The role of electron-impact vibrational excitation in electron transport through gaseous tetrahydrofuran H. V. Duque, T. P. T. Do, M. C. A. Lopes, D. A. Konovalov, R. D. White, M. J. Brunger, and D. B. Jones Citation: The Journal of Chemical Physics 142, 124307 (2015); doi: 10.1063/1.4915889 View online: http://dx.doi.org/10.1063/1.4915889 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/142/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Intermediate energy cross sections for electron-impact vibrational-excitation of pyrimidine J. Chem. Phys. 143, 094304 (2015); 10.1063/1.4929907 Integral cross sections for electron impact excitation of vibrational and electronic states in phenol J. Chem. Phys. 142, 194305 (2015); 10.1063/1.4921313 Differential cross sections for electron-impact vibrational-excitation of tetrahydrofuran at intermediate impact energies J. Chem. Phys. 142, 124306 (2015); 10.1063/1.4915888 Absolute cross sections for vibrational excitations of cytosine by low energy electron impact J. Chem. Phys. 137, 115103 (2012); 10.1063/1.4752655 Electron-impact vibrational excitation of polyatomic gases: Exploratory calculations J. Chem. Phys. 114, 1989 (2001); 10.1063/1.1336567
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THE JOURNAL OF CHEMICAL PHYSICS 142, 124307 (2015)
The role of electron-impact vibrational excitation in electron transport through gaseous tetrahydrofuran H. V. Duque,1,2 T. P. T. Do,3 M. C. A. Lopes,2 D. A. Konovalov,4 R. D. White,4 M. J. Brunger,1,5,a) and D. B. Jones1,a)
1
School of Chemical and Physical Sciences, Flinders University, GPO Box 2100, Adelaide, South Australia 5001, Australia 2 Departamento de Física, Universidade Federal de Juiz de Fora, 36036-330 Juiz de Fora, Minas Gerais, Brazil 3 School of Education, Can Tho University, Campus II, 3/2 Street, Xuan Khanh, Ninh Kieu, Can Tho City, Vietnam 4 College of Science, Technology and Engineering, James Cook University, Townsville, Australia 5 Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia
(Received 23 January 2015; accepted 5 March 2015; published online 25 March 2015) In this paper, we report newly derived integral cross sections (ICSs) for electron impact vibrational excitation of tetrahydrofuran (THF) at intermediate impact energies. These cross sections extend the currently available data from 20 to 50 eV. Further, they indicate that the previously recommended THF ICS set [Garland et al., Phys. Rev. A 88, 062712 (2013)] underestimated the strength of the electron-impact vibrational excitation processes. Thus, that recommended vibrational cross section set is revised to address those deficiencies. Electron swarm transport properties were calculated with the amended vibrational cross section set, to quantify the role of electron-driven vibrational excitation in describing the macroscopic swarm phenomena. Here, significant differences of up to 17% in the transport coefficients were observed between the calculations performed using the original and revised cross section sets for vibrational excitation. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4915889]
I. INTRODUCTION
Ionizing radiation deposits energy into biological systems through successive collisions, which ionize or excite the atoms and molecules making up the living system. Each ionization event produces secondary electrons, leading to a cascade of electrons that also deposit their excess energy through further excitation and ionization processes. This occurs until those electrons thermalise within the system. Owing to their large number, and efficiency in initiating chemical process, electrons are often regarded as the most important species in radiation chemistry.1 Understanding and quantitatively describing how these electrons emanate and propagate through a biological system exposed to primary ionizing radiation is essential for developing targeted radiation-based therapies and quantifying radiation dose on the sub-cellular level. Specifically, it is important to understand where the low-energy electrons thermalise, particularly as electrons with sub-ionization and sub-excitation energies can induce damage to DNA through single and double strand breakages.2,3 The electron interactions with the molecules making up the biological system are governed by cross sections that detail the collisional probability that a particular scattering event will occur. It is these cross sections that determine how easily electrons, with a given energy, can be transported through the biological media, and where they will deposit their energy. a)Authors to whom correspondence should be addressed. Electronic ad-
dresses: [email protected] and [email protected]. au 0021-9606/2015/142(12)/124307/7/$30.00
Having a complete and self-consistent electron scattering cross section set for biomolecules is therefore essential for modelling radiation damage and dose. To be complete and self-consistent, the cross section set must include all chemical processes (over the relevant energy ranges) and have the correct absolute intensity scale for each of those processes. In this way, the correct probability ratios between those scattering processes are preserved. Swarm studies,4,5 where an ensemble of electrons pass through a chamber containing the target gas, at known temperature and pressure, can investigate the completeness and accuracy of an electron scattering cross section set. Here, the electrons drift and diffuse through the gas under the influence of an applied electric field, while the transmitted current is measured as the applied field is varied. The measured currents can then be interpreted in terms of transport coefficients (mobility and diffusion coefficients) and attachment/ionization rates. The applied electric field drives the ensemble of electrons out of equilibrium, and hence, the velocity distribution function for the ensemble of electrons is generally unknown. Using an appropriate transport theory, such as a multi-term Boltzmann equation solution, or Monte Carlo simulation technique, it is possible to relate the individual microscopic electron-molecule interactions (cross sections) to the macroscopically observable transport phenomena (currents). Varying the applied electric field modifies the energy distribution function, and hence, the observed results become sensitive to the microscopic behaviour of the cross sections over the range of energies possessed by electrons in the ensemble. Swarm investigations, therefore, represent a
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sensitive tool for investigating the completeness and accuracy of a cross section set.4,5 Tetrahydrofuran (THF, C4H8O) is a prototypical molecule for the backbone of DNA. With the ability of low-energy electrons to attach to DNA and induce single and double strand breakage, electron interactions with THF have received considerable attention from the electron and positron scattering communities in recent years.6–29 This work has led to a near-complete cross section set being proposed and used as a basis for modelling electron-THF swarms and charged-particle interactions in THF.29–31 THF is therefore becoming one of the benchmark molecular systems for understanding electroninteractions with polyatomic species. Further, the availability of its cross section data is now being utilised to assess transport properties in THF, or THF + water mixtures.30,31 In particular, they are being used to assess the limitations of radiation damage simulations, where one of the major underlying assumptions is that the biological system can be described using water as the medium.32 Here, we also note that there has been a significant effort to extend radiation models beyond water, through projects such as GEANT-DNA.33 In Paper I34 of this journal issue, we reported the first electron-impact differential cross sections for vibrational excitation of THF at intermediate electron energies (up to 50 eV).34 That study extended the available data for electron impact vibrational excitation from 20 eV up to 50 eV. We therefore expand on that study by deriving integral cross sections (ICSs) for electron-impact vibrational excitation of THF in the present paper. This is particularly important for assessing recent computational studies that have truncated the available cross sections at low energies, or proposed an extrapolation of the cross sections to higher energies. We also compare our data to those previously reported at lowerimpact energies,9,16,23 where possible. These results enable us to update the recommended ICS set for vibrational excitation of THF.30 These revised cross sections are then re-employed in the earlier swarm investigations,30 to consider the macroscopic manifestations of this revision to the vibrational cross sections.
