A surface mechanism for O3 production with N2 addition in dielectric barrier discharges

Ozone, O3, is a strong oxidizing agent often used for water purification. O3 is typically produced in dielectric barrier discharges (DBDs) by electron-impact dissociation of O2, followed by three-body association reactions between O and O2. Previous studies on O3 formation in low-temperature plasma DBDs have shown that O3 concentrations can drop to nearly zero after continued operation, termed the ozone-zero phenomenon (OZP). Including small (<4%) admixtures of N2 can suppress this phenomenon and increase the O3 production relative to using pure O2 in spite of power deposition being diverted from O2 to N2 and the production of nitrogen oxides, N x O y . The OZP is hypothesized to occur because O3 is destroyed on the surfaces in contact with the plasma. Including N2 in the gas mixture enables N atoms to occupy surface sites that would otherwise participate in O3 destruction. The effect of N2 in ozone-producing DBDs was computationally investigated using a global plasma chemistry model. A general surface reaction mechanism is proposed to explain the increase in O3 production with N2 admixtures. The mechanism includes O3 formation and destruction on the surfaces, adsorption and recombination of O and N, desorption of O2 and N2, and NO x reactions. Without these reactions on the surface, the density of O3 monotonically decreases with increasing N2 admixture due to power absorption by N2 leading to the formation of nitrogen oxides. With N-based surface chemistry, the concentrations of O3 are maximum with a few tenths of percent of N2 depending on the O3 destruction probability on the surface. The consequences of the surface chemistry on ozone production are less than the effect of gas temperature without surface processes. An increase in the O3 density with N-based surface chemistry occurs when the surface destruction probability of O3 or the surface roughness was decreased.


Introduction
Ozone, O 3 , is widely used in commercial and municipal settings for purification of water [1][2][3]. The generation of O 3 for water purification is typically accomplished using a lowtemperature plasma device, often in a pulsed dielectric barrier discharge (DBD) configuration, where one or both electrodes are coated with a dielectric. DBDs are typically operated in pure O 2 to maximize O 3 production. O 3 is produced from O 2 through a two-step process. Electron-impact dissociation of O 2 produces O atoms, followed by the production of O 3 by a third body mediated reaction, O + O 2 + M → O 3 + M. Production of O 3 decreases in the plasma at elevated gas temperatures due to endothermic processes which destroy the ozone and reduction in the rates of 3-body processes.
In addition to reactions in the plasma, reactions can occur between O 3 and surfaces in contact with the plasma. Itoh et al showed that O 3 could be lost in reactions with the surfaces and that the rate of loss depended on the metal electrode material [4]. Yanallah et al simulated O 3 production and showed that including O 3 loss reactions on the surfaces changed the electrical characteristics of the discharge [5]. Mazánková et al exposed copper and aluminum surfaces to O 3 produced by an ozonizer to study surface composition [6]. They showed that the elemental O composition of those surfaces increased after exposure to O 3 .
The production of O 3 in many commercial DBD reactors is not constant over time. After a long period of operation, the flow rate of O 3 leaving the reactor sometimes drops to nearly zero. This phenomenon was coined the ozone-zero phenomenon (OZP) by Taguchi et al [7]. OZP does not imply that O 3 is not being produced inside the reactor. Instead, OZP refers to the O 3 observed leaving the reactor. The time over which the OZP occurs is much longer than a gas residence time. Taguchi et al proposed that the primary cause of OZP was destruction of O 3 on the surfaces in contact with the plasma due to long term changes in the properties of the surface as opposed to a volumetric process, either a decrease in production or increase in destruction, occurring within the plasma. The rationale is plasma processes should scale with the gas residence time.
The OZP was reproduced by Murayama et al [8]. Auger emission spectroscopy of the electrodes showed that O atoms penetrated the stainless-steel electrode over time and changed the properties of the electrode, possibly contributing to the OZP. Taguchi et al showed that the OZP was dependent on the power per electrode area (W-cm −2 ) [9]. The rate of the decrease in O 3 concentration was higher at larger values of specific power. Recovery from the OZP was shown to occur with continued operation of the reactor. Itoh et al showed the surface of the stainless-steel electrode was oxidized by O 3 and O [10].
The OZP can be suppressed by the addition of nitrogencontaining species into the discharge, in spite of the diversion of power deposition from O 2 into the nitrogen-containing additives and formation of N x O y species. Early work by Taguchi et al showed that adding 0.2% N 2 to pure O 2 DBDs suppressed the OZP and increased the O 3 concentration relative to a baseline of 0.01% N 2 [7]. They hypothesized that NO 2 formed from NO or N 2 in the feed gas aided in the recovery of the OZP. Itoh et al also showed that the OZP was suppressed with a N 2 addition of 0.2% [10]. Seyrling et al confirmed that the addition of N 2 (2.3% by weight) could suppress the OZP [11]. They also showed that after the N 2 flow was stopped, the O 3 generation efficiency declined at a much slower rate compared to experiments with no N 2 flow over time scales much longer than the gas residence time. This indicated that the process by which N 2 suppresses the OZP was not a volumetric process but instead a slowly evolving process on the surface. They also showed that the total amount of N 2 added was the dominant factor in determining the rate of decrease in O 3 efficiency.
