also pointed out and discussed.
2. Experimental method and procedures
In this work, the ratio of electrons transmitted through the
scattering cell in the presence and absence of target in the gas
phase is used to determine the absolute electron-scattering
grand -TCSs according to the Bouguer–de Beer–Lambert
(BBL) attenuation relationship
√
k Tt Tm I0 (E )
ln
,
TCS(E ) =
pL
Ip (E )
where k is the Boltzmann constant; I0 (E ) and Ip (E ) are the
intensities of unattenuated and attenuated transmitted electrons
of energy E, respectively; L is the length of the effective
electron pathway within the target; p is the target pressure
in the cell measured with the MKS capacitance manometer.
As the temperature of the target cell, Tt , measured in the
course of experiment, differs by about 5–25 K from that of
the manometer head, Tm = 322 K, the thermal transpiration
effect (Knudsen 1910) is accounted for.
The apparatus and procedure used in the reported
experiment were based on the electrostatic electron
spectrometer extensively used in series of TCS measurements
performed in our laboratory and described in detail elsewhere
(e.g. Szmytkowski et al 1997, Domaracka et al 2006);
therefore, only a brief summary is given here. The electron
beam is formed by an electron optics system, which comprises
an electron gun followed by an energy dispersing 127◦
cylindrical electrostatic deflector and a zoom lens assembly.
The electrons of desired energy E (E 0.1 eV,
FWHM) are passed through the scattering chamber. Those
which leave the reaction volume through the exit orifice are
energetically discriminated with a retarding potential analyser
2
J. Phys. B: At. Mol. Opt. Phys. 46 (2013) 065203
Cz Szmytkowski et al
been observed during the present long-lasting experiment.
That may somewhat distort the TCS structures visible at low
impact energies. As the contamination lowered gradually the
intensity of the primary electron current, one or two cleanings
of electron optics were necessary in the course of experiment.
A sample of 1-pentene from Sigma-Aldrich with a stated
purity of 98% was, directly before measurements, subjected
to several liquid-nitrogen freeze-pump-thaw cycles to remove
dissolved air and other volatile impurities. To allow stable
experimental conditions, the target handling system was kept
at elevated temperature of about 315 K. Other possible TCS
systematic errors, related to quantities taken in the course
of experiment, are estimated to be less than 1% each. The
overall systematic uncertainty of our absolute TCSs, evaluated
as a sum of all individual potential systematic uncertainties,
amounts to 9–11% below 2 eV, 8–9% between 2 and 4 eV,
decreasing gradually to 4–6% within 4–200 eV, and increasing
again to 6–8% at higher energies applied.
where E is an energy of the incident electron; the elastic atomic
cross section for the ith atom of the target molecule, σiA (E ),
has been derived according to
⎛
⎞
lmax
∞
4π
(2l + 1) sin2 δl(B) ⎠ ,
σ A = 2 ⎝ (2l + 1) sin2 δl +
k
l=lmax
l=0
√
where k = 2E is the wave number of the incident electron;
note that in this section atomic units are used.
To obtain phase shifts, δl , the radial Schrödinger equation
d2
l(l + 1)
2
−
− 2(Vstat (r) + Vpolar (r)) + k ul (r) = 0
dr2
r2
has been solved numerically under the boundary conditions
ul (0) = 0,
where ĵl (kr) and n̂l (kr) are the Riccati–Bessel and Riccati–
Neumann functions, respectively. The phase shifts are
connected with the asymptotic form of the wavefunction, ul (r),
by
Bl
tan δl = .
Al
Like in our earlier studies (Możejko et al 2002, 2012a,
Szmytkowski et al 2010), in the present calculations the
electron–atom interaction has been represented by the static,
Vstat (r) (Salvat et al 1987) plus polarization, Vpolar (r) (Padial
and Norcross 1984) model potentials only. The respective
potentials are given by the following expressions:
3. Theoretical
To obtain more information on the electron scattering from
the 1-pentene molecule, we have extended our experimental
TCS studies towards the theoretical considerations concerning
the elastic and ionization processes. We have calculated
the ECS for the intermediate-energy (20–3000 eV) electron
collisions. Cross sections for electron impact ionization (ICS)
have been calculated for energies ranging from the ionization
threshold at 9.274 up to 3000 eV. Having in hand the total
ECS and the ICS over a wide energy range, we can predict
approximate values of the TCS even far beyond the range of
the present experiment, as the sum of the ECS and the ICS.
Because at intermediate and high energies, the contribution
from the ionization and elastic channels dominates the electron
scattering from molecular targets, such simple approximation
can yield reasonable electron-scattering TCS data at higher
energies for quite complex molecules (cf Możejko et al 2006a,
2006b, Szmytkowski et al 2010, Możejko et al 2012a).
