Chapter 4
Chapter .4.
Electron interaction with c3 / c5
hydrocarbons – present studies
4.1 Introduction
Hydrocarbons play an important role for plasma diagnostics as impurities in the
Tokamak fusion divertor, as seed gases for production of radicals and ions in low
temperature plasma processing, and in many other fields [1]. Carbon based material is
one of the most widely used material for a divertor plate and wall of the magnetically
confined fusion devices. In a next step device, such as ITER, for steady state
operation, it is very important to estimate lifetime of carbon plasma facing
components. Chemical sputtering reduces their lifetime and increases fuel retention
via redeposition [2]. Also electron scattering data for hydrocarbons are important for
modeling electron assisted processes ranging from fuel combustion to interstellar
clouds. Although several experimental investigations of electron interactions with
hydrocarbon molecules have appeared in the literature, the available results are still
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Chapter 4
fragmentary and mostly concern the simplest compounds like CH 4 [3]. In this chapter
we have focused on few molecules containing 3 or 5 carbon atoms, denoted as C3/C5
hydrocarbons, whose TCS (QT) data are available in literature but electron impact
ionization cross sections (Qion) data are scarce.
Towards a literature survey, let us note that in 1994 Nishimura and Tawara [4]
measured total electron impact ionization cross sections for various simple
hydrocarbon molecules from threshold up to 3 keV. They [4] measured the Qion for
C3H6 isomers i.e. Cyclopropane and Propene having the same number of atoms but
different molecular structure. Kim and Irikura [5] have calculated BEB cross sections
for different hydrocarbons including Allene and Propyne i.e. C3H4 isomers, and also
for Propene i.e. C3H6 molecule. Kwitnewski et al. [6] have proposed a regression
formula which relates the grand total cross section and the total ionization cross
section for electron scattering and they have also calculated BEB cross sections for
different isomers of C3 and C4 hydrocarbons using the formula given in [5]. Beran and
Kevan [7] have measured Qion for a large number of molecules, including Propene and
Cyclopropane, at 70 eV electron impact. Also Szmytkowski et al. [8] have calculated
ionization cross sections for C5H10 i.e. 1 Pentene, for which data are rather scarce. In
spite of continuous interest in the electron driven processes for media containing
hydrocarbons, the data for somewhat more complex hydrocarbons still remain
fragmentary. So it is worthwhile to calculate Qion for C5H10 isomers too. It appears
from the above review that the calculations for the targets presented in this chapter are
significant. We have calculated here electron impact ionization cross sections C 3H4
isomers (Allene, Propyne and Cyclopropene), C3H6 isomers (Propene and
Cyclopropane) and C5H10 isomers (1 Pentene and Cyclopentane). A slight difference
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Chapter 4
in the total ionization cross sections for the different isomers can be caused by the
different dissociative pathways of the two molecules. It is well known that the parent
ionization of complex hydrocarbons accounts for only a small fraction of the total
ionization cross sections, while dissociative ionization dominates the ionization
process. The dissociative channels for the different isomers can be expected to differ
for different bonding resulting from different geometry, and this leads to appearance
of various fragment ions at different energies [9]. In this backdrop we have also
compared Qion for isomers of C3H4, C3H6 and C5H10 by electron impact.
In this theoretical work again we have employed the Complex Scattering Potential
ionization contribution (CSP-ic) method developed and applied successfully by us,
over a wide range of molecular targets in the recent years [10-17]. Later on we came
to know about recent work on computation of electron impact total and differential
cross sections for allene [18] i.e. one of the present target, from 0.1 to 2000 eV
energy. This also reflects the importance of the present study.
The underlying theoretical method has been introduced in chapter 2 and few
important present results are already discussed in chapter 3. The present calculations
have been performed in the group additivity approach, as has been necessary for the
large polyatomic molecules, each consisting of several functional chemical groups.
Relevant properties of the target molecules viz., geometry, first ionization threshold
and bond lengths are given in table 4.1. Notably, in each case the C - C bond-length is
relatively larger. All these data are obtained from standard literature [19].
Section 4.2 describes the brief theory used here, followed in the next sections, by the
results and discussions along with conclusions.
