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Ionic Polymerization in Cold Plasmas of Acetylene with Ar and He Miguel Jimenez-Redondo, Isabel Tanarro, Ramón Javier Peláez, Lidia Díaz-Pérez, and Victor J. Herrero J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b06399 • Publication Date (Web): 28 Aug 2019 Downloaded from pubs.acs.org on August 30, 2019
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Ionic Polymerization in Cold Plasmas of Acetylene with Ar and He Miguel Jiménez-Redondo*, Isabel Tanarro, Ramón Peláez, Lidia Díaz-Pérez and Víctor J. Herrero* Instituto de Estructura de la Materia (IEM-CSIC) Serrano 121-123, 28006, Madrid, Spain
[email protected]. Tel. +34 915166800 ext 942325
[email protected]. Tel. +34915901605
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ABSTRACT The ionic polymerization of acetylene in cold plasmas of C2H2/He and C2H2/Ar has been experimentally studied and modeled in rf discharges with conditions selected to avoid particle formation. Steady-state distributions of positive and negative ions were measured with mass spectrometry. All the measured distributions are dominated by ions with an even number of carbon atoms, reflecting the characteristic polyyne structures typical for the polymerization of acetylene. The distributions show a monotonic decrease in intensity from ions with two carbon atoms till the highest number of atoms detected. For cations, the distributions extend till 12 carbon atoms. The anion distributions extend further, and negative ions with 20 C atoms are observed in the C2H2/Ar plasma. From the measured mass spectra it is not possible to decide on the possible presence of aromatic species in ions with more than 6 carbon atoms. A simple model assuming a homogeneous discharge was used to describe the plasma kinetics and could account for the measured ion distributions with reasonable values of charge density and electron temperature. The results of this work stress the important role of the vinylidene anion and indicate that Ar and He do not have much influence on the carbon chemistry.
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1. INTRODUCTION Hydrocarbon plasmas are characterized by a complex chemistry that leads to the formation of particles1. Among them, acetylene discharges, where polymers are readily formed, have received much attention 2. It is known that the dust particles formed in acetylene plasmas are largely made of amorphous hydrogenated carbon 3–10, usually abbreviated a-C:H or HAC. This denomination encompasses a group of solids containing aromatic and aliphatic structures in variable proportions that depend on formation conditions11. The high tendency of acetylene to polymerize is not restricted to plasmas, but is also manifest in pyrolysis and combustion where soot is abundantly formed 12–14 . It has also been claimed that the polymerization of acetylene may play a key role in the formation of polyaromatic dust and polyyines in the last stages of evolved stars 15–19. Possibly, some of the main polymerization mechanisms are the same in all these environments. In fact, a comparison of their respective IR spectra strongly suggests that particles generated in acetylene plasmas are similar to carbonaceous particles in the diffuse interstellar medium 7,8. Experiments and models of varying complexity20–27 established that the first steps of acetylene polymerization lead to neutral and ionic polyynes, with linear chains formed by carbon atoms with alternating single and triple bonds. A common reference in these studies is the experimental work by Descheneaux et al.3, who reported mass spectra of the neutrals, cations, and anions present in a rf discharge of pure C2H2. The dominant peaks in these spectra correspond to species with an even number of carbon atoms, revealing that CC triple bonds are not broken in the plasma and suggesting that C2 units dominate the polymerization routes. Peaks for odd numbers of carbon atoms were also found, but in much smaller amounts. The mass spectra of the neutrals did not go beyond C4Hx, but those of anions and cations extended to masses up to 200 u (C14Hx), highlighting the importance of ionic polymerization pathways. Shortly after the publication of that work, a zero dimensional (0D) kinetic model of the rf plasma, proposed by Stoykov et al.4 including neutrals, ions and linear and cyclic species, could justify that polymerization was indeed mainly caused by addition of C2 growth species and formation of linear molecules. Mass spectra of the positive ions in an rf discharge of C2H2 diluted in Ar were measured by Kovacevic et al.6. They obtained a pattern of dominant peaks for C2nHx+ masses similar to that of Descheneaux et al.3 for a pure acetylene discharge, which suggested that the presence of Ar in the plasma had little influence in the carbon chemistry. This conclusion had already been advanced in an early work by Vasile and Smolinski20 who measured similar cation distributions in rf discharges of pure C2H2 and of C2H2 diluted in Ar or He. The neutral species of the initial polymerization in Ar/He/C2H2 plasmas were studied by von Keudell and co-workers24,25,27 using molecular beam mass spectrometry. By applying Bayesian probability theory, these authors could reconstruct the mass spectra of the original neutral molecules from the fragment ions in their mass spectrometer and provide absolute values of the concentrations. They detected polyynes up to C8H2 and confirmed that the addition sequence leading to CnH2 was the main polymerization route for neutral compounds. These authors also 3 ACS Paragon Plus Environment
