Comparison between electropositive and electronegative cold atmospheric-pressure plasmas: a modelling study

: Cold atmospheric-pressure He + N 2 and He + O 2 plasmas are chosen as the representatives for electropositive and electronegative plasmas, of which the discharge characteristics are studied and then compared to each other by fluid models. As the increase of the impurity (N 2 or O 2 ) fraction from 0 to 10%, for He + N 2 plasmas the electron density and ion density increase, the spatiotemporal distributions of electron density, ion density, electron temperature and electron generation rate change a little. On contrast, for He + O 2 plasmas the electron density decreases, the ion density first increases and then decreases, the electron temperature increases in the bulk region, but decreases in the sheath region, and the plasmas transform from g mode to α mode as the significant change of electron generation rate distributions. Larger electric field is needed in the bulk region to sustain the electronegative plasma, so the electrical characteristics of He + O 2 plasmas transform form capacitive to resistive with increasing O 2 fraction. Meanwhile, the ion-coupling power increases dramatically, which can be estimated by a formula based on the electronegativity. A new criterion for determining the sheath boundary, | ∇ E | = 5 kV/cm 2 , is put forward, which is found suitable for both the electropositive and electronegative plasmas.


Introduction
Cold atmospheric-pressure plasmas (CAPs) have great application prospects in the fields of environmental protection [1], biomedicine [2], nano-technology [3] and so on. Most CAPs are operated in a noble gas, but with a small amount of molecular gases such as N 2 and O 2 [4]. The molecular gases are sometimes artificially mixed into the noble gas to make the plasmas more reactive and hence beneficial for various applications. For example, the typically small fraction between 0.5 and 3% of O 2 is added into helium to optimise the production efficiency of reactive oxygen species [5]. On the other hand, the molecular gases are inevitably existed due to the impurity of industrial noble gases, as well as the inclusion of air when the plasmas are not well sealed [6][7][8][9][10]. The electropositive nature of noble gases allows the plasmas to be sustained in relatively low electric field, which is one of the main reasons that keeping the plasmas cold, diffusive and stable [11]. However, the molecular gases such as O 2 and H 2 O are strongly electronegative, and hence inhibit the plasma generation by absorbing the electrons. The plasma characteristics such as the volt-ampere characteristics can be changed significantly even when the fraction of electronegative gas is as low as 0.1% [4]. The electropositive CAPs and their electronegative counterparts have much different characteristics, which have not yet been well understood. This motivates us to compare the characteristics of those plasmas in quantitative level.
In this paper, He + N 2 and He + O 2 CAPs are chosen as the representatives of the electropositive and electronegative plasmas, respectively. The impurity (N 2 or O 2 ) fraction in the working gas is varied from 0 to 10%, covering most cases of practical applications. The electronegativity of He + O 2 CAPs keeps increasing with the O 2 fraction, allowing the plasma characteristics to be studying for a large electronegative range. A fluid model is used for this study, which has been used for He + N 2 and He + O 2 CAPs as reported previously [12][13][14][15][16]. The spatiotemporal evolution of the electron density, the electron temperature, the electron generation rate as well as the dissipated power density is obtained as a function of the impurity fraction, and they are compared with respect to the electropositive and electronegative plasmas. Moreover, the sheath dynamics is found to be much different for the two kinds of plasmas, and a new criterion is suggested for determining the sheath edge for those plasmas.
The paper is organised as follows: the computation model is described in Section 2, the simulation results are presented and discussed in Section 3, and at last conclusions are given in Section 4.

Description of the computational model
The discharge considered in this study is generated between two circular electrodes with a narrow separation of 0.2 cm and a large electrode width [to facilitate the use of one-dimensional (1D) model], similar to those used in experimental study [17]. One electrode is connected to a sinusoidal voltage with radio frequency of f = 13.56 MHz, the other one is grounded. The dissipated power density is kept constant to be 40 W/cm 3 . For the purpose of comparing the He + N 2 and He + O 2 CAPs, all the discharge conditions are kept the same, and the impurity (N 2 or O 2 ) fraction is varied from 0 to 10%.
1D fluid models are used for He + N 2 and He + O 2 CAPs with their details previously reported [12][13][14][15][16] so just briefly described here. Nine species and 18 chemical reactions are incorporated for He + N 2 plasmas, while 17 species and 60 chemical reactions are incorporated for He + O 2 plasmas. The plasma chemistry used in this study is recommended by the authors [6,13], and the plasma species are listed in Table 1.