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Chapter 4
Table 4.1 Properties of the targets [19]
Target
Chemical
Molecule
Formula
Allene
C3H4
Geometry
CH 2  C  CH 2
Ionization
Bond
Energy
Length
(eV)
(Å)
9.692
C-H 1.087
C=C 1.308
Propyne
C3H4
CH 3  C  CH
10.36
C-H 1.096
C≡C 1.207
Cyclopropene
c-C3H4
9.67
C=C 1.296
C-H 1.088
Propene
C3H6
CH 3  CH  CH 2
9.73
C=C 1.353
C-H 1.117
Cyclopropane
c-C3H6
1 Pentene
C5H10
CH 2  CH  CH 2  CH 2  CH3
9.86
C-H 1.083
9.49
C=C 1.34
C-H 1.089
Cyclopentane
c-C5H10
10.33
C-H 1.114
4.2 Theory
SCOP method [10-17] used in present calculation is one of the simpler approaches to
obtain a family of cross sections. As already stated the Qion are extracted from Qinel by
CSP-ic method. The present chapter mainly includes carbon molecules like C3Hx and
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Chapter 4
C5Hy. The basic inputs of the CSP-ic method i.e. charge density of the target, is
calculated by dividing them in different functional (chemical) groups, and this
depends on the molecular geometry. Calculated cross sections of all the functional
groups in a molecule are added and further calculations start with various interaction
potentials like static, exchange, polarization for the real part VR and absorption
potential as the imaginary VI.
V (r, Ei )  VR (r, Ei )  iVI (r, Ei )
(4.2.1)
VI also depends on the threshold energy parameter ∆, as discussed in the previous
chapters. Then calculation proceeds by different numerical methods like Numerov
method (or the Runge - Kutta method) to solve the Schrödinger equation (or Calogaro
equation). Thus in a standard formulation, we get a family of cross sections like Qel
(total elastic cross sections), Qinel (total inelastic cross sections) and QT (total cross
sections). We have,
QT  Qel  Qinel
(4.2.2)
The main objective of the present study is to find electron impact ionization cross
sections Qion for hydrocarbon isomers. With this aim, we partition the inelastic cross
section as given below.
Qinel   Qion   Qexc
(4.2.3)
The total cross sections, denoted simply as Qion, can be extracted from the total
inelastic cross sections with some reasonable approximations. From our previous
experience and accord of our data for standard atomic molecular targets, we are
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Chapter 4
considering roughly 70% contribution of Qion at peak energy EP of the inelastic cross
section Qinel. By following steps as mentioned above, the Qion for different functional
groups can be obtained. Finally the Qion of all the functional groups are added to get
the Qion of a particular molecule, in the modified group additivity method. As we are
using group additivity, bifurcation of the molecule in functional groups can play an
important role to get accurate values of cross sections.
We emphasize that the calculation of Qion of all the functional groups is done
individually using the ionization energy of the molecule itself. The details of the
group additivity approach are already discussed in the previous chapters. In this
calculation the relative bond-lengths are important in formulating the group additivity
rule (see table 4.1). Also, bond-length effect can cause a slight change in magnitude
of Qion for different isomers.
4.3 Results and discussions
In this chapter, the CSP-ic method followed by group additivity approach has been
adopted to determine electron impact total ionization cross sections for various C3/C5
hydrocarbon isomers. We discuss below our results obtained for these targets
separately, together with comparisons as available.
4.3.1 CH 2  C  CH 2 (C3 H 4 ) Allene
In this molecular target, the C - C bond-lengths are larger than the C - H bond-lengths,
and hence the three carbon atoms serve as approximately independent scattering
centres. The functional groups are the two CH2 groups plus the third carbon atom. The
Qion for all the three scattering centres are evaluated at the ionization energy of the
Allene molecule itself.
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Chapter 4
Figure 4.1: Total ionization cross section for e- - Allene, C3H4. Red solid line; the present
Qion, black solid line; Qion - BEB values of Kim and Irikura [5] and blue solid line with
square; Qion semi-empirical data of Kwitnewski et al. [6]
Electron impact ionization cross section for the C3H4 (Allene) molecule is plotted
along with compared data in figure 4.1. The present Qion matches well with the BEB
cross sections calculated by Kim and Irikura [5] at low and high energy region
whereas at intermediate energy the present Qion are relatively higher. A small shift in
the magnitude at lower energy, along with a small difference in the peak position is
found to be due to the difference in the ionization threshold considered by us for this
molecule. The ionization potential used in present calculation is 9.692 eV [19] while
in the BEB calculation [5] it is 10.22 eV. A good general accord within the error bars
is found with an indirect data-set calculated through the semi empirical regression
formula, by Kwitnewski et al. [6].
The Qion for e- - scattering with Allene are listed in table 4.2.
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Chapter 4
4.3.2 CH 3  C  CH (C3 H 4 ) Propyne
Figure 4.2: Total ionization cross section for e- - Propyne, C3H4. Red solid line; the
present Qion, black solid line; Qion - BEB values of Kim and Irikura [5] and blue solid line
with square; Qion semi-empirical data of Kwitnewski et al. [6]
Figure 4.2 shows the electron impact ionization cross section for the C 3H4 (Propyne)
molecule. The same comparisons are made as in figure 4.1. The present Qion matches
well with the BEB cross sections calculated by Kim and Irikura [5] at all range of
energies except for intermediate energy region. The ionization energy used for present
Qion is 10.36 eV while for BEB calculation it is 10.48 eV. Here the present Qion are
found to merge with BEB cross sections at lower and higher energies. The present
result has a good general agreement with the regression formula, a semi-empirical
approximation made by Kwitnewski et al. [6], in the entire range of energy within the
error bars, of course with a shift in a peak. The Qion data for allene and propyne from
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Chapter 4
[6] are not available directly, so these data are generated from the results provided in
[6]. Present Qion data for C3H4 isomers are listed in table 4.2. It appears that the semi
empirical formula [6] does not predict the peak correctly.