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found that C2H4, present either as an impurity or as a plasma product, played an important role in the chemistry leading to hydrogen-rich CnHx species also observed in the experiments. A self-consistent one dimensional (1D) fluid model of an rf discharge of pure C2H2 was advanced and refined in a series of articles by Bogaerts and coworkers 22,23,26. In the improved version of Mao et al.26 the model could account reasonably well for the distributions of neutrals and ions of the experiments of Descheneaux et al.3 and of Consoli et al.25 The model of Mao et al. included neutrals and ions, as well as linear, branched and cyclic CxHy species, and identified C2H, C2H2+ and C2H– as key active species in the neutral, cationic and anionic polymerization routes respectively. Specifically, the model incorporated a set of dissociative electron attachment reactions to branched chain hydrocarbons, vibrationally excited states, and species of the C2nH2– type for a better description of anion chemistry. In spite of these improvements, the agreement with the measured negative ion distribution was not so good as that with the distributions of neutrals and positive ions. The fact that this model, developed for pure C2H2 plasmas, could account for the experimental results in the Ar/He/C2H2 discharges of Consoli et al.25 suggested again that the presence of the rare gases does not change significantly the C2H2 plasma chemistry. A self-consistent 1D model, including Ar reactions and simplifying the acetylene chemistry of the model of Mao et al.26 was applied by Ariskin et al.28 and by Schweigert et al.29 to the Ar/C2H2 discharge of the experiment of Kovacevic et al.6. The calculations could reproduce approximately the measured cation distributions. The authors of these articles concluded that the densities of negatively and positively charged heavy hydrocarbons were sufficiently large to be precursors for the formation of nanoparticles in the discharge volume. Further experiments and models for rf acetylene discharges have been recently published. Denysenko et al.30 used a volume averaged model with a simplified carbon chemistry to simulate the effect of nanoparticles in the composition of an Ar/C2H2 RF plasma. Within this model, the increase in electron temperature associated with particle charging led to a growth in the density of Ar+ and of metastable Ar atoms, and to a decrease in the densities of acetylene and hydrocarbon ions. The results were in qualitative agreement with the mass spectra of neutrals and positive ions measured by the same authors in a rf Ar/C2H2 discharge. Akhoundi and Foroutan31 used a selfconsistent 1D fluid model to study the effects of gas dilution on the nucleation process in a low pressure rf discharge of acetylene. Contrary to the prevailing opinion 2,6,20,25–27, these authors concluded that the dilution of acetylene in Ar or He has a significant effect on the carbon chemistry, enhancing the importance of radicalic polymerization and largely suppressing ionic routes. The model includes reactions of Ar and He, and changes somewhat the acetylene chemistry with respect to the model of Mao et al.26. New cationic species are introduced, but aromatic chemistry is omitted and the anionic chemistry is simplified. The calculations show that polymerization is enhanced with respect to a pure C2H2 plasma for dilutions up to 40 % due to an increase in the electron density, and this effect is more intense for Ar. There are also appreciable differences between the simulated distributions of neutrals and ions, especially of anions, in the C2H2/He and C2H2/Ar mixtures. Despite the experimental and modelling work on acetylene plasmas mentioned in the previous paragraphs, many relevant aspects of their chemistry remain unknown. It is not clear, for instance, at what point of the nucleation process do aromatic structures form. Descheneaux et al.3 suggested 4 ACS Paragon Plus Environment
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that a slight change in the pattern of the cation distribution, allowing for hydrogen richer CxHy+ ions around C6, could be an indication of the presence of benzene and benzene derivatives. The formation of aromatic compounds, usually limited to two rings, is also incorporated in some of the mentioned chemical models,4,26 which are normally limited to species with 10 or 12 carbon atoms. The predicted concentrations of aromatics in the discharges are small as compared with the major C2nH2 polyynes, but still appreciable. Weak signals attributable to C6H6 molecules were obtained in the molecular beam mass spectrometry measurements of Consoli et al.27 but they could not be unequivocally ascribed to benzene. At present, evidence for aromatic compounds in the early polymerization stages is not conclusive. It is generally assumed that negative ions play a key role in particle nucleation in low pressure plasmas because they remain trapped by the plasma potential and can grow to large sizes providing effective condensation nuclei. In spite of it, there are few data available on negative ions in acetylene plasmas and the model simulations are not so satisfactory as for neutrals or positive ions. As far as we know, the only experimental anion distribution reported in the literature is that of Descheneaux et al.3 for a pure acetylene rf discharge, which has been used as a reference in subsequent modeling. Most models22,23,28–31 include a simplified version of anion cluster growth, based on the so called Winchester mechanism32 and lead to a monotonic decline of the anion intensity with growing carbon atom number, which is at variance with the measured distribution3. Only the model of Mao et al., which, as indicated above, incorporates a more complex anion chemistry and leads to a qualitative agreement with the experimental data. Further measurements of anion distributions would thus be desirable. On the other hand, many studies on C2H2 plasmas and notably those of particle formation are carried out in mixtures with noble gases, mostly Ar, which allow for a better control and a more stable discharge operation. As just mentioned, the general assumption that the carbon chemistry is not appreciably affected by the dilution of acetylene in noble gases has been questioned by the recent model results of Akhoundi and Foroutan31, and there is also some experimental evidence suggesting that differences between the chemistry in C2H2/Ar and C2H2/He plasmas might be at the root of differences in the structure of the generated particles, as revealed by their IR spectra 8. In this work we address polymerization processes in plasmas of acetylene mixed with noble gases, with special emphasis on the ionic species. We provide measurements of the distributions of cations and anions in C2H2/He and C2H2/Ar radiofrequency discharges carried out under strictly comparable conditions for each mixture. The focus is set on the very early polymerization stages, before the onset of particle formation. We introduce also a simple model of the plasma chemistry for the rationalization of the data. The results are discussed and compared with previous work. 2. EXPERIMENTAL SECTION The experimental set-up for plasma generation is based on a capacitively coupled RF discharge reactor designed and mounted in our laboratory. A scheme of the whole reactor and diagnostics is displayed in Figure 1.
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Figure 1 a) Top view of the experimental set-up b) image of the plasma in a He discharge.
