Synergism in SF6 mixtures with C=C−C backbone compounds

A positive synergy in the electric strength was observed in a previous study in SF6/HFO1234ze(E) mixtures which was shown to result from a strong electron energy moderation capability of HFO1234ze(E) combined with thermal electron attachment of SF6 (Egüz et al 2022 J. Phys. D: Appl. Phys. 55 315203). In the present work, the electron energy moderation properties of compounds with a similar C=C−C backbone are investigated. Swarm and breakdown measurements are performed in pure gases and in mixtures with SF6. Compounds with a trifluoromethyl group (−CF3) showed lower characteristic energy and as a consequence a positive synergism with SF6. Descriptors related to electron energy moderation are identified and computed; a clear trend is found from the analysis of descriptors related to inelastic processes which suggest(s) that vibrational excitations may be the main source of electron energy loss in the compounds showing positive synergy.


Introduction
Recently, the positive synergism in HFO1234ze(E)/SF 6 mixtures at low (swarm) and application (breakdown) pressures was shown to result from the combination of strong electron energy moderation of HFO1234ze(E) and thermal electron attachment of SF 6 [1,2]. The present work is a follow-up and investigates compounds with a similar C=C−C backbone as HFO1234ze(E), pure and in mixtures with SF 6 . The main focus is to investigate the electron energy moderation * Author to whom any correspondence should be addressed.
Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. capabilities of these gases and identify molecular properties which could potentially describe the moderation.
The molecular structure of the compounds is shown in table 1. The HFO1234ze(E) and HFO1225ye(Z) molecules have been investigated in [10][11][12][13] and are given here for comparison. Molecular parameters which showed a strong correlation with electric strength in previous works (e.g. in [14,15]) and/or are relevant for the present study are calculated using Turbomole [3]-namely the adiabatic ionization energy ϵ ad i and electron affinity ϵ ad a , the static electric dipole moment µ e and the average static electronic polarizability α (the last two parameters showed good agreement with measurements for a large set of molecules in [15]). The adiabatic ionization energy/electron affinity corresponds to the difference between the ground state electronic energy of the cation/neutral and of the neutral/anion at their optimized (equilibrium) geometries. The simulations are performed as in [15] for the remaining two compounds C 3 H 6 and C 3 H 4 F 2 , using the exchange-correlation Table 1. Molecular structure and simulated properties of the pure compounds using Turbomole and ORCA [3,4]: the adiabatic ionization energy and electron affinity are defined respectively as ϵ ad i = ϵ ad cation − ϵ ad neutral and ϵ ad a = ϵ ad neutral − ϵ ad anion , µe and α correspond respectively to the static electric dipole moment and the average static electronic polarizability. T B is the boiling point (the values without reference are given by the vendor). I IR and I UV correspond to the integral of the IR and UV absorption spectra given in the supplementary section. energy functional BP86 [16,17] and basis sets def-TZVP and def-QZVPP respectively for the calculation of ϵ ad a , ϵ ad i and µ e , α. In addition, the integral of the IR and UV absorption spectra-I IR and I UV -are obtained with the simulation tool ORCA version 5.0.3 [4] using the basis set aug-cc-pVTZ and functional wB97X-D3. 30 excited states are considered in the TD-DFT calculations. The spectra are shown in the supplementary section and the plotted intensities correspond to the absolute square of the transition dipole moments. These properties will be discussed in relation with the experimental results in section 4. The effective ionization rate coefficients of all measured mixtures are shown in the appendix.
The structure of the paper in addition to these two sections is as follows: section 2 describes the experimental methods. The results section is divided into 3 parts: first, the electron swarm parameters measured in propene, 1,1-difluoropropene, HFO1234yf and HFO1225ye(E) are shown. The second part investigates the synergy effect in SF 6 mixtures with these compounds and the third part focuses on the ionization and attachment rates in C 3 H 6 /SF 6 and HFO1234yf/SF 6 mixtures.