The structure of this paper is as follows. In Sec. II, we describe the details of our experiments, data analysis, and computational methods. We then present in Sec. III our newly derived integral cross section data and compare them to the previous measurements. These cross sections are then utilised to revise the recommended electron-impact vibrational cross section set. The macroscopic manifestation of electron-impact vibrational excitation is then investigated in Sec. IV through the calculation of electron swarm transport properties. Finally, in Sec. V the conclusions drawn from this investigation are summarized.
II. METHODS OF DATA ANALYSIS AND COMPUTATIONAL DETAILS
A full discussion of our experimental methodology and our computational details has been described previously.18,34,35 To make this paper as self-contained as possible, we, nonetheless, briefly repeat some of the more pertinent details here. Electron-impact energy loss spectra for tetrahydrofuran have been measured on an apparatus based at Flinders University. These spectra were used to derive differential cross sections (DCSs) for electron-impact vibrational excitation (see Do et al.34 for further details) over the 15–50 eV incident energy and 10◦–90◦ angular ranges. The differential cross sections were reported34 for the composite vibrational modes, as summarised in Table I. In order to model electron driven transport phenomena, integral cross sections, rather than differential cross sections, are of most practical use. Here, the differential and integral cross sections for a given scattering process are related through π σ (E0) = 2π
dσ (E0, θ) sin (θ) dθ. dΩ
(1)
0
To convert experimental differential cross sections measured at discrete scattering angles into integral cross sections, we employ an extrapolation and integration procedure that has
TABLE I. Experimental vibrational-excitation assignments observed in our electron energy loss spectra of THF. Also presented is the breakdown of the spectral intensity (and their respective energetic thresholds, E threshold) used in our modelling. See text for further details. Band
Energy loss, E L (eV)
FWHM (eV)
Assignment
Elastic
0.0
0.06
Elastic
Vib. 1
0.14
0.11
CC-stretch
Vib 2.
Vib. 3 Vib. 4
0.30 0.37
0.11 0.07
0.50
0.14
0.70
0.10
2 × CC-stretch + CH2-stretch Combination 2 × CH2-stretch
Vib. breakdown
E threshold (eV)
0.24 ν 3 0.27 ν 4 0.20 ν 5 0.24 ν 9 0.05 ν 10
0.114 0.134 0.180 0.150 0.083
0.085 ν 1 0.660 ν 6 0.085 ν 11 0.170 ν 12
0.228 0.363 0.270 0.330
1.00 ν 7
0.45
0.30 ν 8 0.70 ν 2
0.65 0.72
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been fully described by Masin et al.36 Note that this procedure employs a statistical weighting method that implicitly includes all of the uncertainty (statistical, transmission, and absolute scale normalisation) from the experiment and a component introduced through the extrapolation of the experimental data to 0◦ and 180◦. In swarm physics, the electron transport through the target gas under the influence of an applied electric field can be semi-classically modelled within a multi-term solution of Boltzmann’s equation, qE ∂ f ∂f +c · ∇f + · = −J ( f , f 0) , (2) ∂t m ∂c to obtain the single particle phase-space distribution function, f (r, c,t). This is a function of the particle’s position, r, and its velocity, c. Here, the acceleration of the particle depends on the electron’s charge, q, and mass, m, and the applied electric field, E. Finally, J ( f , f 0) is the total collision operator, which takes into account all of the binary collision interactions between an electron and a neutral background gas of THF molecules [having a distribution, f 0, based on the gas temperature (fixed at 293 K), and a gas density, N]. It is important to note that this collision operator is implicitly dependent on the electron-collision cross section set.37 The phase space distribution function, f (r, c,t), can then be related to the currents and charged particle densities, n(r,t), measured in swarm experiments through the equation of continuity, ∂n(r,t) + ∇ · Γ (r, t) = S (r,t) . (3) ∂t Here, Γ (r, t) = nc is the electron flux and S (r,t) is the production rate from non-conservative processes (i.e., ionization and attachment). Full details of the calculation methods have been adequately described by Garland et al.,30 so they are not repeated again here. Our electron transport calculations for THF are performed under typical swarm conditions.5 In order to facilitate a comparison, and to assess how the revised cross sections for vibrational excitation manifest themselves in the swarm environment, all other cross
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sections and calculation parameters are identical to those used by Garland et al.30
III. ELECTRON-IMPACT VIBRATIONAL EXCITATION ICS
The present integral cross sections obtained for each composite vibrational feature and the summed cross section for all the vibrational excitation processes are presented in Figures 1 and 2, respectively. These ICS values are also tabulated in Table II. Where possible, the present ICSs are compared against earlier measurements. In this case, we observe an excellent agreement between the present data and the experimental data of Khakoo et al.23 where they overlap. We have also plotted the sum of the recommended vibrational excitation cross sections used by Garland et al.30 in Fig. 2. Here, we see that the Garland et al.30 recommended cross section significantly underestimates the summed cross section magnitude, while also being truncated at a too low impact energy value. The ICSs, summed over all the vibrational excitation processes reported by the 4 different groups are all in reasonable agreement where they overlap. This suggests that the absolute scale of these experimental cross sections is self-consistent and valid. The underestimation of the cross section magnitude, and its truncation at lower-impact energies, suggests a problem with the current recommended cross section set of Garland et al.,30 which may have a bearing on the electron transport properties derived using that cross section set. It is therefore necessary to revise the recommended electron impact vibrational excitation ICS, with the details of this revision as follows. To derive the recommended cross section set for THF, Garland et al.30 used the excitation function measurements from Allan.9 From that study, cross sections for six vibrational modes were obtained. It is important to note that the measurements from Allan were performed with a very high energy resolution of ∼20 meV, so that the excitation functions are for quite specific, and discrete, vibrational excitation
FIG. 1. Integral cross sections for electron-impact vibrational excitation of THF. (a) Composite CC-stretch mode, (b) composite CH2 stretch mode, (c) combination band, (d) 2 × CH2 stretch modes. Where possible, the data are compared to measurements from Khakoo et al.23 and Dampc et al.16 Also shown are our Garland-extended (– –) and revised (——–) cross section sets for each experimental band. See text for further details.
