Modelling of Nonthermal Dielectric Barrier Discharge Plasma at Atmospheric Pressure and Role of Produced Reactive Species in Surface Polymer Microbial Purification

A nonthermal atmospheric plasma reactor was used to sterilize polymer surfaces and satisfy safety constraints in a biological medium. A 1D fluid model was developed using COMSOL Multiphysics software® 5.4 with a helium–oxygen mixture at low temperature for the decontamination of bacteria on polymer surfaces. An analysis of the evolution of the homogeneous dielectric barrier discharge (DBD) was carried out through studying the dynamic behavior of the discharge parameters including the discharge current, the consumed power, the gas gap voltage, and transport charges. In addition, the electrical characteristics of a homogeneous DBD under different operating conditions were studied. The results shown that increasing voltage or frequency caused higher ionization levels and maximum increase of metastable species’ density and expanded the sterilization area. On the other hand, it was possible to operate plasma discharges at a low voltage and a high density of plasma using higher values of the secondary emission coefficient or permittivity of the dielectric barrier materials. When the discharge gas pressure increased, the current discharges declined, which indicated a lower sterilization efficiency under high pressure. A short gap width and the admixture of oxygen were needed for sufficient bio-decontamination. Plasma-based pollutant degradation devices could therefore benefit from these results.


Introduction
Bio-decontamination technologies have emerged due to the development of compatible polymers used in biomedical applications such as medical implants. These heatsensitive materials require both sterile handling and substrate activation before use. Thus, several pre-treatments are needed to obtain the desirable physicochemical surface properties that satisfy safety constraints in the biological medium [1][2][3].
Sterilization methods using an autoclave or an oven, ethylene oxide, gamma irradiation, and ultraviolet radiation are commonly applicable [4][5][6]. However, most of these processes operate in closed spaces, require expensive and complex equipment, and need a lengthy sterilization [7], while others are toxic to human body and difficult to apply to air purifiers as germicidal agents [8]. In addition, traces of active compounds often remain after the application of these techniques and generate an unacceptable risk [9]. Consequently, these methods constitute an inadequate solution for microbial decontamination at ambient temperature.
Nowadays, a particular interest has developed in non-thermal plasma as a useful method to kill bacteria or inhibit their growth [10][11][12]. The moderate neutral gas temperatures and the benefits associated with gas phase processes [13], enable plasma to modify and bio-sterilize small and complex thermolabile polymeric surfaces. Various conventional sterilization methods including heat (steam and dry heat), chemical agents was unclear if this discharge behaved like a glow discharge at low pressure or if it was caused by multiple filaments coupled together.
In this research study, a DBD numerical model in helium-oxygen plasma at atmospheric pressure was developed using COMSOL Multiphysics software ® 5.4 [31]. Our objective was to study the spatial and temporal evolution of the different parameters of discharge and to numerically examine the density distribution of reactive species to show their effect on the microbial inactivation rate. Based on the optimization of external parameters including external voltage frequency, dielectric thickness, interelectrode width, and amplitude, the discharge parametric behavior was analyzed. The main purpose of this paper was to develop an efficient system of sterilization that utilizes a pulsed DBD and is characterized by its appropriate germicidal effect. Figure 1 describes the experimental microbial inactivation setup [32]. In this system, a sinusoidal alternating high-voltage power supply drives the plasma with pulse frequency and voltage equal to 27 kHz and 18 kV, respectively. The pulse rise time is 3 ms. The temperature of the gas is 300 K, and the pressure is 1.01 × 10 5 Pa. The discharge gas is a helium-oxygen mixture (1% O 2 ), and the plasma treatment duration is 1 min. homogeneous barrier discharge could be obtained ((p × d)~500 torr cm) [30], although it was unclear if this discharge behaved like a glow discharge at low pressure or if it was caused by multiple filaments coupled together. In this research study, a DBD numerical model in helium-oxygen plasma at atmospheric pressure was developed using COMSOL Multiphysics software® 5.4 [31]. Our objective was to study the spatial and temporal evolution of the different parameters of discharge and to numerically examine the density distribution of reactive species to show their effect on the microbial inactivation rate. Based on the optimization of external parameters including external voltage frequency, dielectric thickness, interelectrode width, and amplitude, the discharge parametric behavior was analyzed. The main purpose of this paper was to develop an efficient system of sterilization that utilizes a pulsed DBD and is characterized by its appropriate germicidal effect. Figure 1 describes the experimental microbial inactivation setup [32]. In this system, a sinusoidal alternating high-voltage power supply drives the plasma with pulse frequency and voltage equal to 27 kHz and 18 kV, respectively. The pulse rise time is 3 ms. The temperature of the gas is 300 K, and the pressure is 1.01 × 10 5 Pa. The discharge gas is a helium-oxygen mixture (1% O2), and the plasma treatment duration is 1 min. A DBD was generated between the two planar copper electrodes at a 0.2 cm distance ( Figure 2). Round electrodes with a 5 cm radius and 0.2 mm thickness were used, which were covered with alumina dielectric layers (εr = 10) of 0.1 cm in thickness [33].  A DBD was generated between the two planar copper electrodes at a 0.2 cm distance ( Figure 2). Round electrodes with a 5 cm radius and 0.2 mm thickness were used, which were covered with alumina dielectric layers (ε r = 10) of 0.1 cm in thickness [33].