The cylindrical stainless steel chamber of the reactor has a diameter of 40 cm and a height of 30 cm. It has several vacuum flanges of different types and sizes for gas inlets and vacuum pumps, feedthroughs, windows and diagnostic systems. For ease of operation and maintenance, its upper and lower ends can be totally or partially removed thanks to a pair of coupled flanges of 40 and 25 cm diameter placed at each side. Various gas flow controllers (Alicat) with different gas flow ranges (2, 10 and 50 sccm), with their corresponding ball valves, and connected in parallel to a gas mixer tube, allow the control of the gas mixture composition. Under operating discharge conditions, the chamber is evacuated though a 14 m3/h rotary pump. It is connected to a side flange and fitted with a ball valve and a handmade filter of several sheets of porous paper, easily replaceable, piled between two metal grids, which avoid the entrance of undesirable dust to the pump (without appreciably limiting the pumping speed until it gets dirty). The chamber can be evacuated down to a background pressure lower than 10–7 mbar by means of a turbomolecular pump (Oerlikon 350i), backed by a dry pump and placed also laterally. This pump was specially selected because it provides very similar pumping speeds ( 420 l/s) for light (H2 and He) and heavy (Ar and N2) molecules. A capacitive absolute pressure gauge (up to 1 Torr) and a set of Pirani - Penning gauges measure the pressure in the reactor. The discharge is produced between two parallel stainless steel electrodes of 20 cm diameter and 1 cm width, separated by a 3 cm gap, placed in the middle of the reactor. The lower electrode is grounded, as well as the reactor walls; the upper one is connected to a 13.56 MHz, 300 W, rf generator (BDiscom, BDS 300HF-AFP with auto-matching unit BDS AMN 750). For plasma modulation, the rf generator can be controlled by an external TTL (0-5 V) signal. The minimum on or off time is 4 milliseconds. Mass spectrometric diagnostics is performed by means of two quadrupole mass spectrometers placed in two separate vacuum chambers, equipped with their corresponding vacuum gauges and 6 ACS Paragon Plus Environment
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differentially pumped by their respective turbomolecular and dry pumps, which allow residual pressures in the scale of 10–8 mbar. Neutral species up to 100 u are detected by means of a Pfeiffer QMG-200 mass spectrometer, whose chamber is connected to the upper part of the reactor through a ball valve and a fine needle valve. Positive and negative ions up to 512 u can be measured with a Plasma Process Monitor Pfeiffer PPM-421, fitted to the reactor through a gate valve and a bellow manipulator. A dc potential of different polarity (up to ±25 V) can be applied to the extractor plate of the spectrometer, depending on the sign of the ions to be collected. The calibration procedure for the spectrometers was described in Carrasco et al33. Plasma light is collected for emission studies through a fused silica window and two optic fibers connected to two optical spectrometers of different performances. One of them is a high resolution Jobin Yvon-Horiba FHR1000 dispersive spectrometer in Czerny-Turner configuration, with a focal distance of 1 m, a diffraction grating of 1800 mm–1 and a cooled CCD detector. The spectral range for the system with this configuration is 300-800 nm. The input slit width is adjustable, and the usually employed value of 24 µm (similar to the pixel width of the CCD) provides a spectral resolution of 0.020 nm. A more detailed description of the apparatus and its calibration in sensitivity and resolution was given in Jimenez-Redondo et al.34. Integration times, adjusted to obtain a sufficient number of counts for the lines of interest, lead to typical acquisition times of the whole spectrum of some minutes. The second optical spectrometer has a quick response and low spectral resolution. It is a compact grating spectrometer (Ocean Optics, QE65000) in symmetrical crossed Czerny Turner configuration, with no moving parts, 0.1 m focal length, 300 grooves/mm grating , cooled linear CCD-array detector and input slit of 25 μm width. The spectral range of the system is 200-980 nm, with 0.8 nm spectral resolution. Typically, 50 ms are enough to acquire and store a whole spectrum. Dust formation can be monitored by means of Mie scattering of light from the particles. To this aim, two lasers of different wavelengths (red and green) can be used. The lasers propagate at collinear incidence in the plasma region and at mid-height between the two electrodes, in a direction perpendicular to that of light collection by the optical spectrometers. The green laser (532.1 nm) has a power limit of 200 mW and was manufactured by Integrated Optics; the red one is a Schäfter+Kirchhoff laser diode emitting 38 mW at 660 nm. A Mightex high sensitivity CCD monochrome camera, CCE-B013-U, and a narrow bandpass filter centered at 532 nm placed in a window in front of the spectrometers allow the recording of the light from the green laser scattered by the dust cloud. For this application, a small cylindrical lens, placed before the laser exit, expands the beam vertically, so that two dimensional images of the dust can be obtained. For the measurement of ion distributions, particle formation was avoided in the discharges. The fulfillment of this condition was checked by verifying the absence of light scattering from the green laser traversing the plasma volume. C2H2 and either Ar or He were introduced to the reactor through separate flow controllers. The specific flows for the two mixtures studied were C2H2(2 sccm)/Ar(1.25 sccm) and C2H2(2 sccm)/He(3.2 sccm). The total chamber pressure was in the two cases 0.1 mbar. A discharge power of 50 W was used for these experiments. In order to extract the negative ions from the plasma potential, the discharge was pulsed at 100 Hz with a 50% duty cycle so that the negative ions could flow out of the plasma volume in the off part of the cycle. To ensure 7 ACS Paragon Plus Environment
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equal plasma conditions the pulsed discharge was also used for the detection of positive ions. The distance between the sampling orifice of the PPM spectrometer and the edge of the electrodes was 10 cm. A voltage of +24 V was applied to this orifice for a better collection of the negative ions. For the detection of the positive ions, the plate with the extraction orifice was grounded. The experimental conditions for ion detection were found to be very sensitive, especially in the case of negative ions. A decrease in pressure leads to an unstable discharge, whereas an increase in pressure leads to dust formation, which causes the disappearance of the negative ion signals. Positive ion signals are visible over a wider pressure range. 3. KINETIC MODEL A very simple 0D kinetic plasma model including the main reaction pathways for the major species in the plasma is used to simulate the chemistry of ions and neutrals in He + C2H2 and Ar + C2H2 discharges. The formulation is similar to previous models developed in our group 35–37. A set of time-resolved coupled differential equations describing the time evolution of the different species, which accounts for the different physico-chemical processes occurring in the plasma, is numerically integrated until the steady state is obtained. Several parameters are used as input to the model, namely, the reactor dimensions, the flows of precursor species into the reactor, pressure, P, gas temperature, Tg, electron temperature, Te, and charge density, nc. In the plasmas studied in this work, nc corresponds to the positive ion density, but the negative charge is shared between electrons and negative ions. Experimental values have been used wherever possible, but since nc and Te were not measured, they have been adjusted in order to fit the experimental data. A fixed value of Tg = 400 K has been used for all the simulations. The kinetic scheme employed here has been built from previous works. Reactions involving acetylene and its derived species are mostly taken from the work of de Bleecker et al22. Although an extended kinetic scheme has been proposed by the same group26, the simpler version is preferred in this work to facilitate the interpretation of the results. He and H2 kinetics are based on Liu et al38, while reactions with Ar are mainly from Jiménez-Redondo et al36. The full list of reactions considered in the model can be found in Table 1. The species considered in the model include neutral molecules, radicals, positive and negative ions. Only two excited species are included in each mixture: the He metastable states He(2 3S1) and He(2 1S ), noted by He* in Table 1, and the Ar metastables 4 3P and 4 3P , identified as Ar*. Most of the 0 2 0 carbonaceous species included contain an even number of carbon atoms, since those are the main species detected experimentally. A reduced number of positive ions is included in the model to decrease the complexity of the chemistry. To this end, we have followed the kinetic scheme of de Bleecker et al22, which intended to reproduce the experimental distributions of Deschenaux et al3, since our experimental results are found to be close to the latter. This, however, results in the disregard of several of the possible C2nHx+ compositions, including some of the relevant species in our experimental distributions.