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FIG. 2. Summed integral cross section for electron impact vibrational excitation of THF. The present data (■) are also compared against the data from Khakoo et al.23 (•), Allan9 (⋆), and Dampc et al.16 (I). Also shown are the original cross section set from Garland et al.30 (– –), our extended version of the cross section of Garland et al. (· · · ·), and our proposed revised cross section (——–). See text for further details.
processes. Unfortunately, in THF (like most polyatomic species), the vibrational spectrum is quite complex having 33 fundamental vibrational modes, many of which are closely lying in energy (see Khakoo et al.23 for full details). This situation is further complicated by the ability of electrons to excite THF to combination and overtone modes. It is therefore apparent that the ICSs derived from the discrete excitation function measurements of Allan9 do not adequately capture all of the physical vibrational excitation intensity. Specifically, the ICS derived by Allan9 using his energy loss spectra (which sums over all the possible vibrational excitation processes) is somewhat underestimated by the sum of the recommended vibrational cross sections reported by Garland et al.30 as derived from only the 6-discrete excitation function measurements. The composite mode DCS and ICS derived from the present investigation (including Paper I34 and also that from Khakoo et al.23) capture the intensity for excitation of all the vibrational modes. These ICSs can therefore be used to address the deficiencies in the recommended cross section of Garland et al.30 For this purpose, we propose to incorporate an additional 6 vibrational channels for the THF simulations (ν7–ν12). These extra 6-vibrational modes capture the vibrational excitation intensity missing from the original cross section set. Here, we note that while there are 33 fundamental vibrational modes of THF, we partition their excitation intensity into 12 composite vibrational modes. It
is important to note that the number of excitation channels, and when they are energetically opened (i.e., representative energetic thresholds), is a crucial parameter that must be balanced in the computational simulations. The positions and weightings for assigning the present experimental cross section intensity, to individual composite vibrational modes, have been obtained by looking at the relative intensity of features in the high-resolution electron energy loss spectrum of Allan.9 The details of the proposed breakdown of our vibrational cross section intensity into individual bands are described in Table I. Additionally, these weightings are used to partition the spectral intensity of the present measurements across all 12 composite vibrational modes (ν1–ν12) at intermediate impact energies. The cross sections are therefore derived in a self-consistent manner across the entire energy range. Within this procedure, there is an underlying assumption that the ratio of individual features does not change substantially with the impact energy. We feel these assumptions are reasonable given the closeness in the energy of many of these vibrational excitation features and the common character of the vibrations contained within an energy band. The original cross section set of Garland et al.30 (ν1–ν6) and the revised set (ν1–ν6, extended to higher impact energies; plus the additional ν7–ν12 modes) are shown in Figure 3. To assess the reliability of the new recommended cross sections, they are also plotted against the experimentally observed composite bands and summed bands in Figures 1 and 2. Here, we observe that the additional 6-vibrational modes (ν7–ν12) address the aforementioned magnitude differences in the earlier vibrational excitation cross sections. These newer cross sections can therefore be used to investigate the role of electron-impact vibrational excitation in macroscopic phenomena (e.g., electron transport coefficients). As no experimental data exist beyond our data, we truncate these vibrational cross sections so that they go to zero at 55 eV.
IV. SWARM STUDIES
In this section, we study the macroscopic manifestations of changes to the microscopic vibrational cross sections through the calculation of swarm transport parameters obtained using a multi-term solution of the Boltzmann’s equation. Here, the transport properties are investigated as a function of the reduced electric field (E/N), in order to assess the sensitivity, completeness, and accuracy of the cross section set over an extended range of energies. As experimental swarm data for THF are currently unavailable (although we expect them to become available shortly), we focus on understanding the
TABLE II. Experimental integral cross sections (10−20 m2) for electron-impact excitation of THF for each vibrational band resolved in our experiment. Also presented is the experimental integral cross section, summed over all of the vibrational excitation processes. See text and Table I for further details. Energy (eV) 15 20 30 50
Vib. 1 (E L = 0.14 eV)
Error
Vib. 2 (E L = 0.30-0.37 eV)
Error
Vib. 3 (E L = 0.50 eV)
Error
Vib. 4 (E L = 0.70 eV)
Error
Sum
Error
1.743 1.444 0.828 0.380
0.857 0.754 0.440 0.200
0.583 0.327 0.105 0.077
0.288 0.151 0.050 0.038
0.093 0.068 0.021 0.019
0.046 0.032 0.010 0.010
0.050 0.032 0.011 0.009
0.024 0.015 0.006 0.005
2.469 1.870 0.964 0.485
1.215 0.952 0.506 0.252
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FIG. 3. (a) Integral cross sections of THF for the 6-vibration channels (ν1–ν6) originally employed in Garland et al.30 (b) Integral cross sections for the 6-vibrational channels (ν1–ν6) of Garland et al.30 (extended to higher impact energies) and the additional 6-vibrational channels (ν7–ν12) proposed. See text and Table I for further details.