The ECS for electron scattering from 1-pentene has
been calculated with the additivity rule (AR) method
(Mott and Massey 1965) at the static+polarization level of
approximation, while the electron-impact ICSs have been
obtained within the binary-encounter-Bethe (BEB) formalism
(Kim and Rudd 1994, Hwang et al 1996). In this paper, we
provide a brief description of the theoretical methods and
computational procedures used, since they have been presented
in more detail in our earlier studies (e.g. Możejko et al 2002,
Możejko and Sanche 2003).
In the AR approximation, the electron–molecule collision
is reduced to the problem of scattering by individual atoms,
the constituents of the target molecule. In this approach, the
total ECS for electron scattering from the molecule is given
by
σ (E ) =
N
r→∞
ul (r) −→ Al ĵl (kr) − Bl n̂l (kr),
Vstat (r) = −
3
Z
Am exp(−βm r),
r m=1
where Z is the nuclear charge of the atom and Am and βm
are parameters obtained by numerical fitting to the numerical
Dirac–Hartree–Fock–Slater screening function (Salvat et al
1987):
ν(r)
r rc
,
Vpolar (r) =
−α/2r4 r > rc
where ν(r) is the free-electron-gas correlation energy (Pedrew
and Zunger 1981), α is the static electric dipole polarizability
of atom and rc is the first crossing point of the curves of ν(r)
and −α/2r4 (Zhang et al 1992).
According to the BEB model (Kim and Rudd 1994,
Hwang et al 1996), the electron-impact ICS per molecular
orbital is given by
1
ln t
1
ln t
S
BEB
1− 2 +1− −
,
=
σ
t +u+1 2
t
t
t +1
where u = U/B, t = T/B, S = 4π a20 NR2 /B2 , a0 = 0.5292 Å,
R = 13.61 eV and T is the energy of the impinging electron.
Finally, the total cross section, σ Ion , for electron-impact
ionization of molecule can be obtained as
nMO
σ Ion =
σiBEB ,
i=1
where nMO is the number of the given molecular orbital,
B is the electron binding energy, U represents the kinetic
energy of the orbital and N is the orbital occupation number.
Those quantities have been calculated for the ground state
σiA (E ),
i=1
3
J. Phys. B: At. Mol. Opt. Phys. 46 (2013) 065203
Cz Szmytkowski et al
Table 1. Absolute experimental electron-scattering total cross sections (TCSs) for the 1-pentene molecule; in units of 10−20 m2 .
E (eV)
TCS
E (eV)
TCS
E (eV)
TCS
E (eV)
TCS
E (eV)
TCS
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
40.2
39.8
40.4
41.4
42.2
43.4
44.3
45.3
45.5
45.1
45.5
46.7
47.7
48.9
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.2
3.4
3.6
3.8
4.0
4.5
5.0
50.0
50.7
51.3
51.8
52.3
53.0
54.1
55.7
57.5
59.0
60.0
61.4
63.2
65.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
11
12
13
67.1
67.8
68.1
67.7
66.2
64.8
64.0
62.1
60.7
60.4
60.5
60.5
59.9
59.2
15
17
19
21
23
26
28
30
35
40
45
50
60
70
57.9
57.0
56.8
56.7
56.2
55.3
54.5
53.8
52.4
50.1
48.3
46.9
44.2
41.2
80
90
100
110
120
140
160
180
200
220
250
300
38.7
37.0
35.2
33.5
32.0
29.2
27.2
25.4
24.1
22.5
20.9
18.5
Figure 3. Comparison of total absolute cross sections (TCSs)
measured in our laboratory for electron scattering from the ethylene
molecule and ethylene derivatives: H2 C=CH2 , (), Szmytkowski
et al (2003); H2 C=CH–CH3 , (), Szmytkowski and Kwitnewski
(2002); H2 C=CH–CH2 CH3 , (◦), Możejko et al (2012b);
H2 C=CH–(CH2 )2 CH3 , ( •), present.
Figure 2. Cross-sections for electron scattering from the 1-pentene
molecule. Experimental: (•), TCS, present; error bars represent
overall, systematic plus statistical, uncertainties. Theoretical: (– – –),
total ECS calculated with the AR approach, present; (– · · – ), ICS in
the BEB approximation, present; (—), ECS + ICS, present.
