Experimental ion mobility measurements in Xe-C2H6

In this paper we present the results of the ion mobility measurements made in gaseous mixtures of xenon (Xe) with ethane (C2H6) for pressures ranging from 6 to 10 Torr (8–10.6 mbar) and for low reduced electric fields in the 10 Td to 25 Td range (2.4–6.1 kV⋅cm−1⋅ bar−1), at room temperature. The time of arrival spectra revealed two peaks throughout the entire range studied which were attributed to ion species with 3-carbons (C3H5+, C3H6+ C3H8+ and C3H9+) and with 4-carbons (C4H7+, C4H9+ and C4H10+). Besides these, and for Xe concentrations above 70%, a bump starts to appear at the right side of the main peak for reduced electric fields higher than 20 Td, which was attributed to the resonant charge transfer of C2H6+ to C2H6 that affects the mobility of its ion products (C3H8+ and C3H9+). The time of arrival spectra for Xe concentrations of 20%, 50%, 70% and 90% are presented, together with the reduced mobilities as a function of the Xe concentration calculated from the peaks observed for the low reduced electric fields and pressures studied.


Introduction
Measuring the mobility of ions in gases is relevant in several areas, from physics to chemistry, e.g. in gaseous radiation detectors modelling and in the understanding of the pulse shape formation [1][2][3], and also in IMS (Ion Mobility Spectrometry) a technique used for the detection of narcotics and explosives [4]. One of these examples are the so-called Transition Radiation Detectors (TRDs), used for particle identification at high momenta [5,6]. Xenon (Xe) is considered to be the best choice for the main gas, while the choice of the quencher is determined by different parameters [3]. For instance, methane, CH 4 , is an effective quencher but due to its flammability its usage is limited [3]. Nowadays CO 2 is widely used although experiments such as the H1 experiment in HERA Collaboration still make use of Xe-C 2 H 6 based mixtures with Helium (He) [6]. In order to fully understand and model these detectors it is important to have detailed information on the transport properties of ions.

Ion mobility
When we consider a group of ions moving in a weakly ionized gas under the influence of low uniform electric field, these ions will collide with neutral gas molecules, losing energy in collisions while gaining energy from the electric field, eventually reaching a steady state. The resulting -1 -average velocity of the group of ions, v d , also known as drift velocity, is proportional to the electric field, E, and so: v d = KE (1.1) where K is the mobility of the ions and E is the intensity of the drift electric field. This relation is applicable for low E/N, i.e., when the energy gained from the field between collisions is below the thermal energy [4,18]. K is usually expressed in terms of reduced mobility K 0 , suppressing the dependence of the mobility values on the gas pressure. Thus where N is the gas number density and N 0 is the Loschmidt number (N 0 = 2.68678 × 10 19 cm −3 for 273.15 K and 101.325 kPa according to NIST [19]). The mobility measurements are usually presented as a function of the reduced electric field E/N in units of Td (1 Td = 10 −21 V·m 2 ). The reduced mobility obtained is expressed in terms of cm 2 · V −1 · s −1 .

Langevin's theory
According to the Langevin's theory [20], one limiting value of the mobility is reached when the repulsion becomes negligible compared to the polarization effect. This limit is given by: where α is the neutral polarisability in cubic angstroms (α = 4.044 ± 0.013 Å 3 for Xe [21] and α = 4.47 ± 0.01 Å 3 for C 2 H 6 [22]) and µ is the ion-neutral reduced mass in unified atomic mass units. Restrictions to the application of this theory may arise namely if resonant charge transfer occurs [18].

Blanc's law
Blanc's empirical law, which resulted from Blanc's work in the mobility of ions in binary gaseous mixtures, has proven to be most useful when determining ions' mobility using mixtures of gases. Blanc found that the mobility of ions in gaseous mixtures, obeyed a simple relationship as long as the charge transfer interaction is negligible compared to the polarization attraction and short-range repulsion between ion and atoms/molecules. This relationship can be expressed as follows: where K mix is the reduced mobility of the ion in the binary mixture; K g1 and K g2 the reduced mobility of that same ion in an atmosphere of 100% of gas #1 and #2 respectively; f 1 and f 2 are the molar fraction of each gas in the binary mixture [23].

