Temperature Inhibition of Plasma-Driven Methane Conversion in DBD Systems

Low-temperature non-thermal plasmas produce highly reactive chemical environments made up of electrons, ions, radicals, and vibrationally excited molecules. These reactive species, when combined with catalysts, can help drive thermodynamically unfavorable chemical reactions at low temperatures and atmospheric pressure. The conversion of methane (CH4) to produce other value-added chemicals is a good model system because of its applicability to a wide range of industries. To effectively create these plasma catalytic systems, a fundamental understanding of the plasma-phase chemistry alone is imperative. While there have been many studies on methane plasmas and how certain operating conditions (i.e., gas composition and power) affect the plasma, there is limited understanding on how changing bulk reaction temperature affects the plasma properties and ensuing plasma chemistry. In this work, we use a dielectric barrier discharge to investigate the effects of temperature on the reaction chemistry and the plasma’s electrical properties in various methane-gas mixtures. Results show that increasing temperature leads to a reduction in methane conversion as well as changes to both the gas and dielectric material pre-breakdown, which manifests itself in temperature-dependent electrical properties of the plasma. Experiments at various temperatures and power show a positive correlation between key electrical plasma properties (average charge and lifetime per filament) and the measured methane conversion as a function of temperature.


Introduction
In the oil and gas industry, flaring of light hydrocarbons for the safe extraction of oil produces a global loss of natural gas [1,2].However, these hydrocarbons are a valuable and useful resource, and the main component, methane (CH 4 ), is important for chemical and fuel production [3].There is particular interest in reacting methane with nitrogen (N 2 ) [4], which is readily available in the atmosphere, though this requires very specific reaction conditions.While methane reforming can be achieved using thermal catalysis, plasma-assisted catalysis is an attractive alternative because the plasma, and specifically a low-temperature non-thermal plasma (LTP), helps activate ostensibly strong chemical bonds to allow the reaction to proceed under less harsh conditions [5].LTPs produce an abundance of reactive species including high energy electrons, ions, and excited metastables and radicals, and can drive a wide variety of chemistry even in the absence of a catalyst.In order to disentangle the role of the plasma from the role of the catalyst in the design and operation of a plasma catalysis system, it is necessary to understand the plasma behavior alone.
The effects of the plasma alone have been previously studied by observing how specific reactants are converted by the plasma and correlating this to plasma parameters.In plasmadriven reactions, various parameters have been studied to understand their effects on a reaction and to relate specific changes in the plasma to enhance the reaction [6,7].Specifically in plasma-driven methane reactions, conversion of methane has been used as an indicator of how much a key reactant is used to produce more valuable products [8][9][10][11], and several studies have looked at how changing plasma operating parameters such as gas composition [11][12][13], power [10,14], and bulk temperature [8,15,16] affect conversion.
While the majority of the work has delved into the effects of gas composition and power on plasma performance, there is still limited understanding of how the bulk temperature affects plasma reactions.The LTP community has observed changes in plasma behavior in methane plasma at higher temperatures when reacted with carbon dioxide (CO 2 ) [17,18], as indicated by the change in shape of the Lissajous curve, and this has been indicative of a change in the plasma mode.Meanwhile, the plasma-assisted combustion (PAC) community has observed that temperatures can affect methane reaction chain mechanisms [19], where changes in the temperature drastically affects the density of key plasma species and the timescales at which the species occur in the plasma.
In this work, we investigate the effects of bulk temperature on the conversion of methane in a dielectric barrier discharge (DBD).We observe a reduction in the conversion of methane with increasing temperature for different gas mixtures, consistent with our previous observations [9].Furthermore, we observe a strong correlation between the electrical properties of the DBD and temperature, which may influence the conversion behavior.The inhibition of methane conversion is possibly due to the effects of temperature on both the gas pre-breakdown and the permittivity of the dielectric, causing an unfavorable environment for methane reactions.There is also a possibility that the increasing temperature promotes a recombination of species back into methane, which presents as reduced conversion.