In following work, Seyrling et al examined N 2 O and N 2 O 5 concentrations to further investigate the OZP suppression [12]. While both N 2 O and N 2 O 5 were present when N 2 was flowing, only N 2 O 5 was present after the flow of N 2 was turned off. They proposed that N 2 O 5 adsorbs onto sputter products on the surface of the stainless-steel electrodes. Qin et al showed that 4% N 2 in a packed bed DBD increased the O 3 concentration [13]. As the average electric field/gas number density, E/N, in the reactor increased in the packed bed reactor, the admixture of N 2 producing the largest O 3 concentration decreased.
In this paper, we discuss results from a computational investigation in which a general surface reaction mechanism is proposed to explain increased O 3 concentration with the addition of N 2 to O 2 DBDs. The surface reaction mechanism includes formation and destruction of O 3 , adsorption and recombination of N and O, desorption of O 2 and N 2 , and reactions forming or consuming NO x species. While some probabilities for these surface reactions were taken from the literature for borosilicate glass, a dielectric material commonly used in DBDs, many probabilities in the reaction mechanism were estimated to explain why O 3 density can be a maximum at a nonzero N 2 admixture in spite of power being diverted from O 2 to N 2 . This surface reaction mechanism was implemented in a zero-dimensional (0D) plasma chemistry model GlobalKin.
First, the plasma properties and O 3 production were examined without reactions on the surface. With 0.2% N 2 in O 2 , the dominant reactive oxygen and nitrogen species (RONS) were O, N, O 3 , NO, NO 2 , NO 3 , N 2 O, and N 2 O 5 . Without the surface reaction mechanism, O 3 density monotonically decreased as the N 2 admixture increased. An increase in gas temperature results in a decrease in O 3 density. With the surface reaction mechanism, O 3 concentrations decreased relative to O 3 without the surface reactions due to there being a finite probability of O 3 destruction on the surface. However, the O 3 density with the surface reaction mechanism is a maximum with 0.2% N 2 addition compared to otherwise pure O 2 . This favorable influence of N 2 is due to N adsorption occupying sites that would otherwise be available for O 3 destruction. The O 3 density also decreases as the probability of destruction on the surface increases and as the surface roughness increases.
The global plasma chemistry model and the reaction mechanism are described in section 2. In section 3, formation of O 3 without reactions on the surface is examined, including for varying N 2 admixtures (section 3.1) and gas temperatures (section 3.2). The formation of O 3 with the surface reaction mechanism, including destruction of O 3 , is discussed in section 4. The variations in O 3 density with N 2 admixture (section 4.1), surface destruction probability (section 4.2), and surface roughness (section 4.3) are also discussed. Finally, concluding remarks are in section 5.

Description of the model
The model used in this work is GlobalKin, described in detail in [14]. GlobalKin is a 0D plasma chemistry model representing the plasma as a well-stirred reactor. Densities are solved by integrating continuity equations for each species. Electronimpact, ion-molecule and heavy particle reactions, diffusion to surfaces, and flow into and out of the system comprise the sources and losses in the continuity equations. The electron and gas temperatures are solved using their respective energy equations. The electron energy distribution is obtained by solving Boltzmann's equation in the steady state. From the electron energy distributions for a range of E/N (electric field/gas number density), a lookup table of electron-impact rate coefficients for different electron temperatures (mean electron energy) is generated.
The surface kinetics module (SKM), a module in GlobalKin [15,16], is a surface site balance model that produces the occupancy of surface sites. The surface site occupancy θ of species i is determined by The first term is the source of species i from reactions between species k on the surface and flux Γ j of gas phase species j with a probability of reaction p ijk . The second term is a source of species i from reactions between two surface species, k and l, with probability p ′ ikl . The last term is the loss of species i due to reactions with both gas phase and surface species. Unless otherwise noted, the total surface site density is 10 15 sites cm −2 . Using a time-slicing technique, the SKM is integrated for times greater than that between calls to the SKM, allowing the surface species to reach a steady state at a rate commensurate with the gas phase species. In this work, the SKM is called every 50 ns and integrated for 1 ms on each call.
The flux to the surface, appearing in equation (1), is provided using a diffusion length and the reactor averaged density resulting from the global model, In equation (2), Γ jk is the flux of species j to surface k in contact with the plasma, N j is the volume averaged density of species j, and D j is its diffusion coefficient. Λ k is the diffusion length for transport to surface k. In typical DBDs, as addressed here, the axial dimension in the plasma between electrodes or materials covering the electrodes is small compared to the lateral length. As a result, diffusive fluxes to those surfaces dominate. For charged species, D j is the species modified ambipolar diffusion coefficient.