The fluid models solve the mass conservation equation for each species (1), the Poisson's equation (2), and the electron energy conservation equation (3). Given the high collisionality of the discharge, the particles inertia is neglected and the drift-diffusion where n i , G i , μ i , D i , q i , S i , and m i are the density, flux, mobility, diffusion coefficient, charge, net gain/loss rate, and mass of species i, respectively. E is the electric field, ɛ is the mean electron energy, ɛ 0 is the vacuum permittivity, and k B is the Boltzmann constant. R el is the momentum transfer collisional rate between electrons and background gases and T is the temperature of plasma species. ΔE j and R j are the electron energy loss due to inelastic collision j and its corresponding reaction rate, respectively. Subscripts e, +, −, and k represent electron, positive ion, negative ion and background gas species (He, O 2 and/or N 2 ), respectively. The gas temperature is set to be 350 K.
Regarding fluxes to the electrodes, the following boundary conditions are used for charged species G e · n = −sm e E · nn e + 0.25v th,e n e − g p G +,p G + · n = sm + E · nn + + 0.25v th,+ n + (6) where n is the normal vector pointing towards the wall, g is the secondary emission coefficient and v th is the thermal velocity. g is set to 0.03 for positive ions and zero for other species, following the simplistic approach previously used by Shi and Kong [18]. The switching function σ takes a value of one when the drift velocity is directed towards the electrode and zero otherwise [19] For neutral species, the electrode losses are determined by incoming fluxes and surface reactions on the electrodes. These reactions, however, are difficult to predict and reaction rates are often unknown. We assume here that species reaching the electrodes will be adsorbed with a certain probability p i , regardless of what reaction they may undergo [13]. Then, the boundary conditions are G n · n = 0.25v th n i p i Although the value of p i is rarely known, it is predicted that the electrode loss is almost independent of p i when p i > 0.01, and even in that case the electrode loss has little influence on the plasma dynamics [13]. So, in this paper the p i is set to be 0.01 for modelling study.
The electron energy flux to the electrodes is given by [20] G 1 · n = 5 3 where ɛ g is the energy of secondary electron emitted from the electrodes and fixed at 5 eV [20]. The electron mobility and diffusivity are calculated as a function of mean electron energy using Bolsig+ [21], a Boltzmann solver. As to the transport coefficients for other species, please refer to our previous publications [13,15]. The set of equations described above is solved using a time-dependent finite-element partial differential equation solver, COMSOL Multiphysics, and results have been post-processed with MATLAB. Fig. 1 shows the spatiotemporal distributions of electron density, electron generation rate, electron temperature and ion (including He + , He + 2 , N + 2 and N + 4 ) density in He + N 2 CAPs with respect to the N 2 fraction ([N 2 ] for abbreviation). The white curves in the sub-figures indicate the sheath boundaries of the plasmas, which are defined by ∇E | | = 5 kV/cm 2 . This criterion for defining the sheath boundary will be discussed below. The sheath boundary benefits the following discussions on the plasma characteristics. For example, it helps to distinguish the α mode or g mode of a plasma, because in α mode the electron generation rate dominates in the plasma bulk region, but in g mode it dominates in the sheath region [18].

Results and discussions
It can be seen from Figs. 1a-d that the electron density increases with the N 2 fraction, the same as reported in [6]. There are two main pathways for electron generation in He + N 2 CAPs: one is the electron-impact ionisation of the feeding gases (He and N 2 ), and the other is exciting helium first and then generating electrons by Penning ionisation and/or electron-impact ionisation of the helium metastables (He* and He * 2 ).
Pathway 1: As the increase of N 2 fraction, R1 and R5 dominate the electron production at first, and then it changes to R6 and R7, at last it transfers to R2 because the density of helium metastables decreases sharply when [N 2 ] > 0.01%. The electrons oscillate between the two electrodes, which has a density boundary nearly overlaps with the sheath boundary (see Figs. 1a-d ). Although the electrons mainly exist in the plasma bulk, their generation is dominated in the sheath region regardless of the N 2 fraction (see Figs. 1e-h), suggesting that the plasmas keep in g mode. This is because the electron energies needed for ionisation of helium and nitrogen in pathway 1 and an excitation of helium in pathway 2 are high, at least 15.4 eV for the ionisation of nitrogen (R2), and consequently the electrons in the sheath region are most involved in the two pathways for electron generation. The average electron energy in sheath region is much larger than that in the bulk region according to the electron temperature distribution as shown in Figs. 1i-l.