Experimental Apparatus
In this study, a coaxial cylindrical DBD tube reactor was used to generate the plasma, similar to that used in our prior work [9,20], as illustrated in Fig. 1.The tube was made of quartz with a 7 mm outer diameter and 5 mm inner diameter.The high voltage electrode was an inner tungsten rod with a 1.59 mm diameter and the grounded electrode was a stainless-steel mesh (McMaster 200 × 1400 mesh size) affixed to the exterior of the quartz tube and with a 60 mm length.The plasma was generated using an alternating current (AC) high-voltage power supply (PVM/DDR Plasma Drive) with applied voltages ranging from 6 to 8 kV and a sinusoidal waveform with a frequency of about 20 kHz.Mass flow controllers (Omega and Aalborg) were used to regulate the flow of gases into the reactor tube.All experiments in this study had a total flow rate of 50 mL min −1 at atmospheric pressure.Various mixtures of CH 4 (Airgas, 99.999%), N 2 (Airgas, 99.999%), and argon (Ar, Airgas, 99.999%) at a one-to-one (1:1) CH 4 to gas ratio were tested, as well as pure CH 4 .
To achieve precise control of the reaction temperature from 400 to 700 °C, the reactor was placed in a split tube furnace (Thermcraft XST-2-0-12-1V1-F04) that allowed for the bulk gas to be heated to desired temperatures.A thermocouple (Omega HH12B) was placed 30 mm downstream of the DBD reaction zone to record the bulk temperature of the reaction.The thermocouple was placed at a distance that did not interfere with the discharge but was still close enough to record the reaction bulk temperature, which is a combined temperature of the gas and the plasma.Separate test measurements were recorded with the plasma off and on at varying conditions, and it was determined that the plasma itself did not produce significant heating above that generated by the furnace.for the Lissajous curves and 500 MS s −1 for the current-time traces in order to resolve the highly transient and filamentary nature of the plasma.The current-time traces are reported at the sampling mode, while the Lissajous curves are averaged over four cycles to reduce the noise.Plasma power was calculated by multiplying the area inside the Lissajous curve by the frequency [21].

Methane Conversion Characterization
Measurements for methane conversion were performed in an identical DBD reactor, where product gases were collected and analyzed.The effluent gas stream was analyzed by a gas chromatograph (GC, SRI 8610C) equipped with three different detectors: flame ionization detector (FID), thermal conductivity detector (TCD), and photoionization detector (PID).Calibration curves were made to quantify the amount of methane reacted, and measurements were recorded immediately after the initial ignition of the plasma once the desired plasma power was obtained.Initial CH 4 conversion (X CH4 ), which was obtained five minutes after plasma generation, was calculated using

Experimental Procedure, Repeatability, and Uncertainty Estimation
Experimental results were obtained by first flowing a specified gas mixture through the reactor and turning the furnace to a specific temperature.Once the desired temperature was reached, the plasma was initiated, and the plasma power and temperature were adjusted accordingly, which took roughly 5 min.At this time, the first trace was taken with the GC, which we report as the initial conversion as noted above.Similarly, electrical properties were recorded after approximately 5 min of adjusting the plasma power where saving the data from the oscilloscope took roughly two minutes for both the current-time and the charge-voltage traces.Once this was complete, the plasma and gas were turned off, and the reactor was calcined with air for six hours at 700 °C after every run to remove carbon deposits.
To ensure repeatability, conversion experiments at each condition were repeated three times over the course of several days.For current-time traces, two half-cycles were recorded for each experimental condition and the experiments were repeated three times over the course of several days, producing six half-cycle data sets for each condition.Charge-voltage trace experiments were repeated 3 times over different days.All data shown is the average with error bars showing a 95% confidence interval using standard Student's t analysis [22,23].

Temperature Inhibition on Methane Conversion
In a previous study from our groups, Kim et al. [9] explored the effects of temperature on C-H bond activation during plasma-catalytic dry methane reforming in CH 4 /CO 2 mixtures under various conditions using a similar reactor.When operating the DBD in the absence of a catalytic material, a reduction in methane conversion with increasing temperature was observed.In this study, we expand on those initial findings and interrogate the influence of the bulk temperature on methane conversion for pure methane as well as CH 4 /N 2 and CH 4 / Ar mixtures.To limit the effect of other plasma parameters, the DBD plasma was operated at 10 W and the total flow rate was always 50 mL min −1 , where gas mixtures were at a 1:1 ratio of CH 4 to gas.
Figure 2 shows the measured methane conversion for temperatures from 400 to 700 °C, including the data from Kim et al. [9].As the temperature is increased, there is an inhibition of methane conversion.Interestingly, the inhibition occurs regardless of whether the DBD is in pure CH 4 or a mixture with either a molecular (N 2 or CO 2 ) or atomic (Ar) gas.And although the magnitude of conversion (and thus subsequent inhibition) depends on the gas mixture, with greater conversion at lower temperatures for N 2 and Ar mixtures, above 600 °C virtually no conversion is measurable, regardless of the gas mixture.This inhibition phenomena appears to be specific to methane and so it is imperative to understand whether these changes are a result of temperature effects on the plasma, temperature effects on the reaction chemistry, or both.