The geometry modeled in GlobalKin is a DBD with a high surface-to-volume ratio, having a plasma volume of 4.4 cm × 4.4 cm × 300 µm. The pressure is 1 atm and the flow rate is 2 slm producing a residence time of 16 ms. The electrodes in the DBD are covered with borosilicate glass, chosen as a representative dielectric. The DBD operated with a pulse length of 130 ns (20 ns ramp up and 30 ns ramp down) and peak power of 5 kW, which produces an energyper-pulse of 0.625 mJ or 1.1 mJ cm −3 . The pulse repetition rate is 10 kHz (10 −4 s period) which corresponds to average power of 6.25 W or 10.8 W cm −3 . 150 ms (1500 pulses) were modeled in GlobalKin to achieve a pulse-periodic steady state. This gas phase integration time corresponds to approximately 50 min of operation for surface processes. In the base case, the inlet gas temperature and wall temperatures are held at 300 K. The electron temperature T e is calculated during the power pulse and is set to 0.025 eV after the pulse when power is removed.
The operation of typical DBDs relies on the propagation of streamers, or highly localized filaments of plasma. To resolve streamers, a 2D or 3D modeling approach is required. However, performing 2D or 3D simulations for thousands of pulses, which is needed to track the evolution of surface properties, is prohibitively computationally expensive. The use of a global model which addresses reactor average properties enables investigation of many pulses over long periods. As discussed below, this approximation applies provided dominant processes are not non-linear.
The DBD operates in otherwise pure O 2 with admixtures of N 2 . The base case simulates the plasma formed in 0.2% N 2 (99.8% O 2 ). The gas phase reaction mechanism is adapted from Van Gaens and Bogaerts [17]. Additions for excited states of O beyond O( 1 D) were made [18][19][20][21][22][23][24] 685 reactions in the gas phase are included in the mechanism.
The proposed surface reaction mechanism is listed in table 2. The reaction mechanism was developed with the goal of explaining the increase in O 3 density at low admixtures of N 2 in the presence of surface reactions that include destruction of O 3 . The reaction mechanism considers physisorbed species. The surface reaction mechanism includes O 3 destruction by dissociative adsorption of O 3 on a bare wall site, W s , to produce adsorbed O s , Charged Species e, O 2 (The subscript s denotes a surface species.) These reactions for O 3 destruction have been proposed by several researchers [6,13,25]. As will be discussed in section 4, W s is more abundant than O s and is therefore responsible for the majority of O 3 destruction on the surface. N is adsorbed by consuming a W s site. This reaction enables N s to block sites that are otherwise available for O 3 destruction by reaction 5. N desorbs both through Eley-Rideal (reaction 8) and Langmuir-Hinshelwood (reaction 9) mechanisms by N 2s is loosely physisorbed which is then removed from the surface by collisions of O 2 with the surface. Similarly, O adsorbs and desorbs through analogous reactions to N. The probabilities of O and N recombination on surfaces can vary widely depending on the surface material. Dielectric surfaces, as investigated here, typically have lower surface recombination probabilities than metal surfaces. For example, in Stafford et al, a recombination probability of 0.13 was reported for stainless steel during initial plasma exposure [26], while on dielectric surfaces, a recombination probability of 0.002 was reported [27,28].
O s is additionally removed through O 3 formation on the surface by Other mechanisms of O s and N s removal involve formation or destruction of N x O y species. NO is formed through O and N association by N+O s → W s + NO. (12) NO is also formed by O 2 reacting with adsorbed N s by NO is destroyed through N 2 formation by NO forms NO 2 by NO 2 reacts with N s , forming several products by NO 3 is reduced to form NO and NO 2 by Where available from the literature, reaction probabilities for surface reactions were selected for borosilicate glass. Otherwise, the probabilities of reactions were estimated to explain the increase in O 3 density at low N 2 admixtures that is observed experimentally. The reactions that involve NO x species have a probability of 10 −8 , based on the probability for reaction 15 discussed in [29].
Borosilicate glass was chosen due to the availability of reaction probabilities. As mentioned above, other materials, either dielectric (e.g., quartz) or metallic, will quantitatively have different reaction probabilities. However, while the probabilities will differ between different materials, the same general conclusions apply. To extend the surface mechanism to other materials, the general sequence of O 3 quenching and N atom adsorption blocking quenching sites should apply.
Destruction of O 3 does not occur on the surface when the SKM is not executed. In the absence of the surface reaction mechanism employed in the SKM, the only surface reactions are quenching of excited states and recombination of charged particles and atomic species.