role of the vibrational excitation processes in this work. We therefore reprise the swarm transport calculations carried out by Garland et al.30 Here, we carried out calculations using two independent cross section sets. The first employed cross sections for the same 6 vibrational excitation modes that were previously used in Garland et al.,30 after those cross sections had been extended to higher impact energies using our newly derived ICS data. We refer to these results as Garlandextended. By comparing the Garland-extended results to the original data by Garland et al.30 (original), we can evaluate the role of intermediate-energy electron-impact vibrational excitation on the electron transport coefficients. The second set employs the present revised cross sections (revised). The revised calculations are compared to the Garland-extended results so that we can assess which, if any, transport properties are sensitive to the increased probability of electron-driven vibrational excitation processes. As noted earlier, all other cross sections remain the same as those used by Garland et al.30 As the average energy of the electron swarm may vary with respect to the cross section set employed, in Figure 4, the differences in the calculated mean energies are also compared as a function of the average energy (calculated using the Garland-extended set). In Figures 4–6, we present the swarm transport coefficients/properties calculated from the original cross sections30 and compare them to those obtained with the Garland-extended cross sections. In these figures, we obtain a percentage difference by subtracting the revised value from the extended value and then dividing this by the extended value. As noted above, this allows us to assess the impact of extending the vibrational cross sections from 25 to 55 eV. In Figure 4, we observe that there are only small shifts of less than 0.5% in the mean energy over the range of reduced fields considered, which are typically within the associated numerical errors in the Boltzmann equation solution. Differences are peaked at the reduced fields where the energy distribution function significantly samples the intermediate energy regime, where the cross section sets differ most. This relative insensitivity in the mean energy to extending the vibrational cross section set, over the reduced fields considered, also carries over to the
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other transport coefficients including both the drift velocity and diffusion coefficients, as shown in Figure 5. The swarm transport properties, calculated using the revised vibrational cross section set, are also compared to those from the Garland-extended version in Figures 4–6. This allows us to evaluate the importance of the additional six vibrational processes. In particular, we note that the additional channels contribute significant vibrational excitation intensity from threshold out to 55 eV. Differences in the calculated transport properties are therefore observed across a large range of E/N. In Figure 4, we observe that the mean energy obtained using the revised cross sections is up to ∼12% lower than that calculated using either the extended or original cross sections, reflecting the enhanced vibrational cross section in the revised set. This is also reflected in the drift velocity and diffusion coefficients, all of which are reduced for the revised set over that of the extended. From Figure 5, we observe that the maximum differences in the transport coefficients (drift velocity and diffusion coefficients) also appear in the same regime of the reduced field. The most sensitive transport coefficient to such changes in the cross section set appears to be the longitudinal diffusion coefficient, where differences as large as 17% appear. Even though there were relatively small modifications to the vibrational cross sections for energies
FIG. 4. (a) The mean energy of the swarm in THF is plotted against the reduced electric field for our calculations employing either the original cross section set from Garland et al.30 (——–), our Garland-extended cross section set (– –), or our revised cross section set (· · · ·). (b) The percentage difference in the mean energy is compared between the calculations with different cross section sets as a function of the average energy calculated using the Garland-extended cross section set. See text for further details.
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vibrational cross sections should therefore be confirmable when electron-swarm measurements in THF become available, although the challenges in performing such experiments should not be underestimated.30,31 Finally, we consider the impact of the vibrational cross section changes on the attachment and ionization rates, and hence, the breakdown field. In Figure 6, as expected, there is very little impact on the attachment rate, given the small absolute magnitude of that cross section employed using the Garland et al.30 cross section set. There is also essentially no change to the ionization rate when we extend the cross section set to higher impact energies. The enhanced vibrational excitation probability in the revised set, however, reduces the ionization rate, such that an additional 20Td of reduced electric field is necessary to achieve electron avalanche conditions. This could be an important macroscopic manifestation of the role of electron driven vibrational excitation processes. Electron swarm studies in THF are eagerly awaited to verify the predicted macroscopic manifestation of the proposed cross section set, and the reliability of the cross sections by Garland et al.30 for the other scattering processes.
V. CONCLUSIONS
FIG. 5. The percentage differences between the calculated (a) bulk (W Bulk) and flux (W Flux) drift velocities, and (b) reduced transverse (NDT) and longitudinal (NDL) flux diffusion coefficients in THF, with the different cross section sets as a function of the reduced electric field. See text for further details.
less than 5 eV, there can be quite large relative changes in the transport coefficients by the virtue of the rapidly varying collision frequency in that region. We note that for the flux drift velocity differences of the order of 5% are observed. These differences exceed the typical uncertainties placed on an experimental swarm flux drift velocity obtained using a pulsed-Townsend technique.38 The validity of the present
In this paper, we have reported the first integral cross sections for vibrational excitation of a number of composite vibrational modes of THF at intermediate impact energies. Over their common energy ranges, these data agreed well with earlier measurements23 at lower-impact energies up to 20 eV. This suggests that electron-impact vibrational excitation of THF might now be considered as an experimentally benchmarked system. These cross sections were then utilised in swarm studies to evaluate the role of vibrational excitation in electron transport. Here, we found that extending the original cross sections30 to intermediate energies only had a small influence on the calculated transport properties. However, the transport properties and ionization rate may be particularly sensitive to the overall strength of the vibrational excitation processes. Further, the deviations observed are typically larger than the uncertainties on the swarm experiments and thus should be evident when experimental swarm data become available. ACKNOWLEDGMENTS
This research has been partially supported by the Australian and Brazilian Funding organisations (ARC, CNPq). M.C.A.L. acknowledges financial support from CNPq and FAPEMIG. D.B.J. thanks the ARC for provision of a Discovery Early Career Researcher Award. H.V.D. thanks CAPES and the Science Without Borders scheme that supported his studies in Australia. M.J.B. acknowledges CNPq for his “Special Visiting Professor” award at UFJF. 1S.