Numerical Model Equations
A self-consistent fluid model describes the DBD cold plasma using balance equations derived from Boltzmann transport equations [34]. If no radial effects influence the main characteristics of the plasma, a one-dimensional discharge description is performed considering only the axial component x [35].
For all the considered species, continuity and momentum equations are solved using the drift-diffusion flux approximation [36][37][38]. The system of equations used is resolved by coupling the transport equations and the Poisson equation to obtain the electric field. The discharge is governed by the following equations: Continuity equation: where n i represents the density of electrons (e), ions (p), and excited particles (m), and Γ i represents the flux density, according to [39]: where E represents the electric field, and µ i and D i represent the mobilities and the diffusion coefficients of each type of particle. S i represents the source terms for electrons according to [40]: where M is the number of reactions, x j and α j denote the molar fraction of the target species and the Townsend coefficient for the jth reaction respectively, and N n represents the total number of neutral particles. The Equation of electron energy balance: Note that denotes the mean electron energy. S represents the source terms for the energy equation as follows: P is the number of non-elastic collisions of an electron, and ∆ j is the energy dissipation from the jth reaction.
For the electric field computation, the Poisson equation is coupled with the balance equations [41]: where q denotes the unit charge, and ε is the dielectric permittivity. The electric field is resolved inside the dielectrics and in the plasma region and defined as the negative gradient of the electric potential: The electrical properties of the discharge, including the applied voltage V app (t), the gas voltage V g (t), and the discharge current I d , are expressed by [42]:  (11) where V m and f represent the amplitude and the frequency of the applied voltage, respectively. V sd (t) represents the solid dielectrics voltage, C sd its capacitance, and S is the area of the electrode.

Boundary and Initial Conditions
The model considers the effect of the dielectric covering the electrodes, since the discharge is a DBD. Gauss's law is used to describe the influence of charge accumulation on the dielectric metallic at the interface between the dielectric and the plasma [43]: E gas and E diel represent, respectively, the electric field in the gas discharge and inside the dielectric; ε diel and ε gas are the permittivity of the dielectric surface and of the gas, respectively; u n represents the unit vector pointing normally to the wall, where the charge accumulation takes place. The surface charge density on the dielectric is σ and is calculated by dividing the charge particle flux directed to the surface at the cathode and anode [44]: where γ sec is the secondary electron emission term. The electric potential is V = V app at the powered electrode and V = 0 at the ground electrode. The flux particles and the space density boundary values are as follows: at the cathode, Γ e = −γ sec Γ p and ∇n p = ∇n m = 0 at the anode, ∇n p = ∇n e = ∇n m = 0 The initial conditions consist of uniformly distributed electrons, ions, metastable state, and surface charge: n e (t = 0) = n p (t = 0) = 10 16 cm −3 , n m (t = 0) = 10 9 cm −3 , and σ (t = 0) = 10 −8 C/cm 2 .
The chemistry model included in our simulation considers the chemical reactions and the production and loss rates of different species. The reactions of pure helium and of the helium-oxygen mixture are shown in Refs. [45,46].