O 3 formation in a pulsed DBD
In this section, plasma properties and RONS densities without the surface reaction mechanism are discussed for a 0.2% N 2 admixture into otherwise pure O 2 with an inlet gas temperature of 300 K. The gas temperature in the discharge was allowed to vary, but the gas temperature increased by less than 2 K over the entire simulation. The variation of the O 3 density with N 2 admixture, as well as gas temperature, are examined in sections 3.1 and 3.2. Electron density, electron temperature T e , and the power deposition over the last discharge pulse (1500th pulse at 10 kHz) are shown in figure 1. T e increases early during the power pulse, reaching a maximum of 4.4 eV at 0.1 ns. This increase in T e enables avalanching of electrons by electronimpact ionization. The power continues ramping up over 20 ns, leading to a corresponding increase in electron density. The increase in electron density allows T e to decrease while still dissipating the specified power. The power reaches a steady state of 5 kW (8.6 kW cm −3 ). The electron density continues to increase, and T e continues to decrease, over the duration of the pulse as population of excited states enables more efficient multi-step ionization. The electron density reaches 2.7 × 10 11 cm −3 before the power ramps down at which time the electron density and T e both decrease quickly. The electron density is less than 1% of the maximum by 280 ns, or 150 ns after the pulse has terminated. The decrease in electron density following the pulse is dominated by electron attachment to O 2 forming O 2 -. The electron and radical densities discussed here are volume averages, as this is the outcome and limitation of global models. These values may be low compared to peak densities that occur in localized streamers. These global model derived densities should closely approximate the volume average of these quantities in a streamer dominated discharge provided that non-linear processes do not dominate. For example, multi-step ionization is a process that scales nonlinearly with electron density. In short pulse, atmospheric pressure plasmas, excitation and ionization tend to be dominated by collisions with ground state species. Ozone formation is sensitive to gas temperature (decreasing efficiency with increasing pressure). The higher specific power deposition in a streamer will produce a locally higher gas temperature. However, thermal conduction from the narrow streamers (a few hundred microns) to the bulk gas and to the electrodes quickly equilibrate the temperature. RONS production over the 1500 pulses simulated are shown in figure 2. The RONS can be divided into two categories: the long-lived RONS that accumulate over the duration of the discharge (figure 2(a)) and the short-lived RONS whose densities oscillate as the plasma is pulsed (shown in figure 2(b) Several nitrous oxide species, N x O y , are also formed in the discharge. N 2 O is primarily formed by Over the last pulse, NO 2 is formed by NO 3 is formed by N 2 O 5 is formed by As NO 2 and NO 3 are required to form N 2 O 5 , the density of N 2 O 5 increases after several hundreds of pulses after formation of the precursors. O 3 production for water purification is energy intensive, and so maximizing efficiency is a high priority. Comparison can be made of computed characteristics of this device to experimental devices described in the literature. The residence time of gas for our device is about 16 ms, which corresponds to when the majority of RONS densities achieve a steady state in the absence of the surface reaction mechanism. The energy deposition after 16 ms is 137 mJ cm −3 . For an O 3 density of 1.4 × 10 17 cm −3 at 16 ms, this energy deposition equates to a production efficiency of 6.1 eV/O 3 -molecule or production yield of 294 g kWh −1 . DBDs described in the literature operated in pure O 2 have similar efficiencies, ranging from 150 g kWh −1 to 400 g kWh −1 [13,[30][31][32][33].
The short-lived RONS are produced and consumed at different times during the power pulse as shown in figure 2(b). O and N are both produced during the pulse by electron-impact dissociation of O 2 and N 2 . O and N decrease shortly after the power ramps down as the electron density and T e decrease, and production by electron-impact reactions decreases. O is consumed primarily in forming O 3 by reaction 20, while N is consumed by formation of NO by The density of NO increases during the pulse and continues increasing after the pulse, consuming N. Over the last pulse, NO is primarily formed by The density of NO is maximum at about 9 µs after the pulse and decreases until the next pulse begins. NO is consumed in NO 2 formation, including

N 2 admixture
The admixture of N 2 in O 2 affects the power deposition into O 2 as well as the RONS produced. As the admixture of N 2 increases, the availability of N increases, increasing the potential for N x O y formation. The variation of the quasi-steady state O 3 density with the added N 2 is shown in figure 3(a). These results are without the surface reaction mechanism. That is, O 3 destruction on surfaces is not included. With the pressure being held constant at 1 atm, adding N 2 decreases the amount of O 2 . With the maximum N 2 added being 10%, the decrease in O 2 is at most 10%. As the N 2 percentage increases, the O 3 density monotonically decreases. The decrease in O 2 density has some effect on O 3 production but is not the major cause for the decrease in O 3 density. There are two reasons for the decrease in O 3 density: O availability and N x O y production.