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FIG. 6. The calculated reduced attachment (Ra) and ionization (RI) reaction rates of THF for the different cross section sets as a function of the reduced electric field. See text for further details.
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THE JOURNAL OF CHEMICAL PHYSICS 142, 124307 (2015)
The role of electron-impact vibrational excitation in electron transport through gaseous tetrahydrofuran H. V. Duque,1,2 T. P. T. Do,3 M. C. A. Lopes,2 D. A. Konovalov,4 R. D. White,4 M. J. Brunger,1,5,a) and D. B. Jones1,a)
1
School of Chemical and Physical Sciences, Flinders University, GPO Box 2100, Adelaide, South Australia 5001, Australia 2 Departamento de Física, Universidade Federal de Juiz de Fora, 36036-330 Juiz de Fora, Minas Gerais, Brazil 3 School of Education, Can Tho University, Campus II, 3/2 Street, Xuan Khanh, Ninh Kieu, Can Tho City, Vietnam 4 College of Science, Technology and Engineering, James Cook University, Townsville, Australia 5 Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia
(Received 23 January 2015; accepted 5 March 2015; published online 25 March 2015) In this paper, we report newly derived integral cross sections (ICSs) for electron impact vibrational excitation of tetrahydrofuran (THF) at intermediate impact energies. These cross sections extend the currently available data from 20 to 50 eV. Further, they indicate that the previously recommended THF ICS set [Garland et al., Phys. Rev. A 88, 062712 (2013)] underestimated the strength of the electron-impact vibrational excitation processes. Thus, that recommended vibrational cross section set is revised to address those deficiencies. Electron swarm transport properties were calculated with the amended vibrational cross section set, to quantify the role of electron-driven vibrational excitation in describing the macroscopic swarm phenomena. Here, significant differences of up to 17% in the transport coefficients were observed between the calculations performed using the original and revised cross section sets for vibrational excitation. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4915889]
I. INTRODUCTION
Ionizing radiation deposits energy into biological systems through successive collisions, which ionize or excite the atoms and molecules making up the living system. Each ionization event produces secondary electrons, leading to a cascade of electrons that also deposit their excess energy through further excitation and ionization processes. This occurs until those electrons thermalise within the system. Owing to their large number, and efficiency in initiating chemical process, electrons are often regarded as the most important species in radiation chemistry.1 Understanding and quantitatively describing how these electrons emanate and propagate through a biological system exposed to primary ionizing radiation is essential for developing targeted radiation-based therapies and quantifying radiation dose on the sub-cellular level. Specifically, it is important to understand where the low-energy electrons thermalise, particularly as electrons with sub-ionization and sub-excitation energies can induce damage to DNA through single and double strand breakages.2,3 The electron interactions with the molecules making up the biological system are governed by cross sections that detail the collisional probability that a particular scattering event will occur. It is these cross sections that determine how easily electrons, with a given energy, can be transported through the biological media, and where they will deposit their energy. a)Authors to whom correspondence should be addressed. Electronic ad-
dresses: [email protected] and [email protected]. au 0021-9606/2015/142(12)/124307/7/$30.00
Having a complete and self-consistent electron scattering cross section set for biomolecules is therefore essential for modelling radiation damage and dose. To be complete and self-consistent, the cross section set must include all chemical processes (over the relevant energy ranges) and have the correct absolute intensity scale for each of those processes. In this way, the correct probability ratios between those scattering processes are preserved. Swarm studies,4,5 where an ensemble of electrons pass through a chamber containing the target gas, at known temperature and pressure, can investigate the completeness and accuracy of an electron scattering cross section set. Here, the electrons drift and diffuse through the gas under the influence of an applied electric field, while the transmitted current is measured as the applied field is varied. The measured currents can then be interpreted in terms of transport coefficients (mobility and diffusion coefficients) and attachment/ionization rates. The applied electric field drives the ensemble of electrons out of equilibrium, and hence, the velocity distribution function for the ensemble of electrons is generally unknown. Using an appropriate transport theory, such as a multi-term Boltzmann equation solution, or Monte Carlo simulation technique, it is possible to relate the individual microscopic electron-molecule interactions (cross sections) to the macroscopically observable transport phenomena (currents). Varying the applied electric field modifies the energy distribution function, and hence, the observed results become sensitive to the microscopic behaviour of the cross sections over the range of energies possessed by electrons in the ensemble. Swarm investigations, therefore, represent a
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sensitive tool for investigating the completeness and accuracy of a cross section set.4,5 Tetrahydrofuran (THF, C4H8O) is a prototypical molecule for the backbone of DNA. With the ability of low-energy electrons to attach to DNA and induce single and double strand breakage, electron interactions with THF have received considerable attention from the electron and positron scattering communities in recent years.6–29 This work has led to a near-complete cross section set being proposed and used as a basis for modelling electron-THF swarms and charged-particle interactions in THF.29–31 THF is therefore becoming one of the benchmark molecular systems for understanding electroninteractions with polyatomic species. Further, the availability of its cross section data is now being utilised to assess transport properties in THF, or THF + water mixtures.30,31 In particular, they are being used to assess the limitations of radiation damage simulations, where one of the major underlying assumptions is that the biological system can be described using water as the medium.32 Here, we also note that there has been a significant effort to extend radiation models beyond water, through projects such as GEANT-DNA.33 In Paper I34 of this journal issue, we reported the first electron-impact differential cross sections for vibrational excitation of THF at intermediate electron energies (up to 50 eV).34 That study extended the available data for electron impact vibrational excitation from 20 eV up to 50 eV. We therefore expand on that study by deriving integral cross sections (ICSs) for electron-impact vibrational excitation of THF in the present paper. This is particularly important for assessing recent computational studies that have truncated the available cross sections at low energies, or proposed an extrapolation of the cross sections to higher energies. We also compare our data to those previously reported at lowerimpact energies,9,16,23 where possible. These results enable us to update the recommended ICS set for vibrational excitation of THF.30 These revised cross sections are then re-employed in the earlier swarm investigations,30 to consider the macroscopic manifestations of this revision to the vibrational cross sections.