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Surface reactions in the model consist primarily of positive ion neutralizations and deexcitation of metastable states. Ion neutralization is modeled so that the total loss of ions to the surface equals the net production of charged particles in the plasma, keeping the charge density constant and preserving the electroneutrality condition. Further details on the formulation can be found in our previous works35–37. Heterogeneous chemistry in the discharge is simplified with respect to some of our previous models, since only hydrogen recombination is considered and it is a minor species in this type of discharge. The negative ion kinetics proposed in this work is focused on the C2nH2– anions, instead of the more usual C2nH–, since those were the main species observed experimentally. The growth process of C2nH2– through reactions with acetylene molecules is expected to be the same as for C2nH–, however, the initial attachment to form C2H(2)– is not. Electron attachment to acetylene does not yield HCCH–, since it is not stable with respect to autodetachment39, and instead dissociative attachment occurs, mainly producing C2H–. On the other hand, vinylidene anions (H2CC–) are indeed stable, but have not been observed as a product of electron attachment to acetylene40,41 and the formation mechanism in these plasmas is not clear24. In this work, we have taken the same approach as Mao et al26 and assumed that H2CC– ions are produced by electron attachment to C2H2 with a certain ratio. Mao et al. took a ratio of 95%. We have assumed 100%. This is obviously a crude approximation, but we have used it to simplify the model chemistry. Table 1. Full reaction set included in the He/Ar + C2H2 model. Id. Reaction Electron impact Ionization e1 He + e → He+ + 2e e2 He* + e → He+ + 2e e3 Ar + e → Ar+ + 2e e4 Ar* + e → Ar+ + 2e e5 H2 + e → H2+ + 2e e6 H2 + e → H+ + H + 2e e7 H + e → H+ + 2e e8 C2H2 + e → C2H2+ + 2e e9 C2H2 + e → C2H+ + H + 2e e10 C2H2 + e → CH+ + CH + 2e e11 C2H2 + e → H+ + C2H + 2e e12 C4H2 + e → C4H2+ + 2e e13 C6H2 + e → C6H2+ + 2e Dissociation e14 H2 + e → 2H + e e15 C2H2 + e → C2H + H + e e16 C4H2 + e → C4H + H + e e17 C6H2 + e → C6H + H + e e18 C8H2 + e → C8H + H + e e19 C10H2 + e → C10H + H + e e20 C12H2 + e → C12H + H + e Excitation and deexcitation e21 He + e → He* + e e22 He* + e → He + e
Rate coefficient (cm–3 s–1)
Ref.
2.52 × 10–9 Te0.58 exp(–24.93/Te) 5.92 × 10–10 Te0.94 exp(–5.03/Te) 3.06 × 10–8 Te0.45 exp(–16.95/Te) 1.06 × 10–8 Te0.71 exp(–5.26/Te) 1.29 × 10–8 Te0.38 exp(–16.46/Te) 3.16 × 10–10 Te0.76 exp(–25.66/Te) 3.23 × 10–8 Te–0.36 exp(–14.98/Te) 7.35 × 10–8 Te0.26 exp(–16.68/Te) 1.24 × 10–8 Te0.36 exp(–19.41/Te) 2.02 × 10–9 Te0.70 exp(–23.57/Te) 3.01 × 10–10 Te1.26 exp(–20.05/Te) 7.35 × 10–8 Te0.26 exp(–16.68/Te) 7.35 × 10–8 Te0.26 exp(–16.68/Te)
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6.60 × 10–8 Te–0.47 exp(–12.13/Te) 1.12 × 10–8 Te0.39 exp(–9.65/Te) 1.12 × 10–8 Te0.39 exp(–9.65/Te) 1.12 × 10–8 Te0.39 exp(–9.65/Te) 1.12 × 10–8 Te0.39 exp(–9.65/Te) 1.12 × 10–8 Te0.39 exp(–9.65/Te) 1.12 × 10–8 Te0.39 exp(–9.65/Te)
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7.97 × 10–9 Te0.47 exp(–19.98/Te) 5.36 × 10–9 Te–0.46 exp(–0.12/Te)
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42 42 42 42,43 42,43 42 44 44 44 44 22,44 22,44
45 22,45 22,45 22,45 22,45 22,45
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e23 Ar + e → Ar* + e e24 Ar* + e → Ar + e Neutralization e25 He+ + e → He* e26 He2+ + e → He* + He e27 HeH+ + e → He + H e28 Ar2+ + e → Ar + Ar e29 ArH+ + e → Ar + H e30 H+ + e → H e31 H2+ + e → 2H e32 H3+ + e → 3H e33 H3+ + e → H2 + H Attachment and detachment e34 H2 + e → H– + H e35 H– + e → H + 2e e36 C2H2 + e → H2CC– Ion-neutral Collisional detachment in1 H– + H → H 2 + e Positive ion-molecule reactions in2 He+ + H → H+ + He in3 He+ + H → HeH+ in4 He+ + H2 → H+ + H + He in5 He+ + H2 → H2+ + He in6 He+ + C2H2 → C2H+ + He + H in7 He+ + C2H2 → CH+ + He + CH in8 He2+ + H → H+ + 2He in9 He2+ + H2 → H2+ + 2He in10 He2+ + H2 → HeH+ + H + He in11 He2+ + C2H2 → C2H2+ + 2He in12 HeH+ + H → H2+ + He in13 HeH+ + H2 → H3+ + He in14 HeH+ + C2H2 → C2H2+ + He + H in15 HeH+ + C2H2 → C2H+ + He + H2 in16 Ar+ + H2 → H2+ + Ar in17 Ar+ + C2H2 → C2H2+ + Ar in18 Ar2+ + H2 → ArH+ + H + Ar in19 Ar2+ + C2H2 → C2H2+ + 2Ar in20 ArH+ + H2 → H3+ + Ar in21 ArH+ + C2H2 → C2H2+ + Ar + H in22 ArH+ + C2H2 → C2H+ + Ar + H2 in23 H2+ + He → HeH+ + H in24 H2+ + Ar → ArH+ + H in25 H2+ + H → H+ + H2 in26 H2+ + H2 → H3+ + H in27 H2+ + C2H2 → C2H2+ + H2 in28 H3+ + Ar → ArH+ + H2 in29 H3+ + C2H2 → C2H2+ + H2 + H in30 C2H+ + H2 → C2H2+ + H in31 C2H+ + C2H2 → C4H2+ + H in32 C2H2+ + C2H2 → C4H2+ + H2 in33 C4H2+ + C2H2 → C6H4+ in34 C6H2+ + C2H2 → C8H4+
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2.46 × 10–8 Te–0.93 exp(–14.63/Te) 2.87 × 10–9 Te–0.53 exp(–1.31/Te)