As N 2 percentage increases, the maximum O density produced during the discharge pulse decreases. This decrease in O production is due to power being channeled into N 2 instead of O 2 , as shown in figure 3(b). As the N 2 percentage increases, the power channeled into N 2 linearly increases; however, this increase occurs at a rate twice that of the N 2 increase. For example, at 0.5% N 2 , the power deposited into N 2 is 1%. This occurs because N 2 has higher cross-sections for excitation of vibrational and electronic states than the cross-sections for corresponding states in O 2 . The decrease in power going into O 2 leads to a decrease in maximum O density by 25% from 0% N 2 to 10% N 2 . The power going into N 2 leads to more N atom availability, increasing linearly with N 2 percentage to reach a maximum of 4.1 × 10 12 cm −3 over the last pulse at 10% N 2 . The increased availability of N leads to formation of nitrous oxides N x O y . N x O y formation further consumes O that would otherwise be available for O 3 production, and therefore also contributes to the decrease in O 3 density.

Gas temperature
The density of O 3 produced in DBDs is strongly dependent on gas temperature T g due to rates of formation and destruction of O 3 being dependent on temperature. The reactions and rate coefficients responsible for O 3 production are These rate coefficients of O 3 formation decrease with increasing T g . Additionally, as T g increases, the total gas density decreases to maintain a constant pressure of 1 atm. This decrease in gas density decreases the O 2 available for O 3 formation, as well as the density of the third-body M. The decreasing rate coefficients and gas density decrease the overall rate of O 3 formation. At elevated temperatures, O 3 is destroyed in several endothermic reactions with rate coefficients increasing with T g , including The rate coefficients of reactions 37 and 38 are small (<10 −19 cm 3 s −1 ) due to the large activation energy required. However, the rate coefficient of reaction 36 ranges from 8.3 × 10 −15 cm 3 s −1 at 300 K to 1.3 × 10 −13 cm 3 s −1 at 500 K.
The change in O 3 density with the inlet T g and wall temperatures varying between 300 K and 500 K was investigated. While T g in the discharge was solved self-consistently, T g rose by <2 K for all inlet T g investigated. The variation in O 3 density from 300 K to 500 K at different admixtures of N 2 is shown in figure 4. As the rates of O 3 formation decrease and the rates of O 3 destruction increase with T g , O 3 density decreases as inlet T g increases. At each admixture of N 2 , the decrease in O 3 density from 300 K to 500 K is at least a factor of 5.
The relative importance of the decrease of formation rate and increase of destruction rates can be understood by studying the 0.2% N 2 case in detail. The decrease in O 3 is primarily due to the decrease in the formation rate, not the increase in the destruction rate because the rate of destruction is at least an order of magnitude smaller than the rate of formation. At 0.2% N 2 , the maximum rate of O 3 formation over the last pulse decreases by a factor of 6 from 300 K to 500 K inlet T g . This is not due to a lack of atomic O, as the maximum O density over the last pulse actually increases by 5% from 300 K to 500 K. Instead, the decrease in the O 3 formation rate is due to the decrease in the rate coefficient by a factor of 2.4 and a decrease in the gas density by a factor of 1.7 from 300 K to 500 K inlet T g .

Surface destruction of O 3
Reactions of O 3 with surface sites will, in the absence of other effects, generally destroy O 3 . To investigate these processes, simulations were performed with the SKM in GlobalKin using the reaction mechanism discussed in section 2 and summarized in table 2. The consequences of the surface reaction mechanism on the gas phase O 3 density, as well as other RONS, is first discussed for an admixture of 0.2% N 2 . The SKM is called every 50 ns and integrated for 1 ms, leading to the evolution of the surface occurring over longer times than integration of gas phase densities. This time-slicing technique enables the surface site densities to come into a steady state within reasonable computation times. Due to the longer integration time of the SKM, the total inventory of N, including in the gas phase and on the surface, increases relative to without surface reactions. This increase reflects the long term adsorption of N species on the surface over times greatly exceeding the residence time of gas in the reactor. The inventory of N in only the gas phase increases by less than 1% due to including surface reactions.
The RONS densities are shown in figure 5(a) (long-lived) and figure 5(b) (short-lived) for 0.2% N 2 . The short-lived RONs densities are shown over the last discharge pulse. O 3 is the most abundant RONS, with a density is 1.9 × 10 17 cm −3 at 150 ms. The O 3 density without the surface reaction mechanism (section 3) was 2.1 × 10 17 cm −3 at 150 ms. About 10% of the O 3 produced is destroyed on the surface, despite a destruction probability of 0.01. The large amount of O 3 destruction is due to the high surface area to volume ratio (SVR) of the reactor, leading to a short diffusion length of 95 µm and a short timescale of diffusion of 0.9 ms. In a gas residence time of 16 ms, the O 3 encounters the wall about 18 times, increasing the likelihood of destruction over the residence time.