Computational Study
For modelling the plasma behavior and plasma properties of homogeneous DBD discharge, the COMSOL Multiphysics ® 5.4 time-dependent module was used [47]. A 1D fluid model of the helium-oxygen mixture was applied to the parallel-plate geometry at atmospheric pressure while assuming the local electric field approximation. An efficient finite element method led to a reasonable resolution of these partial differential equations. Since particle transport equations and Poisson's equations are strongly coupled, it was imperative to adopt a very appropriate computation time step to obtain a rapid computational time evolution for the physical phenomena's convergence. The numerical simulation was performed using a backward differentiation formula (BDF) solver algorithm [48].

Results
The electrical representation of the voltage and the discharge current are illustrated in one cycle. In addition, the variations of the important physical quantities resulting from the numerical modelling were investigated, first for helium discharge, to validate the simulation model and in a second time, for the helium-oxygen mixture (He-1% O 2 ), to study the inactivation of Bacillus atrophaeus spores on polymer surfaces. Moreover, the efficiency of inactivation was examined according to the process gas and the distance of operation.

Helium DBD Discharge
The helium DBD plasma discharge was induced by 1300 V sinusoidal alternatingvoltage power supply at 10 kHz. The gap distance was 0.5 mm.

Discharge Structure
The evolution of the discharge current I d (t), the implemented voltages V app (t), and the gas voltage V g (t) during one cycle is plotted in Figure 3. First, a sudden increase in current occurred during the positive half-voltage discharge from 1 mA to a maximum of 32 mA. A breakdown of the gas occurred with the abruptly change in current, and the discharge lasted about 5 µs. Simultaneously, the gas voltage V g changed from 760 V at t = 0 s to 1200 V at t = 9 µs, at which voltage, the first discharge appeared. As the current peak was reached, V g caused the extinction of the discharge, and a negative voltage V g was triggered, announcing the ignition of the second discharge through the subsequent half cycle.

Helium DBD Discharge
The helium DBD plasma discharge was induced by 1300 V sinusoidal alterna voltage power supply at 10 kHz. The gap distance was 0.5 mm.

Discharge Structure
The evolution of the discharge current I (t), the implemented voltages V (t) the gas voltage V (t) during one cycle is plotted in Figure 3. First, a sudden increa current occurred during the positive half-voltage discharge from 1 mA to a maximu 32 mA. A breakdown of the gas occurred with the abruptly change in current, and discharge lasted about 5 µs. Simultaneously, the gas voltage V changed from 760 V 0 s to 1200 V at t = 9 µs, at which voltage, the first discharge appeared. As the current was reached, V caused the extinction of the discharge, and a negative voltage V was gered, announcing the ignition of the second discharge through the subsequent half c The discharge current maintained its behavior with a negative V , but in the o site direction, and the negative peak reached 34 mA. According to the discharge cu behavior, the DBD exhibited one breakdown each half-applied voltage cycle in the at pheric glow regime. Hence, there were two breakdown events in each cycle. Throug the discharge interval, the gas voltage and the discharge current profile followed th ternal voltage periodicity. At each half cycle, an opposite voltage called dielectric vol V , was generated by accumulating charges within the dielectric barrier's inner la Finally, the discharge was suppressed when the voltage V decreased, which preve the electric arc generation and the formation of cold plasma.

Predicted Electric Field and Species Distribution
The spatial distribution of the charged particle densities and of the electric field displayed in Figure 4 at the maximal discharge current (t = 10 µs). The discharge characterized by four discharge regions like those of DC glow discharge at low pres [49]. We found (i) a high cathode-fall region, that exhibited a maximal electric field of kV/cm resulting from the wide positive space charges close to the cathode. The discharge current maintained its behavior with a negative V app , but in the opposite direction, and the negative peak reached 34 mA. According to the discharge current behavior, the DBD exhibited one breakdown each half-applied voltage cycle in the atmospheric glow regime. Hence, there were two breakdown events in each cycle. Throughout the discharge interval, the gas voltage and the discharge current profile followed the external voltage periodicity. At each half cycle, an opposite voltage called dielectric voltage, V sd , was generated by accumulating charges within the dielectric barrier's inner layers. Finally, the discharge was suppressed when the voltage V g decreased, which prevented the electric arc generation and the formation of cold plasma.