The ion density increases with the N 2 fraction as shown in Figs. 1m-p. This is in accordance with the trend of electron density because of the electropositive and quasi-neutral nature of the He + N 2 CAPs, i.e. the electron density roughly equals to the ion density. The ion densities peak at the interface of the bulk and sheath regions, because the ions are mainly generated in the sheath and they stay there almost regardless of the oscillation of the sheath boundary. The distribution of ions keeps invariable with time, much different to that of electrons, because the ion mobilities are typically less than the electron mobility by ∼50 folds [22].
Compared to the electropositive CAPs in He + N 2 mixtures, the plasma characteristics of He + O 2 CAPs are much different due to their electronegative nature, as shown in Fig. 2. Some sub-figures in Fig. 2 are similar to our previous reports in [4], but the sheath boundary curves are different due to the change in the criterion. The sub-figures are plotted here to facilitate the comparison between He + O 2 and He + N 2 CAPs.
As shown in Figs − ) are much different to that of the electropositive plasmas, especially for the ion density peaking at the centre position of the discharge gap (see Figs. 2n-p) rather than at the bulk-sheath interface (see Figs. 1n-p). This is mainly because the anions are confined in the bulk region by the ambipolar electric field. The ion density first increases and then decreases with the increasing O 2 fraction, but the electronegativity keeps increasing due to the continuous drop of electron density.
The spatial distributions of the half-cycle averaged electric fields are shown in Figs. 3a and b for He + N 2 and He + O 2 CAPs, respectively. Each curve corresponds to an impurity (N 2 or O 2 ) fraction of 0, 0.1, 1, or 10%. It can be seen that the spatial distribution of the averaged electric field in He + N 2 discharge is relatively independent of the impurity fraction. In contrast, in He + O 2 discharge it decreases in the sheath region and increases in the bulk region as the increasing impurity fraction. The dependence of the electric field on the impurity fraction is similar to that of the electron temperature either for the electropositive or the electronegative CAPs, as shown in Figs. 1 and 2.  Determining the boundary of plasma sheath is very important for characterising a plasma, for which several criteria have been reported, such as 14% of the maximal electric field [23], E = 1 kV/ cm [24], and n e = 0.3(n + -n − ) [4]. These criteria are suitable for electropositive CAPs, but maybe not for electronegative CAPs as reported here. For example, when the O 2 fraction is 10% the averaged electric field in the plasma bulk is ∼2.5 kV/cm, more than one-third of the maximal electric field (see Fig. 3b). One typical feature of CAPs is that the electric field varies little in the bulk region, but keeps rising or dropping from the bulk-sheath interface to the electrode surface, as shown in Figs. 3a and b. This suggests that the gradient of the electric field can be used as a criterion for determining the sheath boundary. In this paper, the absolute value of such gradient, ∇E | | = 5 kV/cm 2 , is chosen as the criterion, which is capable of capturing the turning point of each electric field curve (see the inset images in Figs. 3a and b), and hence suitable for both the electropositive and electronegative CAPs.
Based on the sheath boundary criterion, it is found that the sheath thicknesses of both He + N 2 and He + O 2 CAPs decrease with the increasing impurity concentration, but for He + O 2 CAPs the decrement is larger (see Fig. 3c). This trend also applies for the voltage drops in the sheaths as shown in Fig. 3d. As the increase of oxygen fraction in He + O 2 CAPs, the decrease of electron density in the bulk region (see Figs. 2a-d) leads to the increase of plasma resistance, while the decrease of voltage drop across the sheath region indicates the decrease of plasma capacitance, and therefore the electrical feature of the discharge transforms from capacitive to resistive as it changes from electropositive to electronegative. A similar difference of electrical feature has been reported for low-pressure argon (electropositive) and SF 6 (electronegative) plasmas [25].
In low-pressure plasmas, the total current in the bulk region is carried mostly by electrons [25,26]. This is mainly because the electron mobility is larger than that of ions by ∼50 folds, and the electron density is comparable to the ion density. This situation is changed in atmospheric-pressure plasmas, because most voltage drops in the sheath where the ion density is much larger than the electron density, so much energy is coupled to the ions which may not be ignored. In particular, CAPs are much easier to be electronegative compared to their low-pressure counterparts due to the frequency collisions between electrons and the working gases, and in that case the ion density may be much larger than the electron density, resulting in even larger portion of the discharge energy coupled to the ions. In order to elucidate the energy dissipation characteristics in different kinds of CAPs, we plot in Fig. 4 the spatiotemporal distributions of electron-and ion-coupling power densities for He + N 2 and He + O 2 CAPs, with respect to the impurity fractions of 0, 0.01, 0.1, 1, and 10%. P e and P i are the numerical results for electron-coupling power density and ion-coupling power density, respectively.