Experimental methods: swarm and breakdown experiments
The swarm measurements were performed with a pulsed Townsend experiment (described in [18,19]) at low pressures-ranging from 200 Pa to 25.2 kPa and electrode distances between 11 and 29 mm. Assuming a Gaussian spatial distribution of the electron swarm (boundaries at infinity), the measured electron displacement current can be evaluated according to the analytical expression: with I 0 = N e (0)q/T e the electron current at t = 0 and N e (0) the initial number of electrons. The exponential term describes the growth of the discharge due to ionization and attachment processes via the effective ionization rate ν eff = k eff N with N the gas density. The term in parenthesis accounts for the fraction of electrons absorbed at the anode (and no longer contributes to the current) which depends on the drift time T e (or bulk drift velocity w = d/T e with d the distance between electrodes) of the electron swarm between the electrodes and bulk longitudinal diffusion coefficient D L = 1 2 w 2 τ D . Details on the evaluation method can be found in [10,19]. The evaluated density-scaled diffusion coefficients show a pressure-dependence which is a consequence of neglecting in equation (1) the initial broadening of the swarm and of the limited bandwidth of the experimental system, detailed in [19]. Therefore, diffusion parameters obtained for the lowest pressures should be considered as most reliable.
The breakdown experiments were performed under AC voltage stress and uniform electric field distribution created by two plane electrodes with a Rogowski-shaped edge profile. The voltage rate of rise before the breakdown is 0.1 kV s −1 . The electrode finish is sandblasted and preconditioned in order to reduce the statistical time lag (electron field emission from micro-tips) and prevent trends in breakdown distribution caused by possible accumulation of solid gas decomposition products on the surface [20]. For the present investigations, an electrode spacing of 10 mm is used and the total pressure of the HFO1234yf/SF 6 mixtures is 100 kPa at ambient temperature. In each gas mixture, 40 breakdowns are performed. The breakdown results are presented as median with 84.13 and 15.87 percentiles with 75% of confidence according to [21]. The experimental setup is detailed in [1].

Electron swarm parameters in pure compounds
Measurements of swarm parameterseffective ionization rate coefficient, bulk drift velocity and density-scaled bulk longitudinal diffusion coefficient-in C 3 H 6 are shown in figure 1 from 10 to 270 Td. Below 10 Td, the signal-to-noise ratio is too low and the current signals cannot be evaluated. Below 30 Td, k eff values are negative and decrease with decreasing E/N indicating possible electron attachment process(es) at thermal and sub-thermal electron energies (although only a dissociative attachment process between 5 and 7 eV was observed in [27]). The highest pressure measurements (7.3 kPa) are used to determine the densityreduced critical field from the zero-crossing of k eff : (E/N) crit = 88.7 ± 7.5 Td. No pressure dependence is observed in k eff and w suggesting that two-body (non-conservative) collisions are dominant in these pressure and E/N ranges. As briefly mentioned in section 2, the density-scaled diffusion coefficients are increasingly over-estimated with higher pressures and E/Nvalues. In these conditions, the diffusion of the swarm until arrival at the anode is less pronounced, and neglecting the initial broadening in the evaluation becomes important. In addition, the falling edge of the electron current becomes steeper with lesser diffusion and consequently the measured signal more affected by the bandwidth of the system.