The structure of this paper is as follows. In Sec. II, we describe the details of our experiments, data analysis, and computational methods. We then present in Sec. III our newly derived integral cross section data and compare them to the previous measurements. These cross sections are then utilised to revise the recommended electron-impact vibrational cross section set. The macroscopic manifestation of electron-impact vibrational excitation is then investigated in Sec. IV through the calculation of electron swarm transport properties. Finally, in Sec. V the conclusions drawn from this investigation are summarized.
II. METHODS OF DATA ANALYSIS AND COMPUTATIONAL DETAILS
A full discussion of our experimental methodology and our computational details has been described previously.18,34,35 To make this paper as self-contained as possible, we, nonetheless, briefly repeat some of the more pertinent details here. Electron-impact energy loss spectra for tetrahydrofuran have been measured on an apparatus based at Flinders University. These spectra were used to derive differential cross sections (DCSs) for electron-impact vibrational excitation (see Do et al.34 for further details) over the 15–50 eV incident energy and 10◦–90◦ angular ranges. The differential cross sections were reported34 for the composite vibrational modes, as summarised in Table I. In order to model electron driven transport phenomena, integral cross sections, rather than differential cross sections, are of most practical use. Here, the differential and integral cross sections for a given scattering process are related through π σ (E0) = 2π
dσ (E0, θ) sin (θ) dθ. dΩ
(1)
0
To convert experimental differential cross sections measured at discrete scattering angles into integral cross sections, we employ an extrapolation and integration procedure that has
TABLE I. Experimental vibrational-excitation assignments observed in our electron energy loss spectra of THF. Also presented is the breakdown of the spectral intensity (and their respective energetic thresholds, E threshold) used in our modelling. See text for further details. Band
Energy loss, E L (eV)
FWHM (eV)
Assignment
Elastic
0.0
0.06
Elastic
Vib. 1
0.14
0.11
CC-stretch
Vib 2.
Vib. 3 Vib. 4
0.30 0.37
0.11 0.07
0.50
0.14
0.70
0.10
2 × CC-stretch + CH2-stretch Combination 2 × CH2-stretch
Vib. breakdown
E threshold (eV)
0.24 ν 3 0.27 ν 4 0.20 ν 5 0.24 ν 9 0.05 ν 10
0.114 0.134 0.180 0.150 0.083
0.085 ν 1 0.660 ν 6 0.085 ν 11 0.170 ν 12
0.228 0.363 0.270 0.330
1.00 ν 7
0.45
0.30 ν 8 0.70 ν 2
0.65 0.72
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been fully described by Masin et al.36 Note that this procedure employs a statistical weighting method that implicitly includes all of the uncertainty (statistical, transmission, and absolute scale normalisation) from the experiment and a component introduced through the extrapolation of the experimental data to 0◦ and 180◦. In swarm physics, the electron transport through the target gas under the influence of an applied electric field can be semi-classically modelled within a multi-term solution of Boltzmann’s equation, qE ∂ f ∂f +c · ∇f + · = −J ( f , f 0) , (2) ∂t m ∂c to obtain the single particle phase-space distribution function, f (r, c,t). This is a function of the particle’s position, r, and its velocity, c. Here, the acceleration of the particle depends on the electron’s charge, q, and mass, m, and the applied electric field, E. Finally, J ( f , f 0) is the total collision operator, which takes into account all of the binary collision interactions between an electron and a neutral background gas of THF molecules [having a distribution, f 0, based on the gas temperature (fixed at 293 K), and a gas density, N]. It is important to note that this collision operator is implicitly dependent on the electron-collision cross section set.37 The phase space distribution function, f (r, c,t), can then be related to the currents and charged particle densities, n(r,t), measured in swarm experiments through the equation of continuity, ∂n(r,t) + ∇ · Γ (r, t) = S (r,t) . (3) ∂t Here, Γ (r, t) = nc is the electron flux and S (r,t) is the production rate from non-conservative processes (i.e., ionization and attachment). Full details of the calculation methods have been adequately described by Garland et al.,30 so they are not repeated again here. Our electron transport calculations for THF are performed under typical swarm conditions.5 In order to facilitate a comparison, and to assess how the revised cross sections for vibrational excitation manifest themselves in the swarm environment, all other cross
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sections and calculation parameters are identical to those used by Garland et al.30
III. ELECTRON-IMPACT VIBRATIONAL EXCITATION ICS
The present integral cross sections obtained for each composite vibrational feature and the summed cross section for all the vibrational excitation processes are presented in Figures 1 and 2, respectively. These ICS values are also tabulated in Table II. Where possible, the present ICSs are compared against earlier measurements. In this case, we observe an excellent agreement between the present data and the experimental data of Khakoo et al.23 where they overlap. We have also plotted the sum of the recommended vibrational excitation cross sections used by Garland et al.30 in Fig. 2. Here, we see that the Garland et al.30 recommended cross section significantly underestimates the summed cross section magnitude, while also being truncated at a too low impact energy value. The ICSs, summed over all the vibrational excitation processes reported by the 4 different groups are all in reasonable agreement where they overlap. This suggests that the absolute scale of these experimental cross sections is self-consistent and valid. The underestimation of the cross section magnitude, and its truncation at lower-impact energies, suggests a problem with the current recommended cross section set of Garland et al.,30 which may have a bearing on the electron transport properties derived using that cross section set. It is therefore necessary to revise the recommended electron impact vibrational excitation ICS, with the details of this revision as follows. To derive the recommended cross section set for THF, Garland et al.30 used the excitation function measurements from Allan.9 From that study, cross sections for six vibrational modes were obtained. It is important to note that the measurements from Allan were performed with a very high energy resolution of ∼20 meV, so that the excitation functions are for quite specific, and discrete, vibrational excitation
FIG. 1. Integral cross sections for electron-impact vibrational excitation of THF. (a) Composite CC-stretch mode, (b) composite CH2 stretch mode, (c) combination band, (d) 2 × CH2 stretch modes. Where possible, the data are compared to measurements from Khakoo et al.23 and Dampc et al.16 Also shown are our Garland-extended (– –) and revised (——–) cross section sets for each experimental band. See text for further details.