As no comparisons are available for the closed chain isomer of C 3H4 i.e.
Cyclopropene, its worth to record the data in tabulated forms (see table 4.2).
Table 4.2 Qion (Å2) for e- - C3H4 isomers
Ei
(eV)
Allene
Propyne
Cyclopropene
20
5.09
4.06
5.11
30
8.18
7.20
8.19
40
9.18
8.39
9.17
50
9.26
8.60
9.25
60
9.17
8.62
9.16
70
9.03
8.49
9.02
80
8.79
8.30
8.78
90
8.52
8.06
8.51
100
8.26
7.81
8.25
200
6.38
6.03
6.37
300
5.21
4.91
5.20
400
4.41
4.15
4.41
500
3.82
3.60
3.82
600
3.38
3.18
3.38
700
3.02
2.84
3.02
800
2.74
2.57
2.74
900
2.50
2.35
2.50
1000
2.30
2.16
2.31
2000
1.27
1.19
1.27
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Chapter 4
4.3.3 CH 3  CH  CH 2 (C3 H 6 ) Propene
Figure 4.3: Total ionization cross section for e- - Propene, C3H6. Red solid line; the
present Qion, black solid line; Qion - BEB values of Kim and Irikura [5], green triangles;
Qion by Nishimura and Tawara [4] and blue square; Qion at 70 eV by Beran and Kevan
[7]
As shown in figure 4.3 we have made the comparison of present Qion with other
available measurements and computed cross sections for C3H6 molecule i.e. Propene.
We find from [5, 19], that the ionization energies for present Qion and for BEB cross
sections by Kim and Irikura [5] are 9.73 and 9.95 in eV respectively. The BEB cross
sections by Kim and Irikura [5] are in accordance with present Qion at high energies
above the peak energy. Also, the present Qion matches well with Qion at 70 eV by
Bearn and Kevan [7]. Comparison of present Qion with Nishimura and Tawara [4]
reflects the very good merging within the error bars almost above the peak energy,
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Chapter 4
while the present results are higher at low to peak energy in comparison with [4, 5]
but agreeing with Beran and Kevan [7] at 70 eV.
4.3.4 (c  C3 H 6 ) Cyclopropane
Figure 4.4: Total ionization cross section for e- - Cyclopropane, c-C3H6. black solid line;
the present Qion, red triangles; Qion by Nishimura and Tawara [4] and blue square; Qion
at 70 eV by Beran and Kevan [7]
In figure 4.4 electron impact ionization for Cyclopropane (C 3H6) are reported. The
present Qion for Cyclopropane are compared with Nishimura and Tawara [4] from
threshold to 2000 eV and these [4] are little lower in the beginning i.e. from low to
peak energy region while the data [4] are a little higher in the high energy region.
Other comparison is made with a single point data of Qion by Bearn and Kevan [7] at
70 eV, which is higher compared to both present Qion as well as those of Nishimura
and Tawara [4]. We admit that discrepancies are observed in present comparisons,
these may be due to the approximations involved in the present calculations. The
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Chapter 4
present Qion data for C3H6 isomers both Propene and Cyclopropane are listed in table
4.3.
Table 4.3 Qion (Å2) for e- - C3H6 isomers
Ei
(eV)
Propene
Cyclopropane
20
5.56
5.07
30
9.01
8.21
40
10.13
9.15
50
10.33
9.18
60
10.21
9.14
70
10.05
9.01
80
9.77
8.77
90
9.46
8.50
100
9.16
8.23
200
7.05
6.18
300
5.74
4.99
400
4.85
4.21
500
4.21
3.64
600
3.71
3.22
700
3.32
2.88
800
3.02
2.61
900
2.74
2.39
1000
2.52
2.21
2000
1.38
1.24

4.3.5 Isomer effect (e  C3 H 4 )
It appears that the literature available for the electron impact ionization cross sections
for C3H4 is scarce. So just to get a rough estimation and also to reveal isomer and
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Chapter 4
bonding effect, it is of interest to compare present Qion for different C3H4 isomers. In
figure 4.5 all the calculated Qion for different C3H4 isomers are presented. We can see
that Qion for Allene and Cyclopropene are completely merged with each other at all
range of energies. This is obvious, as the ionization energy for Allene and
Cyclopropene are almost nearer i.e. 9.692 eV and 9.67 eV respectively (see table 4.1).