Impedance of the Circuit Changes with Temperature
In order to understand the impact of temperature on the electrical characteristics of the DBD, experiments were conducted to measure the changes in capacitance of the system prior to and after plasma initiation over a range of temperatures from 400 to 700 °C with 100 °C increments, all at constant plasma power of 10 W and a total flow rate of 50 mL min −1 .Initial experiments were conducted on CH 4 /N 2 plasmas to understand how changing temperatures affect DBD plasma electrical properties.To determine whether Fig. 2 Initial conversion of CH 4 as a function of the bulk temperature for different gas mixtures of CH 4 /N 2 , CH 4 /Ar, CH 4 /CO 2 and pure CH 4 for a 10 W DBD with a total flow rate of 50 mL min −1 and a one-to-one gas composition ratio.The absolute confidence interval for the CH 4 /N 2 initial methane conversion is no greater than 35% and is plotted on a log scale to better show the trends in much lower conversion at higher temperatures the observed trends were only specific to CH 4 /N 2 plasmas, similar experiments were conducted with the exact same conditions for CH 4 /Ar plasmas and all reported trends in this work were similar for both gas mixtures, which are shown in Section 5 of the Supplementary Information (SI).
Figure 3a shows charge-voltage Lissajous curves at 400 °C, 500 °C, 600 °C, and 700 °C.We observe a change in the shape with increasing temperature from a parallelogram shape typical of an ideal DBD to a more almond shape at 700 °C, which other studies have also observed at higher temperatures [21,24].In other studies, these changes have been attributed to a potential change in the resistance of the gas gap and dielectric due to changes in the permittivity and capacitance of the dielectric material itself [25,26].Here we interrogate this behavior further in order to understand if there is a change in the intrinsic nature of the plasma that might affect methane conversion.
Information about the plasma, such as the discharge cell capacitance C cell and the effective capacitance ζ diel , can be obtained from the slopes of the plasma-off and plasma-on regions of Lissajous curves, respectively [27,28]. Figure 3b and c show typical simplified circuits of the plasma-off and plasma-on phase that represent how the capacitances of the gas C gas and the dielectric C diel relate to the extracted properties from the Lissajous curve.Conventionally, dielectric materials such as quartz and gas are treated as purely capacitive with very low electrical conductivity at lower temperatures [29,30] and thus can be analyzed as a series capacitive circuit to obtain C cell shown in Fig. 3b, with some studies adding a stray/parasitic capacitance value for additional capacitances from wires [31,32].Once DBD ignition occurs, the plasma acts as a variable resistor in parallel to the capacitance of the gas, changing the purely capacitive circuit to an impedance circuit, as illustrated in Fig. 3c.
In Fig. 4a and b, we plot the extracted values of C cell and the effective capacitance ζ diel as a function of temperature.We observe an increase in temperature leads to an increase in both the discharge cell capacitance and the effective capacitance.Over the temperature range of 400 to 700 °C, the discharge cell capacitance increased by a factor of about 2.7 from (5.41 ± 1.03) pF to (14.4 ± 1.22) pF, while the effective capacitance increased by a One possible explanation is that C cell and ζ diel are affected by the permittivity of the quartz tube, the dielectric barrier, which changes with temperature.It is well known that the dielectric constant for quartz is a strong function of temperature, increasing by a factor of about five from ~ 40 to ~ 200 over the temperature range from 400 to 700 °C [29,30].Analytically, C cell can be estimated for a dielectric tube reactor via, where and Here ε o is the permittivity of free space, ε g and ε d are the dielectric constants of the gas and the quartz tube respectively, L is the length of the outer grounded electrode, and r o , r 1 , and r 2 are the radius of the high voltage electrode and the inner and the outer radius of the quartz tube, respectively.If we assume the gas to be ideal gas with constant permittivity (ε g = 1), we can analyze the impact of a temperature-varying ε d on C cell below the plasma initiation threshold, where the resistance of the plasma does not affect the circuit (Fig. 3b).Our calculated estimates show that over the range of 400 to 700 °C, C cell would increase by only 0.02 pF from 2.87 to 2.89 pF if the permittivity of the dielectric increases fivefold from ε d = 40 to ε d = 200.This is because C gas ≈ 2.9 pF and thus dominates the total Since a change in the permittivity of the quartz dielectric does not lead to the experimental increase in C cell observed in Fig. 4b at these higher temperatures, it is necessary to change the perspective of the simplified electrical circuits presented in Fig. 3b and  c and consider additional resistances that could potentially present themselves as an impedance in the circuits.Figure 5a and b show impedance circuits that represent potential capacitive/resistive systems for the plasma-off and plasma-on phase respectively.In this new case, Z off is the cumulative impedance of the gas and the dielectric while Z on is the cumulative impedance of the gas, dielectric and the plasma.As stated earlier, these impedances are typically considered to be purely capacitive until the presence of a plasma adds a resistance.From this perspective, we can consider Z off = (iωC cell ) −1 and Z on = (iωζ diel ) −1 .
To isolate the potential impact of temperature on Z off alone, we conducted a series of experiments where the voltage was increased to just below the breakdown voltage, and charge-voltage plots were recorded.As shown in Fig. 6a, at 400 °C the Lissajous curve is a straight line.However, as the temperature increases, the angle of the Lissajous curve increases relative to the voltage axis (rotating counterclockwise), indicating an increased overall capacitance.The Lissajous curve also begins to transform from a straight line and take an almond-like shape.This change in shape cannot be explained by a change in ε d alone, which was confirmed by simulating the circuit using the commercially available circuit analysis software LTspice® as shown in Supplementary Figure S1.(For more details on the LTspice® analyses, see Section 1 in the SI).It is worth mentioning that these LTspice® simulations are all drawn from constant values of capacitance and/or resistance.Therefore, they cannot resemble the parallelogram-shape produced by the switching from plasma-off to plasma-on conditions.Nevertheless, they can provide further insight into the possible changes to C cell without considering the effects of the plasma discharge itself.Fig. 5 Impedance electrical schematics of a DBD system showing a Z off , the cumulative impedance of the gas and the dielectric and b Z on , the cumulative impedance of the gas, dielectric and the plasma.It is typically assumed that Z off is purely capacitive until the resistance of the plasma adds to the capacitance of the system in Z on It is well-known that the transformation of a charge-voltage plot from purely linear to an almond shape, known as a leaky capacitor, as well as the transformation of a DBD Lissajous plot from a parallelogram to an almond shape, is due to additional resistance in the circuit [17,21,33].To assess how additional resistance would affect Z off in our system, we conducted a number of LTspice® simulations for three different potential circuits, adding different resistive elements to Z off , thereby changing the overall impedance, illustrated in Supplementary Figure S2.The first of these assumes the gas itself has an additional resistance, modeled as a parallel resistor to C gas , thereby changing the impedance of the gas Z gas (Figure S2a). Figure 6b shows that if the resistance of this parallel resistor is decreased from 100 to 10 MΩ, the familiar almond shape begins to appear in the simulated charge-voltage curve.As shown in Supplementary Figure S3a, the charge-voltage curves also rotates counterclockwise as the resistance decreases, consistent with the temperature data in Fig. 6a.The second simulated circuit assumes that the quartz tube becomes a leaky dielectric [30,34], such that there is a parallel resistor to C diel , thereby changing the impedance of the dielectric Z diel .The simulated charge-voltage curves shown in Fig. 6c show no discernible transition to an almond shape, which can be attributed to the dominance of the large capacitance of the gas itself.The last simulated circuit considers a secondary discharge outside the tube (between the external grounded electrode and the outer surface of the quartz tube), which is modeled as a resistor in series with C gas and C diel , thereby changing the total impedance Z off directly.Due to the additional resistance presenting itself in series to the capacitors, the resistance is increased rather than decreased from an initial resistance of 0 Ω (still purely capacitive system) to a resistance expected of an additional discharge, 1 MΩ.The simulated charge-voltage curves shown in Fig. 6d also show a transition to an almond shape, but as shown in Supplementary Figure S3(b), the curves rotate clockwise as the resistance increases, inconsistent with the experimental temperature data in Fig. 6a.It is surprising that the impedance of the gas, rather than the impedance of the quartz tube, appears to fully account for the change to an almond shape in the experimental Lissajous plots in Figs.3a and 6a and the measured increase in C cell , and likely ζ diel , in Fig. 4.Many studies have shown an increase in ζ diel with an increase in voltage but have not fully explored changes in C cell [21,35].When the plasma is off (or for cases below the plasma ignition voltage), one would assume that there is no conductive component to the gas.
One possible physical explanation is that there is a dark discharge or Townsend discharge forming prior to DBD formation [36,37].In order to achieve the almond shape and produce charge values comparable to those obtained in Fig. 6a, a simulated resistance of 1 MΩ is required, which is equivalently a gas conductivity of about 85 μS m −1 .The electric field prior to breakdown can be described by Laplace's equation as where V a is the applied voltage [38].For our configuration, this takes a value of roughly 2 × 10 5 V m −1 for an applied voltage of 1500 V. Assuming an electron collision frequency of 3.6 × 10 11 s −1 in a one-to-one gas CH 4 /N 2 gas composition obtained from Bolsig+ [39], this corresponds to a 10 8 cm −3 pre-breakdown electron density (see Section 2 of SI).This appreciable electron density is most likely attributable to a modest decrease in the local gas density as the temperature increases (roughly a 30% decrease for a 300 K increase), resulting in a higher reduced electric field (E∕N) and thus greater pre-breakdown ioniza- tion.Because the Townsend first ionization coefficient α goes exponentially with −(E∕N) −1 [38], a 30% decrease in the gas density leads to a 20% increase in α and thus could produce sufficient ionization.
While the observed temperature-dependent Lissajous behavior appears attributable primarily to stratification of the gas, we cannot entirely rule out that the temperature-dependent permittivity of the quartz does not play a role.The permittivity of the dielectric has a direct influence on the plasma due to its relationship with the electric field.The electric field at the interface of the gas and the dielectric, assuming a perfectly coaxial configuration, can be analytically estimated using where V a is the applied voltage, and r 1 is the radius at the interface (see Section 3 of SI).Plotting the electric field as a function of the dielectric constant of quartz shows the electric field decreases with increasing ε d (Supplementary Figure S5).Thus, as temperature increases, we would expect a 75% decrease in the electric field (and E/N) at the dielectric/ (5) gas interface.This is inconsistent with an enhancement in pre-ionization prior to plasma ignition, and thus may play a minor role in the observed temperature-dependent data.While this analysis is not definitive, it strongly supports the hypothesis that the experimentally observed increases in both C cell and ζ diel with temperature are likely due to local decreased density of the gas, with only a minor, and possibly negligible, contribution to changes in the permittivity of the quartz dielectric.Critically, what this shows is that the plasma is fundamentally changing as the temperature increases due to the gas, which could impact the observed methane conversion.