Predicted Electric Field and Species Distribution
The spatial distribution of the charged particle densities and of the electric field are displayed in Figure 4 at the maximal discharge current (t = 10 µs). The discharge was characterized by four discharge regions like those of DC glow discharge at low pressure [49]. We found (i) a high cathode-fall region, that exhibited a maximal electric field of 16.5 kV/cm resulting from the wide positive space charges close to the cathode. Electric field (V/m) Figure 4. Comparison of calculated and experimental data [50]. Spatial distribution of the electron and ion densities and the electric field in helium plasma at a maximum discharge current time. The right side indicates the anode, and the left side indicates the cathode.
In this zone, limited to 0.3 mm, the ion density reached a maximum of 4.7 × 10 17 m −3 . The electron density attained a maximum of 3.6 × 10 17 m −3 ; (ii) a second negative-glow region extending up to 0.73 mm in length, in which the densities of electrons and ions were equal, and the electric field remained small; (iii) the faraday dark space, with 1.4 mm thickness, where the ion and electron densities were in close proximity to each other as the electric field increased. Here, a little negative space charge occurred; (iv) a positivecolumn zone, occupying the greatest area, whose width was 2.58 mm. In this electrically neutral plasma region, the ion and electron densities were equal and close to 2 × 10 16 m −3 . The electric field was relatively low, corresponding to 2 kV/cm. The electron mobility was reduced by the interaction with the ions. Figure 5 shows the density spatial distribution of metastable helium when there was a maximum discharge current. The metastable density distribution showed a profile similar to the ion and electron density profiles. During the cathode-fall region, a maximum density of 6.3 × 10 17 m −3 was reached, while in the positive-column region, it was constant, with a value of 2 × 10 16 m −3 .  In this zone, limited to 0.3 mm, the ion density reached a maximum of 4.7 × 10 17 m −3 . The electron density attained a maximum of 3.6 × 10 17 m −3 ; (ii) a second negative-glow region extending up to 0.73 mm in length, in which the densities of electrons and ions were equal, and the electric field remained small; (iii) the faraday dark space, with 1.4 mm thickness, where the ion and electron densities were in close proximity to each other as the electric field increased. Here, a little negative space charge occurred; (iv) a positive-column zone, occupying the greatest area, whose width was 2.58 mm. In this electrically neutral plasma region, the ion and electron densities were equal and close to 2 × 10 16 m −3 . The electric field was relatively low, corresponding to 2 kV/cm. The electron mobility was reduced by the interaction with the ions. Figure 5 shows the density spatial distribution of metastable helium when there was a maximum discharge current. The metastable density distribution showed a profile similar to the ion and electron density profiles. During the cathode-fall region, a maximum density of 6.3 × 10 17 m −3 was reached, while in the positive-column region, it was constant, with a value of 2 × 10 16 m −3 . Electric field (V/m) Figure 4. Comparison of calculated and experimental data [50]. Spatial distribution of th and ion densities and the electric field in helium plasma at a maximum discharge curren right side indicates the anode, and the left side indicates the cathode.
In this zone, limited to 0.3 mm, the ion density reached a maximum of 4.7 × The electron density attained a maximum of 3.6 × 10 17 m −3 ; (ii) a second nega region extending up to 0.73 mm in length, in which the densities of electrons were equal, and the electric field remained small; (iii) the faraday dark space, wit thickness, where the ion and electron densities were in close proximity to each the electric field increased. Here, a little negative space charge occurred; (iv) a column zone, occupying the greatest area, whose width was 2.58 mm. In this e neutral plasma region, the ion and electron densities were equal and close to 2 × The electric field was relatively low, corresponding to 2 kV/cm. The electron mo reduced by the interaction with the ions. Figure 5 shows the density spatial distribution of metastable helium when a maximum discharge current. The metastable density distribution showed a pr ilar to the ion and electron density profiles. During the cathode-fall region, a m density of 6.3 × 10 17 m −3 was reached, while in the positive-column region, it was with a value of 2 × 10 16 m −3 .  For validation, it was found that the numerical simulation results of the discharge parameters matched the literature results developed in the same context [50].