HFO1234yf.
Measurements of swarm parameters in HFO1234yf are shown in figure 2. k eff exhibits a pressuredependence in the measured pressure and E/N ranges: the values decrease with increasing pressure which suggests the occurrence of three-body electron attachment process(es). We assume the three-body attachment model described in [28,29] to evaluate the three-body attachment rate and the pressure-independent part k eff,0 of the effective ionization rate coefficient which consists of non-conservative two-body collisions i.e. ionization and potential dissociative attachment and/or three-body attachment processes with long-lived transient anions. The kinetic model in the pure gas is reminded below: Stabilization of the excited anions (HFO − ) * (III), and potentially, electron detachment from (HFO − ) * (IV) occur in collision with a third body -a neutral HFO molecule-with rates k stab N and k det N respectively. In order for these processes   to be observable, their rates need to be in the same order as the auto-detachment rate τ −1 (II), in which case the observed three-body attachment rate is effectively [28]: with k lin = k at τ k stab and N sat = τ −1 (k stab + k det ) −1 . In the measured E/N and pressure ranges, k eff varies linearly with pressure, which corresponds to the region N ≪ N sat (in which the mean time between stabilization/detachment events is much larger than the lifetime τ of the transient anion) [28]: The obtained rates from the linear regression of equation (3) are shown in figure 3 and the resulting fits in figure 2. Results are satisfactory above 80 Td. Compared to HFO1234ze(E) in [10], k eff,0 of HFO1234yf peaks at similar E/N value of around 150 Td, however lower in magnitude, and seems to decrease to zero as E/N → 0. The two-body attachment processes thus have an energy threshold of possibly a few eV in both compounds. The three-body attachment appears to be significantly less efficient in HFO1234yf-k lin is around one order of magnitude lower than in HFO1234ze(E) at E/N values above ∼100 Td. Contrarily to HFO1234ze(E) for which the peak is reached at 110 Td, k lin increases continuously in HFO1234yf in the measured E/N range. Note that in both compounds, the transient anion is produced at energies higher than thermal as e.g. in c- Measurements of swarm parameters in C 3 H 4 F 2 are shown in figure 4 between 30 and 190 Td. No pressure-dependence in k eff and w is observed. Based on the 1.32 kPa measurements, the (E/N) crit is estimated to be 122.8 ± 2.1 Td. Negative k eff values from 30 Td until E/N = (E/N) crit indicate one or several twobody electron attachment processes present at energies above thermal.

HFO1225ye(E).
Measurements of swarm parameters in HFO1225ye(E) are shown in figure 5. Even at these low pressures, it was not possible to evaluate the drift velocity and diffusion coefficient at 550 and 700 Pa between 80 and 240 Td since the electron current reaches zero before the swarm arrives at the anode due to strong electron attachment in this E/N-range. Whether or not k eff varies with pressure is not clear given the small pressure range, although the absolute values for E/N > 310 Td show a decreasing trend with increasing pressure. Efficient three-body attachment with respect to both HFO1234 compounds was observed in the isomer HFO1225ye(Z) in [11] and a similar threebody mechanism is expected in HFO1225ye(E). As for HFO1234yf, an analysis of the three-body electron attachment could similarly be done if measurements at higher pressures were available.

Synergy in mixtures with SF 6
Results of (E/N) crit in SF 6 mixtures with HFO1234yf, HFO1225ye(E), HFO1225ye(Z), C 3 H 6 , C 3 H 4 F 2 and N 2 (for comparison) are shown in figure 6. They are based on effective ionization rate coefficient measurements shown in figures 11-15 in the appendix. Measurements for each mixing ratio have been done for a single pressure, we are thus disregarding in the present study the potential pressuredependence in the mixtures with compounds exhibiting three-body attachment namely HFO1234yf, HFO1225ye(E) and HFO1225ye(Z).
A positive synergy is observed in the mixtures with compounds possessing a trifluoromethyl group −CF 3 , namely, HFO1234yf, HFO1225ye(E) and HFO1225ye(Z). In the case of HFO1234yf and HFO1234ze(E), the optimum mixture is with around 40% SF 6 in which the (E/N) crit is respectively around 14% and 17% higher than that of SF 6 . Both isomers show similar synergy over the whole mixing ratio range. The optimum mixture is reached faster at around 35% with HFO1225ye isomers. Both isomers show a stronger synergy than the HFO1234's above 20% HFO. Note that the three-body attachment rate in the pure compounds follows: HFO1225ye(Z) > HFO1234ze(E) > HFO1234yf. There is  Breakdown measurements: (E/N) bd , density-reduced electric field calculated from breakdown voltages at 1 bar gas pressure. 100 breakdown measurements are performed for each mixture. The median and the 75% confidence interval of the 84th and 16th percentiles are given. a weaker synergy in mixtures with C 3 H 6 and C 3 H 4 F 2 . Even though C 3 H 6 has a lower (E/N) crit than C 3 H 4 F 2 , it appears to be interacting more favourably with SF 6 synergistically. Figure 7 shows the electric strength in SF 6 mixtures with HFO1234yf measured with both swarm and breakdown techniques. (E/N) bd corresponds to the density-reduced electric field calculated from the breakdown voltages measured at