Filamentary Behavior Changes with Temperature
We can similarly analyze the impact of temperature on the filamentary behavior of the DBD by analyzing the current as a function of time.Figure 7a shows a representative portion of a current-time trace for a CH 4 /N 2 plasma at 500 °C, illustrating the filamentary nature of an atmospheric-pressure DBD plasma [21,24,25].(Representative complete current-time traces are shown in Supplementary Figure S6.)In this work, lower temperatures produced visibly more filamentary plasmas with stronger peak currents Fig. 7 a A representative portion of the current-time trace illustrating the cumulative area under the filamentary signals.Note that the capacitive displacement current has been subtracted from the current data to reveal only the filamentary discharge current.b, c and d show the effects of temperature on Q tot , Q avg , and f respectively showing an inverse relationship with increasing temperature for CH 4 /N 2 plasmas at 10 W, a total flow rate of 50 mL min −1 , and a one-to-one gas composition ratio while higher temperatures led to less filamentary plasmas with weaker peak currents (for more details, see Section 4 of the SI).This is similar to trends observed by Zhang and Cha [17,18] in their temperature studies for methane reforming.
Two parameters that can be analyzed from the current-time trace are the total charge per half cycle, Q tot , and the average charge per filament in a half cycle, Q avg .These parameters were chosen as they provide insight into the amount of charged particles at a given time in the plasma, and these charged particles (specifically free electrons) are essential for driving reactions in the plasma.The total charge per half cycle was obtained from the area under the curve of the current trace for one half cycle.The total area was calculated by summing the charge of each individual filament; it can be expressed mathematically as where I i is the instantaneous current of a given filament, t f,i is the duration of a given filament, and N f is the number of filaments in the half cycle.A sampling rate of 500 MS s −1 was used after a test of various sampling rates because it was able to properly resolve the number of filaments in the half cycle (Supplementary Figure S7).The average charge per filament was then calculated by dividing the total charge by the number of filaments in the half cycle, We also extracted the average lifetime of a filament τ f from the current-time trace from the full width at half maximum (FWHM) of each filament using Figure 7b and c show Q tot and Q avg , respectively as a function of temperature for CH 4 /N 2 plasmas for both the positive and negative half cycles.While Q tot and Q avg are generally lower in the negative half cycle than in the positive half cycle due to the asymmetric nature of a single dielectric barrier, regardless of the gas composition with CH 4 , they both decrease with increasing temperature.Q tot decreased from (41.4 ± 4.14)  nC to (1.27 ± 0.11) nC, while Q avg decreased from (235 ± 13.8) pC to (16.1 ± 1.26) pC over the range from 400 to 700 °C.Similarly, Fig. 7d shows an increase in temperature leads to a decrease in the average lifetime per filament for both the positive and negative half cycles, though the value does not change drastically from (7.46 ± 0.12) ns to (5.95 ± 0.12) ns.However, it does support that the plasma becomes less filamen- tary with increasing temperature in our DBD system.This change in the nature of the plasma from a more filamentary mode to a glow-like, diffuse regime with fewer filaments and much weaker peaks could be attributed to a decrease in gas density [40].We note that in the PAC community, plasma instability is the transition from a diffuse, uniform plasma to a more filamentary plasma; and this is attributed to an increase in temperature and a decrease in the gas density.This subsequently leads to an increase in the reduced electric field and electron density [41,42].While we assume the increase ( 7) 1 3 in temperature leads to a reduction of gas density in our system, we observe an opposite effect in that our typically filamentary plasma transitions to a more diffuse mode.