Empirical: (– · –), TCS generated using the Floeder et al (1985)
formula; (· · · · · ·), TCS based on the expression of Wickramarachchi
et al (2009) and Ariyasinghe and Villela (2010).
of the experimental TCS are listed in table 1, while table 2
presents results of the ECS and ICS computations up to
3 keV. Figure 2 shows the variation of the absolute electronscattering TCS for the 1-pentene molecule measured in this
work over the incident energy range from 1 to 300 eV. The
computed cross sections ECS, ICS, and ECS + ICS are also
exposed in figure 2. To complete the electron-scattering data
for 1-pentene, the TCSs estimated using two totally different
empirical expressions—developed for hydrocarbons (Floeder
et al 1985, Wickramarachchi et al 2009, Ariyasinghe and
Villela 2010), are included in figure 2 as well. No other absolute
electron-scattering data for 1-pentene, either experimental or
theoretical, are available in the literature for the comparison.
In addition, in figure 3, we compare the TCS energy
function for the 1-pentene molecule with TCSs for the ethylene
molecule and some ethylene straight-chain derivatives
(propene and 1-butene), in which one hydrogen atom fixed
to the C=C double bond in the H2 C=CH2 molecule is replaced
with the functional unit (figure 4). Note that every molecule
of the geometrically optimized 1-pentene molecule with the
Hartree–Fock method using the GAUSSIAN code (Frisch et al
2003), and Gaussian 6-31 G basis set. Because energies of
the highest occupied molecular orbitals obtained in this way
usually can differ from experimental ones by about 1 eV,
we also performed outer valence Green function calculations
of correlated electron affinities and ionization potentials
(Cederbaum 1975, von Niessen et al 1984, Ortiz 1988,
Zakrzewski and von Niessen 1994) using the GAUSSIAN.
4. Results and discussion
In this section, we present the absolute grand -total electronscattering cross sections (TCSs) for 1-pentene measured
with the linear transmission method. We also report our
computations for 1-pentene: the total ECS using the AR
and the ICS, with the BEB approach. The numerical data
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J. Phys. B: At. Mol. Opt. Phys. 46 (2013) 065203
Cz Szmytkowski et al
Table 2. Ionization (ICS) and integral elastic (ECS) cross sections calculated for electron impact on H2 C=CH–(CH2 )2 CH3 molecules; in
units of 10−20 m2 .
E (eV)
ICS
E (eV)
9.274
10
11
12
13
14
15
16
17
18
19
0
0.122
0.297
0.565
1.038
1.59
2.23
2.92
3.64
4.32
4.98
20
22
25
27
30
35
40
45
50
55
60
65
70
75
(a)
(c)
(b)
(d)
ICS
ECS
E (eV)
ICS
5.62
6.75
8.26
9.10
10.2
11.7
12.7
13.4
13.9
14.2
14.4
14.5
14.5
14.5
64.0
58.5
52.1
48.6
44.4
39.0
35.0
32.0
29.5
80
85
90
95
100
110
120
140
160
180
200
220
250
300
14.4
14.3
14.2
14.1
14.0
13.7
13.3
12.7
12.0
11.4
10.9
10.4
9.69
8.73
25.8
23.1
ECS
21.1
19.4
18.1
16.9
16.0
14.4
13.1
12.1
11.3
10.5
9.61
8.42
E (eV)
ICS
ECS
350
400
450
500
600
700
800
900
1000
1200
1500
2000
2500
3000
7.95
7.30
6.75
6.29
5.53
4.95
4.48
4.10
3.79
3.37
2.75
2.18
1.82
1.56
7.51
6.79
6.20
5.70
4.93
4.34
3.89
3.52
3.22
2.76
2.29
1.82
1.58
1.47
for detecting weak structures. Figure 3 shows that similar,
however more distinct structures in the TCS curves located
within 1.5 and 2.5 eV have also been observed for the ethylene
molecule (H2 C=CH2 ) and its straight-chain derivatives:
propene (H2 C=CH–CH3 ) and 1-butene (H2 C=CH–CH2 CH3 ).
The origin of these structures for molecules of the ethylenic
series has been attributed (for references see Możejko et al
2012b) to the attachment of the impinging electron into the
lowest unoccupied π ∗ molecular orbital associated with the
C=C bond, resulting in the formation of the π ∗ temporary
negative ion state (the π ∗ shape resonance).
Referring to figure 3, one can see also that the low-energy
resonant maximum shifts slightly towards higher energies
(from 1.8 to 2.3 eV) while going from ethylene to 1-butene.
However, for the largest member of the investigated series,
1-pentene, this structure is located at the same energy as for
the smallest one, ethylene. It is also clear that the intensity of
the lowest TCS resonance with respect to the TCS background
decreases with the increasing size of the functional unit
replacing one hydrogen atom in the ethylene molecule.