Attachment and ionization in SF 6 mixtures with propene and HFO1234yf
Using the method described in [33], ionization and attachment rate coefficients in C 3 H 6 /SF 6 and HFO1234yf/SF 6 around the critical field are given in figures 8 and 9. For each data point, the errorbars take into account the uncertainty on k eff and the standard deviation in the values measured at different electrode distances for the same E/N value. We intentionally choose not to include the uncertainties on the remaining parameters which define k i and k a for better readability and comparison of the data between mixtures.
In the case of C 3 H 6 /SF 6 , we see that increasing the amount of C 3 H 6 up to 30% (mixture with 70% SF 6 in figure 8) enhances total ionization in the mixtures and the rate remains relatively constant between 8% (92% SF 6 ) and 30% C 3 H 6 (∼11% higher than in pure SF 6 ). Total attachment is also slightly increased thus maintaining the critical field close to 350 Td up to 30%. From 30% to 50.3% C 3 H 6 (70%-49.7% SF 6 ), attachment drops significantly by 22% which is partly compensated by the decrease in ionization. Note that at ∼50% (49.7% SF 6 ), the ionization rate is comparable in magnitude and E/N-dependence to that in pure SF 6 . Until ∼93% C 3 H 6 (7.1% SF 6 ), ionization progressively drops and seems to stay relatively constant in mixtures with higher C 3 H 6 amounts. However, the drop in attachment is faster hence the critical field decreases monotonically until pure C 3 H 6 .
In HFO1234yf/SF 6 mixtures, similarly to C 3 H 6 /SF 6 (and contrarily to HFO1234ze(E)/SF 6 in [1]), there is a mixing ratio range-0% to around 25% HFO1234yf (between 100% and close to 74.5% SF 6 )-in which total ionization is higher or equal to that in SF 6 . However, the increase in total attachment is more significant and over-compensates that of ionization, thus enhancing (E/N) crit (note that the attachment rate is higher than in both SF 6 /HFO1234ze(E) and SF 6 /C 3 H 6 in this range). Above 25% HFO1234yf (below 74.5% SF 6 ), both ionization and attachment rates decrease continuously (similarly to the other two mixtures). Until ∼60% HFO (42.1% SF 6 ) the synergy effect is nevertheless still enhanced due to faster decrease of total ionization.

Discussion
The comparable electric strengths in the HFO1234 isomers at a given pressure-and particularly k eff,0 values in figure 3 which would correspond to the limiting case where no three-body attachment were present in the pure gases (N → 0)-give reasonable indication that HFO1234yf has similar electron energy moderation capability as HFO1234ze(E) as discussed in [1]. In addition, the ionization rates in HFO1234yf/SF 6 mixtures between 14.3% and 74.5% SF 6 appear to be overall lower than in C 3 H 6 /SF 6 mixtures. These observations motivate to analyse the electron energy moderation capability of the present compounds.