Comparison of Energy Input and Its Effect on CH 4 Conversion
One perspective on the temperature dependence of CH 4 conversion is that there is a correlation between conversion and energy added to the system.(Or similarly between plasma properties and energy added to the system.)As a benchmark, we also varied the DBD plasma power but maintained the reactor temperature at a value of 500 °C.Figure 8 shows the measured CH 4 conversion at powers of 7, 10, and 12 W as well as the extracted average charge per filament Q avg .We observe that an increase in plasma power leads to an increase in CH 4 conversion [14], but we also observe that an increase in power leads to an increase in the average charge per filament.An increase in power from 7 to 12 W leads to an increase in CH 4 conversion from about 6 to 8% (a factor of 1.3) as well as an increase in average charge per filament from (84.7 ± 7.52) to (126.2 ± 8.75) pC (~ 1.5× increase).That is, both conversion/power and power/charge per filament are positively correlated such that CH 4 conversion and charge per filament are positively correlated.This is consistent with the findings when temperature was varied, where CH 4 conversion and charge per filament are positively correlated.However, in the temperature studies, this occurred when the temperature was decreased whereas here, this occurred when the power is increased.While increasing temperature and power are both additions of energy, they have different effects on reaction performance, but produce a similar trend when comparing conversion with plasma properties.