The broad TCS hump for 1-pentene, centred near 6.5 eV,
resembles those observed for many other targets studied so far,
among them hydrocarbons. Appearance of this maximum has
been explained by the elastic scattering with some contribution
from a number of weak inelastic components allowed at these
energies; among them are also the resonant ones. As figure 3
shows, the main TCS maximum shifts to lower energies across
the ethylenic family: it is located near 9 eV for ethylene and
propene, at 8 eV for 1-butene and close to 6.5 eV for the longest
member of the investigated series, 1-pentene. Such behaviour
differs from that for series of alkanes, for which the location of
the main maximum practically does not change (e.g. Sueoka
et al 2005).
Further inspection of figure 3 reveals that the ratio of the
intensity of the low-energy structure (within 1–3 eV) to the
intensity of the next TCS maximum (located between 6–9 eV)
drastically decreases across the ethylenic derivatives with the
increase of the substituent group. While for ethylene these
two TCS features have similar amplitude, for 1-pentene the
ratio falls down to about 1/20 only. Such behaviour might
be due to the different charge redistribution on the site of the
Figure 4. Schematic geometry of (a) the ethylene (H2 C=CH2 )
molecule and its straight-chain derivatives: (b) propene
(H2 C=CH–CH3 ), (c) 1-butene (H2 C=CH–CH2 CH3 ) and
(d) 1-pentene (H2 C=CH–(CH2 )2 CH3 ).
in this series (Cn H2n ) has one carbon atom and two atoms of
hydrogen more than the preceding one.
As shown in figure 2, the measured TCS energy
dependence for the electron scattering from the 1-pentene
molecule is dominated by a prominent, very broad and highly
asymmetric enhancement peaking between 6 and 7 eV. From
the lowest energies applied, the TCS increases rapidly from
about 40 × 10−20 m2 near 1 eV to above 68 × 10−20 m2 in the
maximum around 6.5 eV. From this energy upwards, the TCS
systematically decreases to about 18 × 10−20 m2 near 300 eV.
When considering figure 2 in more detail, one can discern
some weak structures superimposed on the TCS enhancement.
Due to the lack of more comprehensive investigations on the
electron–1-pentene scattering, we shall discuss the origin of
the TCS features based on comparative studies mainly.
A weak feature, with the maximum of about 0.5 ×
10−20 m2 above the TCS background and the width of about
0.6 eV, is visible on the low-energy rising slope of the
TCS curve, in the vicinity of 1.8 eV. In this energy region,
Aflatooni et al (2010) observed a sharply outlined structure in
the derivative with respect to energy of transmitted electron
beam current through 1-pentene in the gas phase. A clearer
appearance of the 1.8 eV feature in their experiment is due
to the fact that the derivative technique is especially suitable
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J. Phys. B: At. Mol. Opt. Phys. 46 (2013) 065203
Cz Szmytkowski et al
measured TCS values. The differences between calculated and
experimental cross sections exceed the estimated uncertainties.
The experimental and calculated values differ at most, by about
9%, around the ICS maximum, near 70 eV. Such a discrepancy
can suggest a considerable role of other inelastic processes
in the electron scattering from 1-pentene; among them is
a multiple ionization—not taken into account in the BEB
approach. Below 30 eV, the present calculations (ECS + ICS)
significantly overestimate the experimental TCS values. Thus,
one would expect that at such low energies the foundations of
the AR approach used to the ECS calculations are not fulfilled
completely.
Finally, we make some comments on TCS values for
1-pentene which we generated using the empirical expressions,
developed for hydrocarbons by Floeder et al (1985) and more
recently by Wickramarachchi et al (2009) and Ariyasinghe and
Villela (2010). Expression of Floeder et al correlates the TCS
with the collisional energy and with the number of molecular
electrons. Wickramarachchi et al and Ariyasinghe and Villela
relate the TCS to energy of the projectile electron and the
atomic constituents of hydrocarbon molecules. As one can see
in figure 2, the empirical TCS for 1-pentene, obtained using
the formula of Floeder et al (1985) are in reasonable agreement
with our experimental TCS between 30 and 300 eV and
nearly coincide with the theoretical values within 80–300 eV.
Such good agreement below 100 eV is somewhat surprising,
as Floeder’s formula was developed based on fits to their
experimental TCS data for hydrocarbons between 100 and
400 eV only. On the other hand, the empirical TCSs based on
the expression of Ariyasinghe agree well with the experiment
above 200 eV and practically converge towards our theoretical
TCS calculations above 400 eV. These two formulae look
to be complementary; Floeder’s one gives reasonable TCS
values for 1-pentene and smaller alkenes at low-intermediate
energies, while Ariyasinghe’s expression predicts well the TCS
for higher energies.