Electron energy moderation in pure compounds
The mean electron energy of the swarm cannot be directly measured in the pulsed Townsend experiment. Instead, the characteristic energy ϵ ch defined as eD/µ (in eV), with D the evaluated diffusion-transverse (D T ) or longitudinal (D L )and µ = w/E the mobility, is commonly used as an approximate measure of the mean energy ⟨ϵ⟩ [34,35]. Assuming a nearly isotropic motion of electrons in velocity space [34] (we disregard the additional terms due to non-conservative collisions in the equations below and assume flux and bulk parameters relatively similar in the measured low E/N ranges): where σ tot (ϵ) is the sum of the elastic momentum transfer cross section and all inelastic cross-sections. f 0 (ϵ) is the spherically symmetric space-time constant electron energy distribution function referred to as EEDF in eV −1 (zeroth order component in the density gradient expansion of the isotropic electron distribution function). F T (E/N) is a dimensionless quantity (which also depends on the mean electron energy) and is around 0.3 according to [35], between 1 and 0.5 according to [34]. If all collisions are elastic, F T ≈ 0.76 [34]. We measure the bulk longitudinal diffusion coefficient in our pulsed Townsend experiment. The diffusion of the swarm is generally anisotropic and in principle, the longitudinal and transverse diffusion coefficients are equal only at very low E/N values [34,36]: The quantity G(E/N) is a function of the small spatial dependence of the electron energy distribution-electrons at the front of the swarm have a slightly higher energy than at the back (first-order component of the density gradient expansion). D L is thus generally smaller than D T . The difference is expected to decrease with higher inelastic and elastic collisions and more speculatively, with higher energy losses in conservative inelastic collisions. Similarly to equation (5), F L = eDL µ⟨ϵ⟩ will therefore be lower than F T . (For different gases for which complete sets of cross-sections are provided on LXCat [37], we obtain using Bolsig+ for F L between 100 and 300 Td: C 3 H 6  Consequently, D L /µ values given in figure 10 represent a fraction of the mean electron energy (possibly between 20% and 60% based on the simulations-no estimate for F L was found from the literature search) which depend on E/N values and gas properties, and thus the comparison between compounds is not so straightforward. Nevertheless, compounds which have a −CF 3 group, i.e. HFO1234ze(E), HFO1234yf and HFO1225ye(E), and which also show a positive synergy with SF 6 , have similar characteristic energies and clearly lower than the other two compounds in the measured E/N range. Assuming relatively close F L values in all compounds, the mean electron energy ⟨ϵ⟩ of both HFO1234 isomers would be a factor of 1.5-2 lower than that of C 3 H 6 and C 3 H 4 F 2around 2-3 times smaller than N 2 -in the measured E/N range.
Therefore, in comparison to C 3 H 6 and C 3 H 4 F 2 , the higher electric strength of HFO1234 isomers seem to result from a higher moderation capability which counters more efficiently the increase of ionization with E/N. Electron attachment plays a more significant role in combination with moderation in the HFO1225 isomers.