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6.76 × 10–13 Te–0.5 7.12 × 10–15 (Te/Tg)–1.5 1.1 × 10–9 Te–0.6 8.5 × 10–7 (Te/0.026)–0.67 (Tg/300)–0.58 1.0 × 10–9 2.62 × 10−13 Te−0.5 5.66 × 10−8 Te−0.6 4.15 × 10−8 Te−0.4 4.15 × 10−8 Te−0.4
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2.90 × 10–11 Te–1.17 exp(–10.13/Te) 2.32 × 10–8 Te2 exp(–0.13/Te) 9.27 × 10–12 Te–0.84 exp(–2.51/Te)
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1.3 × 10–9
38
1.9 × 10–15 1.58 × 10–15 (Tg/300)–0.3 8.3 × 10–14 1.7 × 10–14 8.75 × 10–10 7.70 × 10–10 3.5 × 10–10 3.5 × 10–10 1.76 × 10–10 1.90 × 10–9 9.10 × 10–10 1.77 × 10–9 7.00 × 10–10 2.10 × 10–9 8.9 × 10–10 4.20 × 10–10 3.78 × 10–10 7.10 × 10–10 6.3 × 10–10 3.16 × 10–10 8.54 × 10–10 1.35 × 10–10 2.1 × 10–9 6.40 × 10–10 2.00 × 10–9 4.82 × 10–9 1.0 × 10–11 3.50 × 10–9 1.70 × 10–9 1.85 × 10–9 5.6 × 10–10 1.52 × 10–10 4.3 × 10–11
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in35 C6H4+ + C2H2 → C8H6+ in36 C8H4+ + C2H2 → C10H6+ in37 C8H6+ + C2H2 → C10H6+ + H2 in38 C10H6+ + C2H2 → C12H6+ + H2 Negative ion-molecule reactions in39-43 C2nH2– + C2H2 → C2n+2H2– + H2
7.00 × 10–11 5 × 10–11 5 × 10–11 5 × 10–11 1.0 × 10–12
49 49,
est est 49, est 49,
n=1…5
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Ion-ion Neutralization ii1 He+ + H– → He + H ii2 He2+ + H– → 2He + H ii3 HeH+ + H– → He + H2 ii4 Ar+ + H– → Ar + H ii5 Ar2+ + H– → 2Ar + H ii6 ArH+ + H– → Ar + H2 ii7 H+ + H– → 2H ii8 H2+ + H– → H2 + H ii9 H3+ + H– → 2H2 ii10-15 He+ + C2nH2– → C2nH2 + He ii16-21 HeH+ + C2nH2– → C2nH2 + He + H ii22-27 Ar+ + C2nH2– → C2nH2 + Ar ii28-33 ArH+ + C2nH2– → C2nH2 + Ar + H ii34-39 H2+ + C2nH2– → C2nH2 + H2 ii40-45 H3+ + C2nH2– → C2nH2 + H2 + H ii46-99 C2nHx+ + C2mH2– → C2mH2 + C2nHx
2.3 × 10–7 (Tg/300)–0.5 1 × 10–7 1 × 10–7 3.5 × 10–7 (Tg/300)–0.5 3.5 × 10–7 (Tg/300)–0.5 3.5 × 10–7 (Tg/300)–0.5 1.8 × 10–7 (Tg/300)–0.5 2 × 10–7 (Tg/300)–0.5 2 × 10–7 (Tg/300)–0.5 ~1.9 × 10–7 (Tg/300)–0.5 ~1.7 × 10–7 (Tg/300)–0.5 ~8.7 × 10–8 (Tg/300)–0.5 ~8.7 × 10–8 (Tg/300)–0.5 ~2.5 × 10–7 (Tg/300)–0.5 ~2.1 × 10–7 (Tg/300)–0.5 ~7 × 10–8 (Tg/300)–0.5
Neutral-neutral Penning ionization n1 He* + He* → He2+ + e n2 He* + He* → He+ + He + e n3 Ar* + Ar* → Ar2+ + e n4 Ar* + Ar* → Ar+ + Ar + e
2.03 × 10–9 (Tg/300)0.5 8.7 × 10–10 (Tg/300)0.5 5.7 × 10–10 6.3 × 10–10
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Neutral reaction n1 He* + H2 → 2H + He n2 Ar* + H2 → 2H + Ar n3 H + C2H2 → C2H3 n4 H + C4H2 → C4H3 n5 H + C6H2 → C6H3 n6-10 H + C2nH → C2nH2 n11 H + C2H3 → H2 + C2H2 n12 H + C4H3 → H2 + C4H2 n13 H + C6H3 → H2 + C6H2 n14 CH + H2 → CH2 + H n15 CH2 + H → CH + H2 n16 CH2 + CH2 → C2H2 + H2 n17 CH2 + CH → C2H2 + H n18 C2H + H2 → C2H2 + H n19 C2H + H → C2H2 n20 C2H + C2H2 → C4H2 + H n21 C2H + C4H2 → C6H2 + H n22-24 C2H + C2nH2 → C2n+2H2 + H n25 C2H + C2H3 → C2H2 + C2H2 n26-30 C2nH + H2 → C2nH2 + H
1.4 × 10–11 7.0 × 10–11 7.25 × 10–12 exp(–1212.7/Tg) 2.82 × 1025 Tg–11.67 exp(–6441/Tg) 7.1 × 1021 Tg–10.15 exp(–6667.6/Tg) 1.66 × 10–7 Tg–1 n=2…6 –11 6.6 × 10 2.4 × 10–11 6.6 × 10–11 1.82 × 10–16 Tg1.79 exp(–840.4/Tg) 2.7 × 10–10 5.3 × 10–11 6.6 × 10–11 1.82 × 10–11 exp(–1443/Tg) 1.82 × 10–7 Tg–1 5.8 × 10–11 6.6 × 10–11 5.0 × 10–11 n=3…5 –11 5.0 × 10 1.82 × 10–11 exp(–1443/Tg) n=2…6
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n=1…6 n=1…6 n=1…6 n=1…6 n=1…6 n=1…6 n,m=1…6
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n31-34 n35 n36 n37 n38 n39
C2nH + C2H2 → C2n+2H2 + H C2H2 + C2H → C4H3 C2H3 + CH → C2H2 + CH2 C4H2 + C2H → C6H3 C4H3 + H → C2H2 + C2H2 C6H3 + H → C4H2 + C2H2
6.6 × 10–11 1.82 Tg–6.3 exp(–1404/Tg) 8.3 × 10–11 1.82 Tg–6.3 exp(–1404/Tg) 2.65 × 10–5 Tg–1.6 exp(–1117/Tg) 3.98 × 10–5 Tg–1.6 exp(–1409/Tg)
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n=2…5
22 22 22 22 22 22
Surface processes Neutralization w1 He+ + wall → He w2 He2+ + wall → 2He w3 HeH+ + wall → He + H w4 Ar+ + wall → Ar w5 Ar2+ + wall → 2Ar w6 ArH+ + wall → Ar + H w7 H+ + wall → H w8 H2+ + wall → H2 w9 H3+ + wall → H2 + H w10 CH+ + wall → CH w11 C2H+ + wall → C2H w12 C2H2+ + wall → C2H2 w13 C4H2+ + wall → C4H2 w14 C6H2+ + wall → C6H2 w15 C6H4+ + wall → C6H2 + H2 w16 C8H4+ + wall → C8H2 + H2 w17 C8H6+ + wall → C8H2 + 2H2 w18 C10H6+ + wall → C10H2 + 2H2 w19 C12H6+ + wall → C12H2 + 2H2 Deexcitation w20 He* + wall → He w21 Ar* + wall → Ar Recombination w22
1
γ = 0.03
H + wall → 2 H2
Tg given in K, Te in eV est. indicates rate coefficients estimated in this work
4. RESULTS AND DISCUSSION Mass spectrometry measurements of the main stable neutral species in the plasma do not show large amounts of new species being produced in the discharge, including the expected polymerization products. The small quantities detected are only found in the time-resolved measurements right after the ignition of the discharge, as depicted in the left panel of Figure 2.