The effect of the reactions on the surface can be compared to the effect of gas temperature for 0.2% N 2 . The O 3 density at 150 ms is 1.9 × 10 17 cm −3 with the surface reaction mechanism and 3.4 × 10 16 cm −3 at 500 K without the surface reaction mechanism. For comparison, without the reactions on the surface at 300 K, the O 3 density at 150 ms is 2.1 × 10 17 cm −3 . Therefore, the gas temperature can reduce the O 3 density substantially more than surface destruction. The steady state compositions of other RONS are similar with and without the surface reaction mechanism. At 150 ms, NO is increased by 0.2% by the surface reaction mechanism. This increase occurs because of there being a limited number of reactions consuming NO on the surface. While all these reactions have the same probability, the reaction O 2 + N s → O s + NO occurs with a higher rate because O 2 is the most abundant molecule in the gas and therefore has the largest flux to the surface. NO 2 is decreased by 9% compared to without surface reactions. NO 2 is more reactive with the surface than NO, being more likely to be destroyed than formed. Production of NO 2 on the surface stems from NO and NO 3 . Since NO and NO 3 have lower densities than NO 2 at 150 ms, the rates of production are lower than the rate of NO 2 destruction. NO 3 decreases by 6% compared to without surface reactions. NO 3 is only consumed on the surface and is not produced, decreasing the gas phase concentration of NO 3 . N 2 O 5 decreases by 16% compared to without surface reactions. The decrease in N 2 O 5 is due to the decrease in its precursors, NO 2 and NO 3 . N 2 O is increased by less than 2% compared to without surface reactions, as N 2 O is formed in a surface reaction but is not destroyed on the surface.
The short-lived RONS are shown in figure 5(b) over the last pulse. Compared to without the surface reactions, O in the gas phase is largely unchanged. The maximum density of O decreases by less than 0.3%. In spite of the adsorption of O onto the surface, O s remains low (<3% of the surface sites). Therefore, the O density is minimally affected by adsorption as production of O from electron-impact dissociation of O 2 is essentially unaffected by the surface mechanism. However, the maximum N density over the last pulse decreases by 31% compared to without surface reactions. This decrease is due to adsorption of N on the surface. Since N 2 is only 0.2% of the gas mixture, this loss of N is not immediately replenished by electron-impact dissociation of N 2 to form N. The decrease in N with and without surface reactions is not as severe at larger N 2 admixtures. With 10% N 2 , the decrease in the maximum N in the gas phase is only 2%.
The surface site occupancies are shown in figure 5(c). The gas phase densities come into equilibrium with the surface sites on the order of diffusion times to the surface-at most a few ms-for a given surface composition. (Recall that the surface evolves over longer timescales due to numerical time slicing.) Initially, the surface is covered with empty wall sites W s . At 3000 s, adsorbed N s occupies 35% of the surface sites, while empty wall sites W s comprise 64% of the surface. The decrease in W s is largely due to the increase in N s . With this high site occupancy, N s blocks some of the W s that could otherwise destroy O 3 through O 3 + W s → O s + O 2s . O s occupies 0.9% of the surface sites. O 2s and N 2s occupy less than 0.1% of the surface as their binding energies are small and they are removed from the surface by collisions with O 2 . Even with a low probability of desorption, the flux of O 2 is high, and O 2s and N 2s are rapidly removed.
Despite N s and O s having the same adsorption and recombination probabilities, their surface occupancies are very different. O s has a much lower surface occupancy than N s because the removal rates of O s are higher than the removal rates of N s . Both N s and O s can be removed from the surface by O 2 ; however, O s is removed in O 3 formation (reaction 10) with a probability of 0.004, while N s is removed in NO formation (reaction 13) with a probability of 10 −8 . O s is also removed from the surface in O 3 destruction (reaction 6). The probability of O 3 destruction by O s is 0.01, while the other reactions that remove N s from the surface have probabilities of 10 −8 . O s also experiences more oscillation than N s . While the rates of removal of O s by O 3 and O 2 remain constant over the pulse, other reactions that adsorb or remove O s do not. O s is adsorbed while O is present during or shortly following the pulse, while O s is removed by recombination to form O 2 . While these same adsorption and desorption mechanisms exist for N s , N s has a much higher occupancy and is not as affected by the dynamics over one pulse.

N 2 admixtures
A monotonic decrease in O 3 density with increasing N 2 occurred without considering surface reactions. However, with the reactions on the surface, increasing N 2 admixture changes the surface occupancies and, therefore, the destruction of O 3 occurring on the surface.
The effect of N 2 admixture on O 3 density when including the surface reaction mechanism is shown in figure 6(a). The trend in O 3 density is no longer a monotonic decrease in O 3 with increasing N 2 . The O 3 density increases from 0% N 2 to 0.2% N 2 prior to decreasing with further increase in N 2 percentage. The increase in the O 3 density at N 2 admixtures below 0.2% is explained by the surface occupancies, shown in figure 6(b). O 3 is destroyed by reactions on the surface with W s and adsorbed O s . O s at the end of the simulation is below 1.5% of the surface sites for all N 2 percentages, while W s occupies at least 7% of the surface sites for all N 2 percentages. Therefore, O 3 is mostly destroyed in reactions with W s . The surface occupancy of W s decreases as N 2 percentage increases corresponding to an increase in sites with adsorbed N s . Therefore, N s occupies surface sites that would otherwise be available for O 3 destruction.