The ionization energy for the Propyne molecule is 10.36 eV, which can easily reflect
that their cross sections must be less than that of Allene and Cyclopropene. Also bond
effect (triple bond) can play a role in Propyne.
Though, isomer effect is rather weak for ionization cross sections it’s worthwhile to
have such comparison for providing more precise recommended data for them.
Figure 4.5: Isomer effect. Total ionization cross section for isomers of C3H4. Red solid
line: the present Qion for Allene; green solid line with stars; the present Qion for
Cyclopropene and black solid line: the present Qion for Propyne
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Chapter 4

4.3.6 Isomer effect (e  C3 H 6 )
In figure 4.6 comparisons for C3H6 isomers are made. It is clearly seen that cross
sections for Cyclopropane are less than the cross sections for Propene. Though the
number of constituents atoms are same, this difference is observed due to the change
in molecular geometry. The similar observation for Propene and Cyclopropane is
reported by Nishimura and Tawara [4]. Individual comparisons are already made in
figure 4.3 and figure 4.4. Also it is seen from figures 4.5 and 4.6 that cross sections
for C3H6 are higher than those of C3H4, and this appears to be a general trend.
Figure 4.6: Total ionization cross section for isomers of C3H6. Red solid line: the present
Qion for Cyclopropane and black solid line: the present Qion for Propene

4.3.7 (e  C5 H10 ) 1 Pentene and Cyclopentane
In spite of continuous interest in the electron driven processes for systems containing
hydrocarbons, the data for somewhat more complex compounds like C5 molecules
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Chapter 4
still remain fragmentary. So here in figure 4.7 electron impact ionization cross
sections are presented for C5H10 isomers. As the data for the present C5H10 isomers are
scarce, we have shown Qion for both 1 Pentene and Cyclopentane to offer a
comparison in figure 4.7.
Table 4.4 Qion (Å2) for e- - C5H10 isomers
Ei
(eV)
1 Pentene
Cyclopentane
20
9.13
6.80
30
14.25
11.86
40
15.83
13.64
50
16.01
13.97
60
16.03
13.99
70
15.76
13.80
80
15.35
13.50
90
14.89
13.14
100
14.44
12.76
200
11.11
9.67
300
9.08
7.84
400
7.70
6.62
500
6.68
5.74
600
5.91
5.07
700
5.30
4.54
800
4.80
4.12
900
4.39
3.78
1000
4.05
3.49
2000
2.25
1.96
The only comparison has been made in figure 4.7 for 1 Pentene with BEB cross
sections calculated by Szmytkowski et al. [8]. Present Qion are higher in comparison
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Chapter 4
with BEB cross sections of Szmytkowski et al. [8] and running parallel with it at high
energy region. The present Qion for Cyclopentane are smaller than the Qion for 1
Pentene. Our results agree with the observations by Bettega et al. [20] that cross
sections for closed chain isomers are always lower than the open chain isomers. It is
also noted that cross sections for C3 hydrocarbons are less than the cross sections C5
hydrocarbons due to the less total number of atoms.
Figure 4.7: Total ionization cross section for isomers of C5H10. Black solid line: the
present 1 Pentene; green solid line: Qion by Szmytkowski et al. [8] and red solid line: the
present Qion for Cyclopentane
4.4 Conclusions
This chapter is completely devoted to hydrocarbon molecules containing 3 or 5 C
atoms in their molecules. Here the cross sections for electron scattering with C3H4
isomers (Allene, Propyne and Cyclopropene), C3H6 isomers (Propene and
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Chapter 4
Cyclopropane) and C5H10 isomers (1 Pentene and Cyclopentane) are calculated by
complex scattering potential ionization contribution method (CSP-ic) plus group
additivity approach. Comparisons for all the results are made wherever other data are
available. In almost all calculations good accord and desired results are obtained. Also
the current calculation satisfies the general trends, as outlined below.
i.
Cross sections increase when the number of atoms are increased and vice
versa.
ii.
When ionization energy increases the cross section decreases and vice versa.
iii.
Cross sections for closed chain molecules are lower than the open chain
molecular isomers.
This is also observed in case of C3H4, but difference is too small so that it looks like
overlapping of their values. So here we can conclude that CSP-ic method has been
successfully applied for complex molecular systems and satisfactory results are
obtained for the lesser known targets. Discrepancies observed are also noted.
Now, we turn to the next chapter. As we shall see, a similar theoretical method is also
successfully applied for other projectile i.e. Positron; we have diversified our study
and reported the similar calculations for the well known atmospheric molecules N2
and CO2. The results are compared from both theses projectiles in the next chapter.
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Chapter 4
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