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Figure 2. Time evolution of the main neutral species in the first seconds after plasma ignition (t=0) for a mixture of He (3.2 sccm) and C2H2 (2 sccm) at 50 W. Left panel: experimental abundances detected with the mass spectrometer. Right panel: densities predicted by the kinetic model for these same species.
As soon as the rf voltage is applied, acetylene quickly disappears from the reactor, while the signal for hydrogen increases. Hydrogen reaches a maximum value and then starts decreasing again, eventually stabilizing at a value above the plasma off signal. In the first few (~10) seconds of the discharge, changes in the signals of mass 50 (C4H2) and 74 (C6H2) are found, but they quickly return to the background values after that time. Mass scans after the stabilization of the discharge did not result in the detection of other hydrocarbons. This behavior found at the beginning of the discharge can be compared with the model predictions for the densities of the same molecules, shown in the right panel of Figure 2. This is a very rough estimation of the time evolution of these species, since the model assumes constant values of the electron temperature and density from the plasma ignition until the steady state, but nevertheless results in a behavior that is qualitatively consistent with the experimental trends. In the model, acetylene is also found to decay as soon as the plasma is started. Molecular hydrogen, a product of acetylene dissociation, quickly grows and becomes the second most abundant neutral species after He, however, the peak found experimentally cannot be reproduced in the simulations, possibly due to the limitations of the model. The growth and decay behavior for diacetylene and triacetylene is found also in the simulations. The timescale given by the model (~20 s) is larger than the one observed experimentally (~10 s), but that might be a detection issue due to the low signal for these masses. An illustration of the ion distributions provided by model calculations is displayed in Figure 3. It corresponds to the steady state of the C2H2/He discharge. The values of the plasma parameters nc and Te were chosen to reproduce the envelopes of the experimental C2nHx ion distributions of Figures 4 and 5. As indicated in the previous section, only the dominant ions in the experimental distributions were included in the model.
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Figure 3. Model flux mass spectra of the main cations (upper panel) and anions (lower) in the steady state of the C2H2/He discharge. They correspond to nc = 109 cm–3 and Te = 3 eV (see text).
Besides the main carbon containing ions, the model includes the Hn+ ions (n=1-3) as well as He+, HeH+ and He2+ cations, which are also observed in the experiments, but represent only a minor fraction of the total ion flux. The anion H–, also contemplated in the model, was not observed in the experiments. Similar synthetic ion mass spectra were produced for the C2H2/Ar plasma (not shown for brevity). Figure 4 shows the experimental mass spectra of the positive ions for the C2H2/He and C2H2/Ar plasmas. The spectrum of the C2H2/Ar discharge has a maximum at mass 26 (C2H2+) and that of the C2H2/He plasma has two similar maxima at masses 27 (C2H3+) and 51 (C4H3+). After these peaks, the distributions show an overall decline with increasing mass, which is punctuated by a series of maxima corresponding to ionic oligomers and polymers of acetylene with an even number of carbon atoms and a variable number of hydrogen atoms. The spectra extend beyond 150 u (C12). Groups of peaks for odd carbon numbers are also observed but their intensities are much lower than those of the neighboring even carbon peaks. Over the whole spectral range the maxima in a given C2nHx+ group are always larger than those in the corresponding C2n–1Hx+ group. Besides the peaks of hydrocarbon species, masses 40 (Ar+), 41(ArH+) and 80(Ar2+) are observed in the C2H2/Ar discharge and masses 4 (He+), 5 (HeH+) and 8 (He2+) appear in the C2H2/He plasma. Masses 1 (H+), 2 (H2+) and 3 (H3+) of hydrogenic ions, and a group of peaks between 10 and 20 u corresponding most likely to of small contaminants, like H2O, and to products of dissociative ionization are also present in the two plasmas.
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The Journal of Physical Chemistry
Figure 4. Upper panel: Experimental flux mass spectra of the positive ions in the C2H2/He discharge. The dashed line corresponds to the envelope of the CnHx+ ion distribution calculated with the model for nc = 109 cm–3 and Te = 3 eV. Lower panel: id. For the C2H2/Ar plasma. In this case the dashed line corresponds to model calculations for nc = 8×108 cm–3 and Te = 3.3 eV.