Based solely on the increase of N s and decrease of O 3 destruction on the surface, O 3 density would be expected to increase as N 2 admixture increases. However, above 0.2% N 2 , the density of O 3 decreases. This decrease occurs because more power is deposited into N 2 compared to O 2 as the N 2 percentage increases as discussed in section 3.1. Therefore, less O is produced in the gas phase. O can also be diverted from O 3 production to form N x O y species, further decreasing the O 3 density. The competition between decreased surface destruction of O 3 and increased power into N 2 as N 2 percentage increases creates a maximum in O 3 at 0.2% N 2 .
Experimental observations have shown that even after the N 2 flow has been turned off, the O 3 percentage remains elevated for some period of time before decreasing [11,12]. The surface mechanism can reproduce this behavior. A simulation was initialized with the species densities and surface occupancies at the end of the 0.2% N 2 case, and only O 2 was flowed into the reactor. The O 3 density decreased as the N s was removed from the surface by desorption or reactions to form N x O y species. At 1000 s of surface reactivity, N s was reduced to 7% of the surface sites from its initial value of 35%. The O 3 density after 1500 pulses of pure

Probability of O 3 destruction
The probability of O 3 destruction on the surface directly affects the O 3 density in the reactor. As the precise values of probabilities of these destruction processes are not well The O 3 densities at different destruction probabilities and N 2 admixtures are shown in figure 7. As expected, the O 3 density decreases as the surface destruction probability increases. This decrease occurs simply because more O 3 is being destroyed on the surface. At 0.2% N 2 and a probability of 0.01 for O 3 destruction, the O 3 density is 2.0 × 10 17 cm −3 , only slightly lower than without the surface reactions (2.1 × 10 17 cm −3 ). This decrease, even at low destruction probabilities, occurs because the reactor has a high SVR and O 3 encounters the surface many times before flowing out of the reactor.
In addition to the decrease in O 3 density with increasing surface destruction probability, the admixture of N 2 where the O 3 density is maximum increases with increasing destruction probability. At probabilities of O 3 destruction of 0.001 and 0.005, the O 3 density is maximum at essentially 0% N 2 , matching the results when reactions on the surface are not considered. This maximum at 0% N 2 is due primarily to the low amount of O 3 destruction on the surface. The maximum in O 3 density shifts to 0.2% N 2 at 0.01 destruction probability. At 0.02 destruction probability, the maximum in O 3 density shifts to 1% N 2 , and at 0.05 destruction probability, the maximum in O 3 further shifts to 2% N 2 . This shift in the N 2 percentage where the O 3 density is maximum is due to the need for N atoms to occupy a larger fraction of surface sites, blocking O 3 destruction processes, when the destruction probability increases. In spite of there being more power being channeled into N 2 with increasing N 2 percentage, the benefit of blocking sites where O 3 destruction can occur at higher rates is more beneficial. Increasing N 2 percentage increases the rate of production of N atoms that block the sites.

Surface roughness
The roughness of the dielectric surface can vary between different reactors by choice of materials and materials processing, and during the lifetime of the reactor. The surface roughness will affect several of the model parameters, including reaction rates. In the context of this study, the roughness of the surface is represented by the surface site density and the net surface occupancy. A plane-view of a rough surface has more surface sites per unit area than smooth surfaces.
The O 3 density and N s fractional occupancy are shown in figures 8(a) and (b), respectively, for different surface site densities-higher surface site densities correspond to rougher surfaces. The probability of destruction of O 3 on the surface is 1%. At 0% N 2 , the O 3 density is essentially the same for all surface sites densities. Since increasing the site density does not decrease the O 3 density, the flat-surface site density of 10 15 cm −2 is sufficient to interact with the O 3 that diffuses to the wall. With increasing N 2 percentage, power is diverted from O 2 which creates O atoms to N 2 . The benefit of N 2 then comes from N adsorption on surface sites. With a larger number of surface sites that occurs with increasing roughness, the likelihood for O 3 destruction increases. However, for a fixed power, the production of N atoms is fixed (and independent of surface roughness). There are not enough N atoms being produced (and adsorbed) to offset the increased likelihood for O 3 destruction. N s does block some empty W s sites that could otherwise destroy O 3 . However, the occurrence of unblocked sites increases more rapidly than sites occupied by N s as the total site density increases.