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FIG. 2. Summed integral cross section for electron impact vibrational excitation of THF. The present data (■) are also compared against the data from Khakoo et al.23 (•), Allan9 (⋆), and Dampc et al.16 (I). Also shown are the original cross section set from Garland et al.30 (– –), our extended version of the cross section of Garland et al. (· · · ·), and our proposed revised cross section (——–). See text for further details.
processes. Unfortunately, in THF (like most polyatomic species), the vibrational spectrum is quite complex having 33 fundamental vibrational modes, many of which are closely lying in energy (see Khakoo et al.23 for full details). This situation is further complicated by the ability of electrons to excite THF to combination and overtone modes. It is therefore apparent that the ICSs derived from the discrete excitation function measurements of Allan9 do not adequately capture all of the physical vibrational excitation intensity. Specifically, the ICS derived by Allan9 using his energy loss spectra (which sums over all the possible vibrational excitation processes) is somewhat underestimated by the sum of the recommended vibrational cross sections reported by Garland et al.30 as derived from only the 6-discrete excitation function measurements. The composite mode DCS and ICS derived from the present investigation (including Paper I34 and also that from Khakoo et al.23) capture the intensity for excitation of all the vibrational modes. These ICSs can therefore be used to address the deficiencies in the recommended cross section of Garland et al.30 For this purpose, we propose to incorporate an additional 6 vibrational channels for the THF simulations (ν7–ν12). These extra 6-vibrational modes capture the vibrational excitation intensity missing from the original cross section set. Here, we note that while there are 33 fundamental vibrational modes of THF, we partition their excitation intensity into 12 composite vibrational modes. It
is important to note that the number of excitation channels, and when they are energetically opened (i.e., representative energetic thresholds), is a crucial parameter that must be balanced in the computational simulations. The positions and weightings for assigning the present experimental cross section intensity, to individual composite vibrational modes, have been obtained by looking at the relative intensity of features in the high-resolution electron energy loss spectrum of Allan.9 The details of the proposed breakdown of our vibrational cross section intensity into individual bands are described in Table I. Additionally, these weightings are used to partition the spectral intensity of the present measurements across all 12 composite vibrational modes (ν1–ν12) at intermediate impact energies. The cross sections are therefore derived in a self-consistent manner across the entire energy range. Within this procedure, there is an underlying assumption that the ratio of individual features does not change substantially with the impact energy. We feel these assumptions are reasonable given the closeness in the energy of many of these vibrational excitation features and the common character of the vibrations contained within an energy band. The original cross section set of Garland et al.30 (ν1–ν6) and the revised set (ν1–ν6, extended to higher impact energies; plus the additional ν7–ν12 modes) are shown in Figure 3. To assess the reliability of the new recommended cross sections, they are also plotted against the experimentally observed composite bands and summed bands in Figures 1 and 2. Here, we observe that the additional 6-vibrational modes (ν7–ν12) address the aforementioned magnitude differences in the earlier vibrational excitation cross sections. These newer cross sections can therefore be used to investigate the role of electron-impact vibrational excitation in macroscopic phenomena (e.g., electron transport coefficients). As no experimental data exist beyond our data, we truncate these vibrational cross sections so that they go to zero at 55 eV.
IV. SWARM STUDIES
In this section, we study the macroscopic manifestations of changes to the microscopic vibrational cross sections through the calculation of swarm transport parameters obtained using a multi-term solution of the Boltzmann’s equation. Here, the transport properties are investigated as a function of the reduced electric field (E/N), in order to assess the sensitivity, completeness, and accuracy of the cross section set over an extended range of energies. As experimental swarm data for THF are currently unavailable (although we expect them to become available shortly), we focus on understanding the
TABLE II. Experimental integral cross sections (10−20 m2) for electron-impact excitation of THF for each vibrational band resolved in our experiment. Also presented is the experimental integral cross section, summed over all of the vibrational excitation processes. See text and Table I for further details. Energy (eV) 15 20 30 50
Vib. 1 (E L = 0.14 eV)
Error
Vib. 2 (E L = 0.30-0.37 eV)
Error
Vib. 3 (E L = 0.50 eV)
Error
Vib. 4 (E L = 0.70 eV)
Error
Sum
Error
1.743 1.444 0.828 0.380
0.857 0.754 0.440 0.200
0.583 0.327 0.105 0.077
0.288 0.151 0.050 0.038
0.093 0.068 0.021 0.019
0.046 0.032 0.010 0.010
0.050 0.032 0.011 0.009
0.024 0.015 0.006 0.005
2.469 1.870 0.964 0.485
1.215 0.952 0.506 0.252
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FIG. 3. (a) Integral cross sections of THF for the 6-vibration channels (ν1–ν6) originally employed in Garland et al.30 (b) Integral cross sections for the 6-vibrational channels (ν1–ν6) of Garland et al.30 (extended to higher impact energies) and the additional 6-vibrational channels (ν7–ν12) proposed. See text and Table I for further details.