Helium-Oxygen DBD Discharge
The helium-oxygen plasma discharge, He/O 2 (1% O 2 ), was operated by a 30 kV highvoltage sinusoidal alternating power supply at 10 kHz. The gap distance was 0.2 mm [51]. Figure 6 illustrates the spatiotemporal evolution of the electric field ( Figure 6a) and potential (Figure 6b) in the interelectrode distance. Indeed, the potential and the electric field changed as a function of the position. The length of the sheath region could be determined with the electric field root-mean-square value [52]. Due to the plasma diamagnetic property, the electric field in the inter-electrode distance was reduced when there was an electrical discharge. For validation, it was found that the numerical simulation results of the discharge parameters matched the literature results developed in the same context [50].

Helium-Oxygen DBD Discharge
The helium-oxygen plasma discharge, He/O2 (1% O2), was operated by a 30 kV highvoltage sinusoidal alternating power supply at 10 kHz. The gap distance was 0.2 mm [51]. Figure 6 illustrates the spatiotemporal evolution of the electric field ( Figure 6a) and potential (Figure 6b) in the interelectrode distance. Indeed, the potential and the electric field changed as a function of the position. The length of the sheath region could be determined with the electric field root-mean-square value [52]. Due to the plasma diamagnetic property, the electric field in the inter-electrode distance was reduced when there was an electrical discharge.  Figure 7a illustrates the spatiotemporal distribution of electron density versus the gap extension. Indeed, two discharges occurred in each cycle, one in the positive half of the voltage cycle, and the other in the negative one. The first discharge event occurred close to the powered electrode, on the left-hand side of the picture. The maximum electron density reached approximately 3.5 × 10 19 m −3 . Figure 7b shows the electron temperature evolution at the gap center. Due to the two discharges events in a cycle, as shown in Figure  3, the electron temperature changed twice in each period.
(a) (b) Figure 6. Spatiotemporal evolution of the electric field (a) and potential (b) in the interelectrode gap. Figure 7a illustrates the spatiotemporal distribution of electron density versus the gap extension. Indeed, two discharges occurred in each cycle, one in the positive half of the voltage cycle, and the other in the negative one. The first discharge event occurred close to the powered electrode, on the left-hand side of the picture. The maximum electron density reached approximately 3.5 × 10 19 m −3 . Figure 7b shows the electron temperature evolution at the gap center. Due to the two discharges events in a cycle, as shown in Figure 3, the electron temperature changed twice in each period.

Role of Different Radical Species Produced by a Dielectric Barrier Discharge in Microbial Inactivation
In a DBD discharge, a large amount of charged particles collides with N 2 , O 2 , and H 2 O, generating active particles and free radicals along with ultraviolet radiation and shock waves. Both oxygen and nitrogen reactive species (RONS) are generated in atmospheric plasma through complex chemistry [53]. Experiments from the literature, including photographs taken with a Vis-IR digital camera confirmed the formation of atomic oxygen, and light emission spectra affirmed the generation of oxygen radicals during plasma operation [54]. These reactive radicals play a significant role in (i) killing bacteria, (ii) causing membrane damage, and (iii) degrading DNA [55].
This study excluded the influence of plasma heat on inactivating B. atrophaeus spores. Indeed, a variety of proteins in these bacteria increase their resistance to chemical and physical antimicrobial agents [56]. Further, atmospheric pressure plasma operates in a burst mode which reduces the temperature on the target, while maintaining antimicrobial effectiveness [57]. gap extension. Indeed, two discharges occurred in each cycle, one in the positive half of the voltage cycle, and the other in the negative one. The first discharge event occurred close to the powered electrode, on the left-hand side of the picture. The maximum electron density reached approximately 3.5 × 10 19 m −3 . Figure 7b shows the electron temperature evolution at the gap center. Due to the two discharges events in a cycle, as shown in Figure  3, the electron temperature changed twice in each period. Oxygen admixed with helium plasma generates reactive species such as atomic oxygen, oxygen molecules in excited state, and ozone, that have antibacterial properties, which are responsible for increasing bacterial inactivation significantly. Hence, plasma disinfection and surface processing are primarily driven by reactions initiated by reactive oxygen and nitrogen reactive species (RONS) [58].
As illustrated in Figure  . Subsequently, plasma disinfection and surface processing were primarily determined by the initiated reactions of atomic oxygen and excited oxygen molecules [59]. This confirmed the results of Dobrynin et al. [60] who illustrated that oxygen is essential for a speedy as well as efficient sterilization process, regardless of the composition of the used gas. Figure 9 illustrates the significant growing density of ozone. The results showed that ozone accumulated in the gap during every discharge event, reaching a density of 2.8 × 10 14 m −3 .