For He + N 2 CAPs, most of the input power is coupled to the electrons, but in the sheath a unnegligible portion of the input power is coupled to the ions (see Fig. 4). This is in accordance to the He + O 2 CAPs when the oxygen fraction is low (electronegativity < 1). However, when the electronegativity is high, much more power will be coupled to the ions, and even when [O 2 ] = 10% the ion-coupling power dominates.
The spatiotemporal averaged power dissipations on electrons and ions in He + N 2 and He + O 2 CAPs are shown in Fig. 5, as a function of the impurity fraction from 0.01 to 10%. Besides the numerical results (P e and P i ) of solid curves, two dash curves namely P e,ohm and P i,es are also plotted in Fig. 5 for the purpose of theoretical analysis. P e,ohm represents the power dissipated for ohmic heating of electrons, which can be calculated as follows [27] S ohm = 0.5m e n m l B n e G 2 e (11) where v m is electron neutral collision frequency (∼10 12 s −1 at atmospheric pressure) and l B is the plasma bulk length. P i,es represents the power dissipation on the ions that estimated according to their densities and mobilities. In the bulk regions of plasmas, the electrons and ions are assumed to have densities invariable with the electrode gap position, and therefore their density relationship can be roughly estimated by the neutralisation feature of the plasmas, as given by (n + + n e )/n e = 2j + 1 (12) where j represents the electronegativity. Assuming the ions have the same mobility of μ ion = 20 cm 2 /s, while for electrons it is 1056 cm 2 /s [28]. The ion-coupling power density in the bulk region can be calculated as follows where P ion,b represents the ion-coupling power density in the bulk region and P in the input power density which is assumed invariable with the locations. In the sheath region, the relationship of ion density and electron density cannot be roughly estimated by the electronegativity. However, the ion current should equal to the electron current due to the quasi-neutral nature of the plasmas, and hence the ioncoupling power can be roughly estimated the same as the electron-coupling power in the sheath. For the entire plasma, the spatiotemporal averaged power coupled by ions can be given by where l s is the sheath thickness and l is the total gap between electrodes. It can be seen from Fig. 5 that about 90% of the input power is coupled to the electrons in He + N 2 CAPs, relatively independent of the N 2 fraction. On contrast, the electron-coupling power decreases with the increasing O 2 concentration in He + O 2 CAPs, in particular, it is smaller than the ion-coupling power when [O 2 ] ∼0.5%. The calculated results of electron-coupling power densities are similar to the numerical ones, suggesting that the ohmic heating is the main electron heating mechanism. Moreover, the calculated results of ion-coupling power densities agree well with the numerical ones for He + N 2 CAPs, and they are a little smaller, but with a similar trend to the numerical results for He + O 2 CAPs. Therefore, formulas (11) and (14) for calculating the electron-and ion-coupling powers are reliable, which can be used for estimating the power dissipation characteristics of CAPs.

Concluding remarks
In this paper, He + N 2 and He + O 2 CAPs are chosen as the representatives for electropositive and electronegative plasmas, of which the discharge characteristics are studied and then compared to each other by fluid models. As the increase of the impurity (N 2 or O 2 ) fraction, for He + N 2 CAPs the electron density and ion density increase, the spatiotemporal distributions of electron density, ion density, electron temperature, and electron generation rate change a little, e.g. the ion density has two peaks at the bulk-sheath interface, and the electron generation rate dominates in the sheath which indicates that the plasmas are kept in g mode. On contrast, for He + O 2 CAPs the electron density decreases, the ion density first increases and then decreases, the electron temperature increases in the bulk region, but decreases in the sheath region, and the plasmas transform from g mode to α mode as the distribution of electron generation rate changes a lot.
The He + N 2 CAPs are capacitive in nature, but the He + O 2 CAPs becomes more and more resistive as the increase of O 2 fraction. This is because the electron density in the bulk region decreases sharply and hence larger electric field is needed to sustain the plasmas. The increase of electric field in the bulk region makes the sheath boundary more difficult to be determined, and several criteria reported in the literature are found to be not applicable. A new criterion of the sheath boundary, ∇E | | = 5 kV/cm 2 , is put forward, which is found suitable for both the electropositive and electronegative CAPs.
Most of the input power is dissipated into electrons in He + N 2 CAPs via ohmic heating, but for He + O 2 CAPs more and more input power is coupled to ions with increasing O 2 fraction. The ion-coupling power even dominates when [O 2 ] > 0.5%. A formula is put forward to estimate the ion-coupling power, of which the calculated results are similar to the numerical ones. 6 References