role of the vibrational excitation processes in this work. We therefore reprise the swarm transport calculations carried out by Garland et al.30 Here, we carried out calculations using two independent cross section sets. The first employed cross sections for the same 6 vibrational excitation modes that were previously used in Garland et al.,30 after those cross sections had been extended to higher impact energies using our newly derived ICS data. We refer to these results as Garlandextended. By comparing the Garland-extended results to the original data by Garland et al.30 (original), we can evaluate the role of intermediate-energy electron-impact vibrational excitation on the electron transport coefficients. The second set employs the present revised cross sections (revised). The revised calculations are compared to the Garland-extended results so that we can assess which, if any, transport properties are sensitive to the increased probability of electron-driven vibrational excitation processes. As noted earlier, all other cross sections remain the same as those used by Garland et al.30 As the average energy of the electron swarm may vary with respect to the cross section set employed, in Figure 4, the differences in the calculated mean energies are also compared as a function of the average energy (calculated using the Garland-extended set). In Figures 4–6, we present the swarm transport coefficients/properties calculated from the original cross sections30 and compare them to those obtained with the Garland-extended cross sections. In these figures, we obtain a percentage difference by subtracting the revised value from the extended value and then dividing this by the extended value. As noted above, this allows us to assess the impact of extending the vibrational cross sections from 25 to 55 eV. In Figure 4, we observe that there are only small shifts of less than 0.5% in the mean energy over the range of reduced fields considered, which are typically within the associated numerical errors in the Boltzmann equation solution. Differences are peaked at the reduced fields where the energy distribution function significantly samples the intermediate energy regime, where the cross section sets differ most. This relative insensitivity in the mean energy to extending the vibrational cross section set, over the reduced fields considered, also carries over to the
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other transport coefficients including both the drift velocity and diffusion coefficients, as shown in Figure 5. The swarm transport properties, calculated using the revised vibrational cross section set, are also compared to those from the Garland-extended version in Figures 4–6. This allows us to evaluate the importance of the additional six vibrational processes. In particular, we note that the additional channels contribute significant vibrational excitation intensity from threshold out to 55 eV. Differences in the calculated transport properties are therefore observed across a large range of E/N. In Figure 4, we observe that the mean energy obtained using the revised cross sections is up to ∼12% lower than that calculated using either the extended or original cross sections, reflecting the enhanced vibrational cross section in the revised set. This is also reflected in the drift velocity and diffusion coefficients, all of which are reduced for the revised set over that of the extended. From Figure 5, we observe that the maximum differences in the transport coefficients (drift velocity and diffusion coefficients) also appear in the same regime of the reduced field. The most sensitive transport coefficient to such changes in the cross section set appears to be the longitudinal diffusion coefficient, where differences as large as 17% appear. Even though there were relatively small modifications to the vibrational cross sections for energies
FIG. 4. (a) The mean energy of the swarm in THF is plotted against the reduced electric field for our calculations employing either the original cross section set from Garland et al.30 (——–), our Garland-extended cross section set (– –), or our revised cross section set (· · · ·). (b) The percentage difference in the mean energy is compared between the calculations with different cross section sets as a function of the average energy calculated using the Garland-extended cross section set. See text for further details.
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vibrational cross sections should therefore be confirmable when electron-swarm measurements in THF become available, although the challenges in performing such experiments should not be underestimated.30,31 Finally, we consider the impact of the vibrational cross section changes on the attachment and ionization rates, and hence, the breakdown field. In Figure 6, as expected, there is very little impact on the attachment rate, given the small absolute magnitude of that cross section employed using the Garland et al.30 cross section set. There is also essentially no change to the ionization rate when we extend the cross section set to higher impact energies. The enhanced vibrational excitation probability in the revised set, however, reduces the ionization rate, such that an additional 20Td of reduced electric field is necessary to achieve electron avalanche conditions. This could be an important macroscopic manifestation of the role of electron driven vibrational excitation processes. Electron swarm studies in THF are eagerly awaited to verify the predicted macroscopic manifestation of the proposed cross section set, and the reliability of the cross sections by Garland et al.30 for the other scattering processes.
V. CONCLUSIONS
FIG. 5. The percentage differences between the calculated (a) bulk (W Bulk) and flux (W Flux) drift velocities, and (b) reduced transverse (NDT) and longitudinal (NDL) flux diffusion coefficients in THF, with the different cross section sets as a function of the reduced electric field. See text for further details.
less than 5 eV, there can be quite large relative changes in the transport coefficients by the virtue of the rapidly varying collision frequency in that region. We note that for the flux drift velocity differences of the order of 5% are observed. These differences exceed the typical uncertainties placed on an experimental swarm flux drift velocity obtained using a pulsed-Townsend technique.38 The validity of the present
In this paper, we have reported the first integral cross sections for vibrational excitation of a number of composite vibrational modes of THF at intermediate impact energies. Over their common energy ranges, these data agreed well with earlier measurements23 at lower-impact energies up to 20 eV. This suggests that electron-impact vibrational excitation of THF might now be considered as an experimentally benchmarked system. These cross sections were then utilised in swarm studies to evaluate the role of vibrational excitation in electron transport. Here, we found that extending the original cross sections30 to intermediate energies only had a small influence on the calculated transport properties. However, the transport properties and ionization rate may be particularly sensitive to the overall strength of the vibrational excitation processes. Further, the deviations observed are typically larger than the uncertainties on the swarm experiments and thus should be evident when experimental swarm data become available. ACKNOWLEDGMENTS
This research has been partially supported by the Australian and Brazilian Funding organisations (ARC, CNPq). M.C.A.L. acknowledges financial support from CNPq and FAPEMIG. D.B.J. thanks the ARC for provision of a Discovery Early Career Researcher Award. H.V.D. thanks CAPES and the Science Without Borders scheme that supported his studies in Australia. M.J.B. acknowledges CNPq for his “Special Visiting Professor” award at UFJF. 1S.
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FIG. 6. The calculated reduced attachment (Ra) and ionization (RI) reaction rates of THF for the different cross section sets as a function of the reduced electric field. See text for further details.
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