Method and experimental setup
The mobility measurements presented in this study were obtained using the experimental system described in [7]. A UV flash lamp with a frequency of 10 Hz emits photons that impinge on a 250 nm thick CsI film deposited on the top of a Gas Electron Multiplier (GEM) placed inside a gas vessel. The photoelectrons released from the CsI film are guided through the GEM holes by the electric field created by applying an adequate voltage across its electrodes. After gaining enough energy, the electrons will ionize the gas molecules encountered along their paths. While the electrons are collected at the bottom of the GEM electrode, the cations formed will drift across a uniform electric field region towards a double grid; the first one acts as Frisch grid while the second one, at ground voltage, collects the ions' charge. The pulse collected at the collecting grid is converted from current to voltage by a pre-amplifier originating a time of arrival spectrum that is recorded in a digital oscilloscope (Tektronix TDS 1012), set to continuously average 128 pulses, and fed to a PC for further processing. After subtracting the background spectra, obtained without the voltage applied to the GEM (i.e. without drifting ions), to these time of arrival spectra, Gaussian curves are fitted to the peaks in the spectra using Matlab. The trigger in the system is set by the UV flash lamp, providing the initial time information.
Since the peaks' centroid corresponds to the average drift time of the ions along a known distance (4.2725 cm), the drift velocity is determined, and the mobility can then be calculated using expression 1.1. The system relies on the voltage across the GEM (V GEM ) to control the maximum energy of the electrons, which helps in the primary ion identification. Identifying the primary ions will allow to pinpoint secondary reaction paths that lead to the identification of the detected ions.
Since impurities play an important role in the ions' mobility, before each experiment the vessel was vacuum pumped down to pressures of 10 −6 to 10 −7 Torr and a strict gas filling procedure was carried out. No measurement was considered until the signal stabilised, and all measurements were done in a 2-3 minutes time interval to ensure minimal contamination of the gas mixture, mainly due to outgassing processes.
The method described together with the knowledge of the dissociation channels, product distribution and rate constants represent a valid, although elaborate, solution to the ion identification problem.

Results and discussion
The mobility of the ions originated in Xe-C 2 H 6 mixtures has been measured for different reduced electric fields E/N (from 10 to 25 Td) and 8 Torr pressure at room temperature (293 K).
The range of the reduced electric field values used to determine the ions' mobility is limited by two distinct factors: one is the electric discharges that occur at high E/N and the limit of applicability of the low field regime (below about 30 Td). The other is the deterioration of the time of arrival spectra for very low values of E/N (below 5 Td or 1.2 kV · cm −1 · bar −1 ), which has been attributed to collisions between the ions and impurity molecules.
Previous works on the mobilities and ionization processes of Xe [7] and C 2 H 6 [10] in their parent gases have already been performed in our group.
The range of E/N values considered in this work is within the conditions of low reduced field (E/N < 30 Td for the working pressures used).

Xenon (Xe)
Regarding the pure xenon (Xe) case, only one peak is observed for electron impact energy of about 20 eV using a reduced electric field of 15 Td and a pressure of 8 Torr at room temperature. The ion responsible for the peak observed is the Xe dimer ion (Xe + 2 ). While the atomic ion (Xe + ) is a direct result of electron impact ionization (see [24]), Xe + 2 is the result of the following reaction:

Ethane (C 2 H 6 )
In pure C 2 H 6 two peaks have been observed as reported in a previous work [10]. These two peaks were identified as corresponding to two groups of ions: 3-carbon (C 3 H + n ) and 4-carbon (C 4 H + n ) ions, which result from reactions involving intermediary products and C 2 H 6 molecules. Following direct electron impact ionization the primary ions (CH + 3 , C 2 H + 2 , C 2 H + 3 , C 2 H + 4 , C 2 H + 5 and C 2 H + 6 ) are formed (table 2), but they rapidly undergo reactions, which transform them into secondary ions, these being the end products collected at the grid. Table 3 presents a summary of the possible reactions along with their product distribution and respective reaction rates, for the processes between the ions resulting from primary ionization (table 2), and C 2 H 6 molecules, at room temperature. From tables 2 and 3 two groups of ions become evident as already mentioned: one with 3-carbons -C 3 H + n (n = 5,6,7,8 and 9) and another with 4-carbons -C 4 H + n (n = 5,7 and 9) [10]. Nevertheless, their relative abundance is not fully explained by the data in the tables 2 and 3. In fact, -4 -the unexpected higher relative abundance of C 4 H + n can be explained by the fact that the primary ion -C 2 H + 4 may not lead to C 3 H + 7 as shown in table 3, but to an intermediary product, C 4 H + 10 due to the incomplete reaction between C 2 H + 4 and C 2 H 6 at 293 K (our experimental conditions). This is, according to [30], a 2-step reaction:

Xe-C 2 H 6 mixture
In xenon-ethane (Xe-C 2 H 6 ) mixtures, starting with pure C 2 H 6 (0% Xe) and up to pure Xe (100% Xe) two peaks were continuously observed. The ions responsible for these peaks are the two groups identified in pure C 2 H 6 : C 3 H + n (with higher mobility) and C 4 H + n (the most intense). Since the electron impact ionization cross section of Xe [24] is higher than that of C 2 H 6 [28], it is expected that even for low concentrations of Xe (down to about 30% of Xe), Xe + ions are preferentially produced. These Xe + ions rapidly undergo one of the possible reactions with C 2 H 6 , as shown by the rate constants in table 4, rather than with Xe (reaction (3.1)).
The reactions involving Xe + ions and C 2 H 6 molecules lead to the formation of some of the primary ions found in pure C 2 H 6 (C 2 H + 4 , C 2 H + 5 and C 2 H + 6 ), which will also react with the C 2 H 6 molecules (see table 3) producing mainly ions with 3-carbons (C 3 H + 7 , C 3 H + 8 and C 3 H + 9 ) but also -5 - ions with 4-carbons (C 4 H + 9 and C 4 H + 10 ). However, there is a slight difference between the pure C 2 H 6 and the Xe-C 2 H 6 case -the supression of C 2 H + 3 , C 2 H + 2 and CH + 3 . As observed in pure C 2 H 6 , the reaction involving C 2 H + 4 with C 2 H 6 is incomplete, therefore contributing to the C 4 H + n peak area instead of to C 3 H + n . In figure 1 several time of arrival spectra are presented, where 2 peaks are clearly observed, the main and slower corresponding to the 4-carbon group and the faster and smaller to the 3-carbon group, as in pure ethane. Increasing the Xe concentration in the mixture both the peaks' area and ion mobility decrease. For Xe concentrations above 70% and for reduced electric fields higher than 20 Td, a small peak starts to appear at the right side of the main one. Looking at table 3 it is possible to see that Xe + 2 can react with C 2 H 6 resulting in XeC 2 H + 6 which has a lower mobility than the other ions and could explain the appearance of this bump, meaning that Xe + 2 would need to be originated under these circumstances. However, since the reaction for the formation of Xe + 2 (eq. (3.1)) is much slower than the competitive ones displayed in table 3, XeC 2 H + 6 is not expected to be present as can be observed in figure 2. In this figure the ion fraction as a function of time, obtained from the cross sections -7 -and reaction rates for the different primary ions for two Xe concentrations (in figure 2a 50% and in figure 2b 90% of Xe) is presented. As no alternative reaction was found in literature that justifies the presence of this peak, we believe that the mechanism responsible for its appearance is the resonant charge transfer of C 2 H + 6 to C 2 H 6 [18], which will affect the mobility of the product ions (C 3 H + 8 and C 3 H + 9 ), slowing them down. As can be seen, increasing Xe concentration will lead to a significant increase in the reaction time of C 2 H + 6 with C 2 H 6 , which will contribute to the higher influence of the resonant charge transfer on the overall drift time of C 3 H + 8 and C 3 H + 9 , as observed in previous studies [7][8][9].
In addition, a shift of the peaks towards lower drift times (increasing mobilities) with decreasing Xe concentration can be observed. This effect can be explained by the lower polarizability of Xe atoms and higher reduced mass involved in the collisions of the drifting ions formed with Xe atoms which reduces their mobility, as expressed by the Langevin limit formula (eq. (1.3)).
In order to clarify the ion identification hypothesis given earlier, Blanc's law was used as a cross check method. Figure 3 shows the reduced mobility of the ions produced in the Xe-C 2 H 6 mixture for different mixture ratios for a pressure range of 6-10 Torr and for E/N of 15 Td at room temperature, together with Blanc's law prediction for the main candidate ions -C 3 H + n (red) and for C 4 H + n (orange). K g1 and K g2 in Blanc's law (eq. (1.4)), were obtained either using experimental values from literature or, when not possible, by using the Langevin limit formula (eq. (1.3)). -8 -C 3 H + n and C 4 H + n display a small decrease in mobility as Xe percentage increases, both described almost correctly by Blanc's law for all the mixtures studied, except for Xe concentrations above 70%, where a slight deviation from the theoretical curves can be observed. As for the third peak appearing for Xe concentrations above 70%, the mobility was seen to decrease faster than the other peaks, and since a resonant charge transfer is involved in the ion formation process, not much can be expected regarding Blanc's law compliance, as it fails to describe properly such cases. Table 5 summarizes the results obtained.
No significant variation of the mobility was observed in the range of pressures (6-8 Torr) and of E/N (10-25 Td) studied.

Conclusion
In the present work we measured the reduced mobility of ions originated by electron impact in the Xe-C 2 H 6 mixture under different pressures (from 6 to 10 Torr), low reduced electric fields (from 10 to 25 Td) and different mixture ratios.
Our experimental results seem to be relatively consistent with the ones predicted by the Blanc law throughout the mixture range studied.
The two peaks observed consistently for different concentrations of Xe in the mixture are thought to be originated by 3-carbon (C 3 H + 5 , C 3 H + 6 C 3 H + 8 and C 3 H + 9 ) and 4-carbon (C 4 H + 7 , C 4 H + 9 and C 4 H + 10 ) ion groups. The ions' mobility were seen to vary with the mixture composition deviating slightly from the theoretical values predicted by Blanc's law for both C 3 H + n and C 4 H + n , for Xe concentrations above 70%. The C 4 H + n peak area indicates a higher abundance of this group of ions when compared with the 3-carbon group. For Xe concentrations above 70%, a bump starts to appear at the right side of the main peak for reduced electric fields higher than 20 Td, which was attributed to the resonant charge transfer of C 2 H + 6 to C 2 H 6 that can affect the mobility of its ion products (C 3 H + 8 and C 3 H + 9 ). Additionally we verified that the experimental mobility values did not display a significant dependence over the studied range of pressure and E/N (6-10 Torr and 10-25 Td, respectively). Future work is expected with other gaseous mixtures. It is our intention to proceed this line of investigation using mixtures such as Ar-N 2 for the ALICE collaboration, Ar-CF 4 and Ar-CF 4 -IsoButane (T2K mixture) necessary for the LCTPC collaboration, namely in the ILC/ILD experiment.