The dashed lines in Figure 4 are the envelopes of synthetic spectra of the C2nHx+ distributions for the two plasmas. They were obtained by varying the electron temperature and density in the model calculations to match the observed cation distributions. The same nc and Te values were found to provide a good description of both the cation and anion mass spectra for each gas mixture, which supports the consistency of the simple model used. The sensitivity of the model to the change in the plasma parameters is discussed in detail below. The mass spectra of Figure 4 can be compared with positive ion distributions reported in the literature for acetylene plasmas. As mentioned in the introduction, all these spectra always have a pattern dominated by species with an even number of carbon atoms and the maxima of the distributions depend on the specific conditions of each experiment. Kovacevic et al.6 and Denysenko et al.30 studied RF discharges of C2H2/Ar under conditions relatively similar to those of the present work and found also maxima for C2H2+ but had slower decays toward higher masses. In the experiment of Descheneaux et al.3 with a pure C2H2 plasma, the maximum in the cation distribution was found for C4H2+ and the post maximum decay was similar to that found here. A maximum for C4H2+ was likewise observed in the experiments of Vasile and Smolinski20 with plasmas of pure C2H2 and of C2H2/Ar and C2H2/He. A detailed inspection of Figure 4 reveals that the CnHx+ profiles are specific for each Cn and in most cases very similar for the two plasmas, which indicates that the carbon chemistry is indeed not 15 ACS Paragon Plus Environment
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much affected by the nature of the noble gas present in the discharge. For n=2 and 4, the peaks of CnH2+ and CnH3+ stand out clearly from the rest. For n=6 and 8 the dominant ion is CnH4+ followed by either CnH2+ or CnH5+, and CnH3+ is always a local minimum. In general, for six carbon atoms or more, ions with a higher number of hydrogen atoms are formed in relatively high amounts. Descheneaux et al.3 suggested that it could be an indication of the formation of benzene. Although this possibility cannot be excluded, the peak at mass 78 (C6H6+), which is the expected maximum in the electron impact ionization of benzene, is a comparatively minor peak in the C6Hx+ group. In any case, the higher hydrogenation with growing carbon number could just reflect the increased possibilities to form more complex structures, either cyclic or branched, in addition to the prevailing species with a polyyne skeleton. The negative ion distributions are displayed in Figure 5. The mass spectra show again the predominance of species with an even number of carbon atoms characteristic of acetylene polymerization through addition of C2 units. The anion distributions of the two plasmas show maxima for mass 26 (C2H2–) and then decrease with growing mass. They extend to higher masses than those of cations. For the C2H2/Ar plasma, masses up to 250 u, corresponding to 20 carbon atoms, are detected. For the C2H2/He plasma, the mass spectrum reaches 180 u (14 C atoms). In the case of the C2H2/Ar plasma the decay in the intensity with growing anion mass is slower than that of the corresponding cation distribution (Figure 4). In the C2H2/He plasma, the relative decrease in intensity with growing mass is similar for anions and cations. In the anion distribution for C2H2/Ar the predominance of the peaks with even number of carbon atoms is maintained throughout the spectrum, although for masses higher than 180 u (C15) the intensities of the peaks for odd and even carbons are more similar. In the C2H2/He plasma the odd/even alternation is not strictly maintained and the peak at C9H4– is higher than all peaks in the C10Hx– group. The lowest CnHx– groups with an even number of carbon atoms (up to six), are characterized by a very dominant single peak at CnH2– . With increasing n and especially beyond C8 the detected anions become richer in hydrogen. A comparison of Figures 4 and 5 shows clearly that ion hydrogenation is higher for cations and starts at lower masses. As an illustration, the C6Hx– groups are clearly dominated by C6H2– whereas in the cation distributions at least three peaks: C6H4+ (maximum), C6H2+ and C6H5+ are relevant. As in the case of cations, it is worth looking at the distinct CnHx– profiles in Figure 5. They are highly specific and, for a given Cn, very similar in the C2H2/Ar and C2H2/He plasmas. This resemblance is again a very strong indication that the same carbon chemistry takes place in the two discharges.
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Figure 5. Upper panel: Experimental flux mass spectra of the negative ions in the C2H2/He discharge. The dashed line corresponds to the envelope of the C2nHx+ ion distribution calculated with the model for nc = 109 cm–3 and Te = 3 eV. Lower panel: id. For the C2H2/He plasmas. In this case the dashed line corresponds to model calculations for nc = 8×108 cm–3 and Te = 3.3 eV.
The dashed curves in Figure 5 represent the envelopes of the C2nHx¯ distributions derived with the chemical model. They extend just to species with 12 C atoms which is the highest number of carbon atoms included in the calculations and account well for the observed decline with growing anion mass. Toward the highest masses, the curves tend to level-off or even rise in the C2H2/Ar discharge, deviating from the measured values. This is due to the fact that all anions larger than C12H2– are accumulated in this ion in the model calculations (see below). According to the model, anions account for 60% (C2H2/He) and 75% (C2H2/Ar) of the total negative charge in the plasma. The anion chemistry of the model is very simple and includes just a variant of the Winchester mechanism32 by which a C2nHx– anion reacts with a C2H2 molecule to yield a C2n+2Hx– anion plus a H2 molecule (reactions in39-43 of Table 1). This simple mechanism, which is included in all models of C2H2 plasma chemistry, is enough to account for the observed monotonic decline in our anion distributions. However, the present model has an important peculiarity. As discussed in the method section, it is assumed that the anion polymerization chain is initiated by H2CC– (vinylidene) instead of by C2H– (ethynide), which is the obvious anion expected from the dissociative electron attachment to C2H2. The choice of vinylidene is based on the observation that the major ions in our distributions are always of the C2nH2– type. The relevance of the H2CC– ion was also stressed by Mao et al.26 who refined the anion chemistry of previous models in an attempt to account for the results of Descheneaux et al.3, where C2nH2– ions were also found in appreciable amounts. In a recent work, Akhoundi and Foroutan31 applied a 1D self consistent model to 50% mixtures of C2H2
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with Ar and He in an rf discharge and found a much faster decay of the anion flux with growing anion mass for the C2H2/Ar mixture. The opposite trend is found in our experiments (see Figure 6). The anion distributions of Figure 5 can also be compared to that of Descheneaux et al.3, measured for a plasma of pure acetylene. That distribution shows the usual predominant groups of peaks with an even number of carbon atoms, but has a maximum at 73 u (C6H–) and this peak is larger by an order of magnitude than the second highest peak in the distribution (C8H2–). Such a big difference could not be reproduced even by the refined kinetic model of Mao et al.26 which could just account qualitatively for the position of the C6H– maximum. In the distribution measured by Descheneaux et al., singly hydrogenated anions are preponderant for anions with four and six carbon atoms. This is in stark contrast with the distributions of the present work, where the maxima correspond always to anions with two hydrogen atoms. Since the electron temperature and total charge density of the plasma were not experimentally measured, model simulations have been used to determine the effect of these parameters on the positive and negative ion distributions. Figure 6 shows the effect of Te on the positive and negative C2nHx ion distributions, depicted here as the envelopes of the simulated ion fluxes, for a constant charge density of 109 cm–3 in the C2H2/He discharge. In the case of positive ions, C6H2+ and C8H4+ were not represented for clarity, since C6H4+ and C8H6+ are found in larger concentrations (see Figure 3). The C2H2/Ar plasma presents a very similar behavior and has not been included for brevity.