While the overall O 3 density decreases with increasing surface site density, the N 2 admixture where there is some benefit to O 3 density occurs also shifts. The N 2 admixture where the maximum in O 3 density occurs decreases with surface roughness. At a site density of 10 15 cm −2 the maximum in O 3 density occurs at 0.2% N 2 . At a site density of 2 × 10 15 cm −2 , the maximum in O 3 density shifts to 0.1% N 2 and shifts further to 0.05% N 2 at a site density of 3 × 10 15 cm −2 . At a site density of 5 × 10 15 cm −2 , the maximum in O 3 density occurs at 0% N 2 . The benefit of N 2 admixtures is small due to the higher rates of O 3 quenching on the larger number of surface sites.
As discussed above, the benefit of the N 2 admixture increases with increasing probability of quenching O 3 . The higher the destruction probability, the greater the benefit of N s blocking a site that can destroy O 3 . The variation in O 3 density is shown in figure 8(c) for different surface site densities for higher surface destruction probability of O 3 of 0.02. Similar to the 0.01 surface destruction probability of O 3 , the O 3 density decreases with increasing surface site density, and the N 2 admixture where the maximum in O 3 density occurs decreases. However, the decrease is more pronounced. For a site density of 10 15 cm −2 , the maximum O 3 density occurs at 1% N 2 and decreases to 0.1% N 2 for a surface site density of 5 × 10 15 cm −2 .

Concluding remarks
O 3 destruction on the walls of DBD reactors has been hypothesized to be the cause of the OZP. Addition of N 2 into an otherwise pure O 2 discharge has been shown to suppress the OZP and increase O 3 concentration, despite the discharge power that is diverted from O 2 into N 2 and the corresponding increase in N x O y species. A general surface reaction mechanism including destruction of O 3 on the surface was proposed in this work to explain the increase in O 3 concentration at nonzero admixtures of N 2 . The general surface reaction mechanism was coupled to a global plasma chemistry model, and a DBD having a high SVR was simulated for 1500 discharge pulses corresponding to 50 min of surface evolution.
The results of the simulation were first analyzed without including O 3 destruction on the surface. The O 3 concentration decreases when the admixture of N 2 increases. This decrease is due to a decrease in the power deposited into O 2 and a corresponding increase in the power deposited into N 2 , in addition to formation of nitrogen oxides consuming O that could otherwise form O 3 . When the inlet gas temperature is increased, the O 3 density steadily decreases as the rate of O 3 formation decreases at elevated temperatures.
The reactions on the surface, including O 3 destruction, were then included in the simulation. The overall O 3 density decreases due to its destruction on surfaces, while most other RONS have a similar concentrations. For an O 3 destruction probability of 0.01, increasing the admixture of N 2 increases the O 3 density up an addition of 0.2% N 2 and then decreases the O 3 density at higher N 2 admixtures. The increase at low N 2 admixtures is due to N s occupying surface sites that otherwise might be used for O 3 destruction. The decrease at higher N 2 admixtures is due to less power being deposited into O 2 and formation of N x O y . The maximum at 0.2% N 2 agrees qualitatively with previously published results, where O 3 concentration was boosted with 0.2%-4% N 2 dependent on the reactor geometry.
The O 3 density decreases as the probability of surface destruction increases. However, a significant fraction of this O 3 loss can be recovered by adding N 2 . For example, for an O 3 destruction probability of 0.05, about half of the loss can be recovered by N 2 addition of about 2%. For these conditions, the benefit of removing quenching sites for O 3 by occupying those sites with N s outweighs the loss incurred by power flowing into N 2 . As surface roughness increases, O 3 concentration generally decreases due to there being more sites for O 3 loss. Some of this loss can be recovered by N s passivation. However, the N flux to the surface must increase in greater proportion than the increase in site density.
O 3 * , a vibrationally excited state of O 3 was not included in mechanism due to its low fluxes to surfaces at atmospheric pressure. O 3 * has a large quenching coefficient to the ground state on surfaces [34] while we expect O 3 * will be more likely to dissociate on surfaces due to its lower activation energy for this process. If this expectation is met, then conditions which produce larger fluxes of O 3 * to surfaces will also likely enhance the beneficial effect of N 2 addition on net ozone production. The surface reaction mechanism proposed is general. Probabilities of reactions on the surface were taken for borosilicate glass, a common dielectric, where possible and were otherwise estimated to explain the increase in O 3 density at nonzero N 2 admixtures. The reactions on the surface and their associated probabilities will vary depending on the material in contact with the plasma. The surface composition of the materials in contact with the plasma could change with increasing plasma exposure, processes that were not considered in this investigation. Metal electrodes could oxidize, changing the probabilities of reactions on the surface as the surface composition changes over the reactor lifetime. Catalytic materials could change the reactions occurring on the surface. However, the trends discussed here can help guide selection of materials to decrease the OZP. Based on our results, materials should have, as first order, low surface destruction probability of O 3 , high rates of adsorption of N, and low surface roughness to help suppress the OZP.

Data availability statement
The data that support the findings of this study are included in this article and available from the corresponding author upon reasonable request.