Power Distribution
With the proposed model, it was possible to determine the average consumed power by the DBD as follows [61]: In Figure 10, the total power distribution in the center of the gap is shown and appears to change two times in one period, due to two discharges phenomena per period [62]. According to Equation (15), the power rose with the voltage, indicating an increase in efficiency.

Power Distribution
With the proposed model, it was possible to determine the average consumed by the DBD as follows [61]:

P = V (t)I (t)dt
In Figure 10, the total power distribution in the center of the gap is shown pears to change two times in one period, due to two discharges phenomena per [62]. According to Eq.15, the power rose with the voltage, indicating an increase ciency.

Power Distribution
With the proposed model, it was possible to determine the average consumed po by the DBD as follows [61]: In Figure 10, the total power distribution in the center of the gap is shown and pears to change two times in one period, due to two discharges phenomena per pe [62]. According to Eq.15, the power rose with the voltage, indicating an increase in ciency.  Figures 11 and 12 represent the variations of current, gas voltage, electron den and temperature depending on external voltage amplitude and frequency for the He (1% O2) plasma gas.   Figure 11. Calculated current density and gas voltage waveforms (a) and spatial electron density and temperature distribution at maximum discharge current (b) for different external voltages.  Figure 11. Calculated current density and gas voltage waveforms (a) and spatial electron density and temperature distribution at maximum discharge current (b) for different external voltages. Particularly, Figures 11a and 12a show a proportional relationship between the voltage gas amplitude on the one side and the current density on the other for different amplitude and frequencies of the external voltage. It was observed that the shape of the gas voltage profiles remained the same, whereas the frequency and amplitude of the external voltage had a significant impact on the current density profiles [63]. Figures 11b and 12b show that both electron temperature and density increased with the voltage amplitude and frequency. Indeed, this rise in electron density at a higher applied voltage led to an increase in transported charges per voltage cycle and then to an enhancement in discharge efficiency [64].

Influence of External Voltage and Frequency Modulation
Namely, when rising the external voltage amplitude from 15 kV to 30 kV, the electron temperature changed abruptly. Indeed, an important distortion of the electric field occurred above 15 kV due to the higher space charges emitted by the cathode. A significant rise in electron temperature results from this high gradient in the electric field distribution in the discharge gap [65]. After this abrupt increase, the electron temperature became less sensitive to changes afterward. As shown in Figure 12b, the electron temperature increased slightly with the external voltage frequency. Particularly, Figures 11a and 12a show a proportional relationship between the voltage gas amplitude on the one side and the current density on the other for different amplitude and frequencies of the external voltage. It was observed that the shape of the gas voltage profiles remained the same, whereas the frequency and amplitude of the external voltage had a significant impact on the current density profiles [63]. Figures 11b and 12b show that both electron temperature and density increased with the voltage amplitude and frequency. Indeed, this rise in electron density at a higher applied voltage led to an increase in transported charges per voltage cycle and then to an enhancement in discharge efficiency [64].
Namely, when rising the external voltage amplitude from 15 kV to 30 kV, the electron temperature changed abruptly. Indeed, an important distortion of the electric field occurred above 15 kV due to the higher space charges emitted by the cathode. A significant rise in electron temperature results from this high gradient in the electric field distribution in the discharge gap [65]. After this abrupt increase, the electron temperature became less sensitive to changes afterward. As shown in Figure 12b, the electron temperature increased slightly with the external voltage frequency.