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Figure 6. Evolution of the envelopes of the maxima in the C2nHx ion distributions as a function of electronic temperature for a total charge density of 109 cm–3, in the C2H2/He plasma. Upper panel: positive ions. Lower panel: negative ions.
Both ion distributions show a marked difference between low (≤ 2 eV) and high values of the electron temperature. In the low temperature regime, high polymerization conditions are found, with a steady increase of the abundance as the ion mass grows in the case of positive ions. The sharp increase at the largest ion considered in the model (C12H6+ or C12H2–) for both distributions is due to the absence of the destruction mechanism through C2H2 collisions to produce larger ions. The flux of C12H6+ and C12H2– can then be considered to also include the flux of all larger ions. With higher Te values, the distributions evolve to resemble the behavior observed in the mass spectrometry measurements. For positive ions, the maximum of the distribution is either found at C2H2+ or C4H2+, while the anions have a strictly decreasing distribution. Notably, the drop in the cation distribution is heavily altered by the electron temperature, while the anion distribution remains largely unaffected.
Figure 7. Evolution of the envelopes of the maxima in the C2nHx ion distributions as a function of charge density for a fixed electron temperature of 3 eV in the C2H2/He plasma. Upper panel: positive ions. Lower panel: negative ions.
The resulting ion distributions for different values of the total charge density are represented in Figure 7, for a fixed value of Te of 3 eV and for the C2H2/He plasma. The behavior found is very similar to the one shown before for the electron temperature, with low values leading to high 19 ACS Paragon Plus Environment
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polymerization and higher values producing distributions closer to the experimental ones. However, a key difference is found for the negative ion distributions, since in this case the drop in the distribution is affected by the value of nc. This allows us to estimate the values of nc and Te using the ion distributions, by finding the right value of nc to reproduce the anion distribution and then varying Te until a good agreement is found for the cation distribution. This process leads to the values of nc = 109 cm–3 and Te = 3 eV for C2H2/He and nc = 8×108 cm–3 and Te = 3.3 eV for C2H2/Ar used in the results shown in previous figures. These values can be compared with the simulations of Akhoundi and Foroutan31, which show a total charge density value 2-3 times higher for Ar than for He, contrary to what is derived in this work, but expected due to the lower ionization threshold of Ar. However, it should be noted that their simulations also predict a more gradual drop in the anion distribution for He and a steeper one for Ar, which contradicts our experimental observations from which the nc and Te values are inferred. 5. CONCLUSIONS The early stages of ionic polymerization in plasmas of C2H2/He and C2H2/Ar have been studied by means of mass spectrometry in rf discharges at a pressure of 0.1 mbar. Steady-state distributions of positive and negative ions were measured under conditions selected to avoid particle formation, and a simple chemical model was applied to provide an overall picture of the plasma chemistry. In all cases, the distributions are dominated by ions with an even number of carbon atoms, revealing a polyyne skeleton, and the peak intensity decreases with growing ion mass. In the C2H2/He plasma the major cations are C2H3+ and C4H3+, with comparable intensities, whereas in the C2H2/Ar discharge, C2H2+ dominates the positive ion distributions. In both plasmas the cation distributions extend to ions with 12 carbon atoms. In the two anion distributions, C2H2– was the highest peak and ions of the C2nH2– type are also dominant for four and six carbon atoms. The negative ion distributions extend to higher masses than their cationic counterparts, especially in the C2H2/Ar mixtures, where anions with more than 20 atoms were detected. Both for cations and anions, the CnHx peak profiles were found to be highly specific for each Cn group and very similar in the C2H2/He and C2H2/Ar discharges, which lends support to the general assumption that acetylene plasma chemistry is not much affected by the rare gases. The number of hydrogen atoms in the ions increases with growing carbon atom number, indicating a deviation from the dominant polyyne chains, but the mass spectra are not sufficient to draw any conclusion about the possible presence of cyclic structures in ions with more than six atoms, and it is thus not clear whether aromatic rings start forming at the very beginning or start forming at a later stage. The 0D chemical kinetic model gives a good account of the observed steady-state ion distributions with reasonable values of the total charge density ( 109 cm-3) and electron temperature ( 3 eV) of the plasmas. The model includes the main types of ions observed and incorporates basically radicalic and ionic polymerization mechanisms leading to polyyne structures by addition of C2 growth precursors. The carbon anion chemistry, based exclusively on the Winchester mechanism, is particularly simple, but can account for the monotonic decline of the peak intensity with growing anion mass observed in the experiments. According to the model, in the steady state a large fraction of the negative charge (60-75%) resides in the anions. To justify the observed dominance of C2nH2– 20 ACS Paragon Plus Environment
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ions it was necessary to assume that the anionic polymerization route is initiated by the vinylidene anion (H2CC–) instead of by the ethinide anion (C2H–) assumed in most literature models. The positive ion distributions are in qualitative agreement with other measurements from the literature on plasmas of pure C2H2 and of C2H2 with Ar or He. We are not aware of anion distributions published for C2H2/He or C2H2/Ar plasmas, and those of the present work are at variance with the negative ion distribution reported in the literature for pure acetylene plasmas3 which has a pronounced maximum for C6H-. Given the similitude found in the acetylene chemistry in the two plasmas investigated here, it is not likely that the early polymerization stages can explain possible differences in the structures of dust particles generated in C2H2/He and C2H2/Ar discharges8. ACKNOWLEDGEMENTS Funding from EU project ERC-2013-Syg-610256 and from the MINECO of Spain under grant FIS2016-77726-C3-1P is gratefully acknowledged. REFERENCES (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
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