Synergism with SF 6
The clear correlation that gases with lowest characteristic energy show positive synergy with SF 6 supports the hypothesis that it is their moderation capability that is mainly responsible for the positive synergy. Note that in compounds with higher number of fluorine atoms i.e. HFO1225 isomers (and C 3 F 6 as observed in [29]), which show stronger three-body attachment, these processes may contribute further to the synergy, at high (breakdown) pressures in particular, from enhanced three-body attachment rate in mixtures with SF 6 .
In the case of C 3 H 6 /SF 6 mixtures, direct attachment to SF 6 dominates over two-body attachment processes to C 3 H 6 . It seems from figure 8 that the low energy part of the SF 6 EEDF is distorted by the addition of C 3 H 6 and shifted towards lower energies where attachment to SF 6 is most efficient (possibly due to resonant-type inelastic collisions such as indirect vibrational excitations). However, overall the moderation is not strong enough to sustain the decrease of electron attachment due to lower SF 6 concentrations in the mixtures.
In HFO1234yf/SF 6 mixtures, different attachment processes may be occurring (as in HFO1234ze(E)/SF 6 [1]): dissociative two-body attachment to SF 6 and to HFO1234yf, apparent two body attachment to parent SF 6 molecule, threebody attachment to HFO1234yf through stabilization by both HFO1234yf and SF 6 and potentially, because of the higher electron affinity of SF 6 molecules (1 eV [44]) compared to the calculated electron affinity for HFO1234yf of −0.166 eV (table 1), indirect (three-body) attachment to SF 6 through charge transfer from metastable HFO1234yf anions. Both three-body collision rates depend on the total gas pressure which is varied between 200 and 300 Pa depending on the mixing ratio. The detailed analysis of these processes is not within the scope of this study. Nevertheless, based on the analysis of the previous section and comparable results in breakdown measurements at 1 bar, these processes should be comparatively small and attachment should predominantly be direct attachment to SF 6 . The variation with mixing ratio in ionization and attachment rates in the mixtures (figure 9) are therefore mainly due to the change in electron energies. The trends of both rates are very similar to those in C 3 H 6 /SF 6 except for the magnitude of the changes, in the attachment rate in particular.

Potential descriptors for moderation
We have carried out preliminary investigations to identify molecular quantities which could potentially be used as descriptors (and more optimistically predictors) for moderation via elastic and conservative inelastic processes. There are already several predictive studies which correlate molecular properties to the electric strength of a gas [9,14,15,45]. It was shown that for polar molecules (which is the case for the present compounds), a high static electric dipole moment µ e and average polarizability α was beneficial (for high electric strength) which was related in [15] to high elastic collision cross section, inline with earlier studies which estimated the amplitude of the elastic cross section at low electron energies varying as µ 2 e [15,46,47]. Furthermore in [14], the integrated optical absorption spectrum which estimates the amount of light absorbed in molecular electronic excitations, showed a significantly high correlation with electric strength (R 2 = 0.726). These quantities should therefore be potential descriptors of the electron energy moderation capability of weakly-attaching molecules in particular. From the simulation results in table 1, a few observations can be made: compounds with −CF 3 group seem to have overall a slightly higher permanent dipole moment and average polarizability (the latter probably due to the higher number of electrons), which suggest higher elastic cross sections. The integral of the simulated IR and UV spectra is proportional to the total photon absorption cross section in vibrational and electronic excitations respectively [48]. These quantities could potentially give an estimate of the amplitude of the total electronmolecule vibrational and electronic collision cross sections. From the results in table 1, a clear trend appears: compounds with −CF 3 group show highest absorption in the IR range. I IR values are similar in all 4 compounds and more than 45% and 84% higher than in C 3 H 4 F 2 and C 3 H 6 respectively. In the UV range however, the former show the lowest cross sections (this is also the case when disregarding electronic excitations above the ionization energy which would have much less effect on the electric strength). Note that the transition due to the presence of the double bond which should be situated around 5.5 eV in HFO1234ze(E) and observed experimentally in [49], is not present in the calculated UV spectrum. Based on these descriptors, the electron-molecule elastic collisions and especially vibrational excitations may be more significant in moderating electron energies in these compounds.

Conclusion
In this work, we investigated the electron energy moderation properties and synergy in electric strength with SF 6 of compounds with a similar C=C−C backbone as HFO1234ze(E). We measured the swarm parameters in the pure compounds and the synergy in mixtures with SF 6 . Our findings indicate that molecules with the trifluoromethyl group −CF 3 have a lower mean electron energy and as a consequence, show a positive synergy in mixtures with SF 6 . Therefore, the presence of −CF 3 appears to enhance the electron energy moderation capability in C=C−C backbone compounds. In a second step, molecular quantities related to moderation were identified and calculated for the pure gases. Elastic collisions and vibrational excitations particularly may be more efficient in compounds with −CF 3 group. Further work is needed in this direction.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).