Effect of Secondary Electron Emission Coefficients and Dielectric Constant of the Barrier Material
The parameters of barrier material, such as the dielectric constant ε r and the secondary electron emission coefficient γ i , can significantly alter the discharge characteristics. Their influence on the gas voltage and current properties is shown in Figures 13 and 14 using He-O 2 (1% O 2 ) plasma gas. As illustrated in Figure 13b, the γi coefficient of the barrier material influenced the current waveforms in the discharge structure. Several peaks in the current waveform can be seen because of the rising γ i coefficient from 0.01 to 0.05. It was found that the number of micro-discharges increased, which reduced their duration in response to a higher electric field [66].
The tendency shown in Figure 14 is the same as that observed when the external voltage amplitude was changed (see Figure 11a). Due to higher dielectric constants in the dielectric barriers, the voltage drop was smaller. This resulted in an enhanced plasma density at the same external voltage amplitude [67].
Consequently, plasma discharges can be operated at a low applied voltage and a high plasma density using higher values of γ i and ε r dielectric barrier materials. These results represent good guidelines to choose the suitable barrier material for each application.
using He-O2 (1% O2) plasma gas. As illustrated in Figure 13b, the γi coefficient of the barrier material influenced the current waveforms in the discharge structure. Several peaks in the current waveform can be seen because of the rising γi coefficient from 0.01 to 0.05. It was found that the number of micro-discharges increased, which reduced their duration in response to a higher electric field [66].  The tendency shown in Figure 14 is the same as that observed when the external voltage amplitude was changed (see. Figure 11a). Due to higher dielectric constants in the dielectric barriers, the voltage drop was smaller. This resulted in an enhanced plasma density at the same external voltage amplitude [67]. barrier material influenced the current waveforms in the discharge structure. Several peaks in the current waveform can be seen because of the rising γi coefficient from 0.01 to 0.05. It was found that the number of micro-discharges increased, which reduced their duration in response to a higher electric field [66].  The tendency shown in Figure 14 is the same as that observed when the external voltage amplitude was changed (see. Figure 11a). Due to higher dielectric constants in the dielectric barriers, the voltage drop was smaller. This resulted in an enhanced plasma density at the same external voltage amplitude [67].  Figure 15 shows a slight decrease in the maximum current density and a widening current pulse as oxygen was added. On the other hand, by adding oxygen, electrons and metastable molecules were quenched, resulting in a decreased density for both species. Therefore, the inactivation efficiency dropped with the increase of oxygen addition, because the number of reactive species attending the polymer surface was reduced.

Influence of the Discharge Gap
In addition to the process gas, the operating distance also has a significant effect in the inactivation efficacy. In Figure 16, we positioned the polymeric samples under He-O 2 (1% O 2 ) plasma at different distances. current pulse as oxygen was added. On the other hand, by adding oxygen, electrons metastable molecules were quenched, resulting in a decreased density for both spe Therefore, the inactivation efficiency dropped with the increase of oxygen addition, cause the number of reactive species attending the polymer surface was reduced.

Influence of the Discharge Gap
In addition to the process gas, the operating distance also has a significant effec the inactivation efficacy. In Figure 16, we positioned the polymeric samples under He (1% O2) plasma at different distances.