Table 3. Selected parameters of alkene compounds: permanent
electric dipole moment, μ, and electrical polarizability, α (from
Lide 1995); the gas-kinetic collisional cross-section, σgk , estimated
from van der Waals constant b (Lide 1995).
Molecule
μ
(Debye)
α
(10−30 m3 )
σgk
(10−20 m2 )
H2 C=CH2
H2 C=CH–CH3
H2 C=CH–CH2 CH3
H2 C=CH–(CH2 )2 CH3
0
0.366
0.359a ; 0.438b
0.5
4.25
6.26
7.97; 8.52
9.65
10.1
12.7
15.3
17.9
a,b
For the skew and syn conformer of the 1-butene molecule,
respectively.
C=C bond across ethylenic derivatives and, in consequence,
different interaction between the substituent group orbitals and
the orbitals of the double bond (Libit and Hoffmann 1974).
On the descending side of the broad TCS enhancement for
1-pentene, two shoulders are visible: the first one is located
around 11 eV and the next, much broader, is spanned between
15 and 30 eV. Such shoulders are also perceptible in TCS
curves for smaller alkenes (figure 3). However, while barely
distinguishable for ethylene, the shoulders become more and
more distinct as the compounds increase in length. Similar
behaviour of TCS curves in the energy region beyond the
main TCS maximum has already been observed for a series
of alkane molecules (Sueoka et al 2005). The shoulders in
this energy range were attributed to contribution from the
direct scattering overlapping with numerous weak resonances
associated with available unoccupied molecular orbitals in
the low-intermediate energy range (e.g. Lopes et al 2004).
Interestingly, the location of these shoulders moves towards
lower energies for successive ethylenic derivatives.
It is apparent from figure 3 that above 3 eV the magnitude
of the TCS generally increases across the investigated series of
targets. The substitution of ethylene with functional units
of the increasing length (figure 4) increases the size of the
resulting target molecule that, in consequence, reflects in the
increase of the respective electron-scattering TCS values. It is
interesting that above 30 eV, the increase of the TCS at the
given electron impact energy is nearly the same when going
across the ethylenic series which suggests that the impinging
electrons of intermediate and of high impact energy perceive
the molecule rather as an aggregate of individual atoms. For
the lowest impact energies, deviations from this general TCS
trend can be related to more subtle differences in the structure
of molecules and different distribution of the electric charge
within the molecular target (table 3). This leads to differences
in the low-energy electron–molecule interaction and reflects
in the shape (e.g. resonant structures) as well in the magnitude
of the TCS curve (direct scattering). Finally, it is worth noting
that the gas-kinetic collisional cross sections (σgk ) for each
next molecule in the series, going from ethylene to 1-pentene,
increases by about 2.6 × 10−20 m2 (see table 3).
Regarding the computations, figure 2 shows that within
30 and 300 eV the general energy dependence of the computed
TCS (sum of the total ECS and ICS) for 1-pentene is similar
to that of the experimental TCS. However, in this energy
range, the ECS + ICS results lie systematically below the
5. Summary
Absolute total cross sections (TCSs) for electron scattering
from the 1-pentene molecule, H2 C=CH–(CH2 )2 CH3 , have
been measured at impact energies from 1 to 300 eV. The TCS
energy function for 1-pentene exhibits a very weak low-energy
resonant maximum located near 1.8 eV and a very broad
enhancement peaking around 6.5 eV; above 7 eV the TCS
continuously falls down. In the overlapping energy range, the
sum of calculated elastic cross section (ECS) and ionization
cross section (ICS) reasonably reproduces the experimental
TCS data. One can expect, therefore, that also beyond the
energy range of the present TCS experiment, above 300 eV, the
calculated ECS + ICS values represent the TCS satisfactorily.
Finally, we observe general similarity in the shape of the
TCS curves for the ethylene (H2 C=CH2 ) molecule and its
open-chain derivatives: for propene (H2 C=CH–CH3 ), 1-butene
(H2 C=CH–CH2 CH3 ), as well as for 1-pentene. The magnitude
of the TCS for a series of compared molecules increases with
the increase of the size of molecular target.
6
J. Phys. B: At. Mol. Opt. Phys. 46 (2013) 065203
Cz Szmytkowski et al
Acknowledgments
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The work was supported by the Polish Government (MNiSzW)
research funds for 2011–2012. Authors acknowledge Czesław
Jakonis and Bogdan Ruzik, from the Faculty Mechanical
Workshop, for their technical contribution. The numerical
computations have been performed at the CI TASK in Gdańsk.
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