Influence of the Discharge Gap
In addition to the process gas, the operating distance also has a significant effect in the inactivation efficacy. In Figure 16, we positioned the polymeric samples under He-O2 (1% O2) plasma at different distances.   Figure 16a shows the characteristics of the current voltage DBD for several gap widths. A linear rise in the discharge current was illustrated with higher electrode gap distance and applied input voltage. For different applied voltages, the increase in the current was very small with a gap of 0.2 mm, but as the gap increased up to 0.2 mm, the current increase became linear. For a 0.3 mm electrode gap, the discharge was found to be more uniform, and a higher number of micro-discharges was observed [68].
Therefore, by increasing the distance, the inactivation efficiency dropped. Indeed, the longer path that the reactive species had to cover to attain the polymer surface and the small lifetimes for the oxygen atoms (in the order of milliseconds [69]) resulted in fewer reactive species attending the surface and possibly inactivating microbial growth. In addition, the area of the polymer strips covered by the plasma significantly decreased.
A linear relationship was found between electrode gap and breakdown voltage at atmospheric pressure, as illustrated in Figure 16b.
The breakdown voltage increased when the gas pressure increased, and the gap distance remained constant, according to Paschen's law [70]. Meanwhile, as displayed in Figure 17, the discharge current gradually decreased with the rising pressure. This could be attributed to the lower generation rate of effective electrons during discharge, which indicated that surface sterilization was reduced under high pressure.
A linear relationship was found between electrode gap and breakdown voltag atmospheric pressure, as illustrated in Figure 16b.
The breakdown voltage increased when the gas pressure increased, and the gap tance remained constant, according to Paschen's law [70]. Meanwhile, as displayed in ure 17, the discharge current gradually decreased with the rising pressure. This could attributed to the lower generation rate of effective electrons during discharge, which dicated that surface sterilization was reduced under high pressure.

Conclusions
Throughout this research, a suitable non-thermal DBD discharge plasma at atm pheric pressure was developed for the bio-decontamination of polymer surfaces con ered as heat-sensitive materials. This work was focused on the role of reactive spe produced by helium and helium-oxygen plasma DBD in the inactivation of Baci atrophaeus spores. A 1D simulation model was developed using the COMSOL Multiph ics® 5.4 package to examine the DBD characteristics and active species' densities. The havior of glow discharges including a single peak current in each half cycle was well flected by the simulation results of the discharge current variation. A time-depend analysis of electron temperature and density was carried out. The charged plasma spe present in the discharge gap, significantly change the electric field and potential.
The species distribution between the plasma electrodes was obtained by numeric solving the transport of reactive species. Based on the substantial densities of (ROS) a RNS, it was revealed that they were liable for the surface treatment and plasma disin tion process. Bacterial death was mainly caused by membrane damage and DNA deg dation induced by reactive oxygen species (ROS).

Conclusions
Throughout this research, a suitable non-thermal DBD discharge plasma at atmospheric pressure was developed for the bio-decontamination of polymer surfaces considered as heat-sensitive materials. This work was focused on the role of reactive species produced by helium and helium-oxygen plasma DBD in the inactivation of Bacillus atrophaeus spores. A 1D simulation model was developed using the COMSOL Multiphysics ® 5.4 package to examine the DBD characteristics and active species' densities. The behavior of glow discharges including a single peak current in each half cycle was well reflected by the simulation results of the discharge current variation. A time-dependent analysis of electron temperature and density was carried out. The charged plasma species present in the discharge gap, significantly change the electric field and potential.
The species distribution between the plasma electrodes was obtained by numerically solving the transport of reactive species. Based on the substantial densities of (ROS) and RNS, it was revealed that they were liable for the surface treatment and plasma disinfection process. Bacterial death was mainly caused by membrane damage and DNA degradation induced by reactive oxygen species (ROS).
A glow discharge can be stable, with higher microbial purification efficiency, depending on the operational parameters, including external voltage amplitude and frequency, dielectric barrier thickness, and discharge gap width.
A higher applied voltage led to an increase in transported charges per voltage cycle and then to an enhancement in discharge efficiency. In addition, the electron temperature changed abruptly with the external voltage. On the other hand, it was possible to operate plasma discharges at a low applied voltage and a high plasma density using dielectric barrier materials with higher values of γ i and ε r .
A linear relationship was found between breakdown voltage and electrode gap at atmospheric pressure. With increasing gas pressure, the breakdown voltage rises, and the current discharges declines at a constant gap width. Thus, a small gap width and the admixture of oxygen are needed for sufficient bio-decontamination. Plasma-based pollutant degradation devices could therefore benefit from these results.
Author Contributions: Conceptualization, methodology, software, validation, formal analysis, investigation, resources, data curation, writing-original draft preparation, writing-review and editing, visualization, project administration, S.E. and N.A.M.A. All authors have read and agreed to the published version of the manuscript.