Direct Relationships Arise Between CH 4 Conversion and Plasma Properties
Relationships between CH 4 conversion and electrical plasma properties arise specifically when we look at conversion as a function of the average charge per filament and the average filament lifetime.While the filamentary charge does not directly relate to conversion, this indicator of the temporal amount of charged species, and specifically electrons that plotted against increasing power for a CH 4 /N 2 plasma with a total flow rate of 50 mL min −1 and a one-to-one gas composition ratio.Environment temperature was kept constant at 500 °C.An increase in Q avg with increasing power is observed drive chemical reactions, shows a good correlation with conversion.Figure 9 plots all our experimental data points, whether with changing temperature or power, and we observe a positive relationship between CH 4 conversion and the average charge per filament (Fig. 9a).
Similarly, an increase in the average filament lifetime led to a higher conversion of CH 4 (Fig. 9b).Regardless of the changing operating conditions, there is an apparent correlation between changes in the plasma properties and the measured conversion of CH 4 .One thing to note is that changes in temperature cause a much more significant change in conversion and plasma properties than power.An increase in power from 7 to 12 W (71%) increases conversion by about 2%, while a 300 K increase in temperature (44%) decreases conversion by 14%.While these plasma properties cannot be controlled directly, this gives insight into how changing operating conditions, specifically temperature, play a key role in the effects on CH 4 conversion.That is, for this DBD tube reactor, increases in temperature led to a decrease in the resistance of the gas gap due to ionization prior to plasma ignition thus causing changes in the plasma that inhibit CH 4 conversion.

Temperature Effects on Thermal Reaction Kinetics
While our measured data suggest a relationship between plasma properties and CH 4 conversion that is due to temperature-related density effects, we cannot rule out other temperature-related chemistry effects on CH 4 conversion.Molecules in the plasma can undergo various reactions: electron-temperature dependent reactions through electron impact collisions, including excitation and dissociation, and bulk temperature-dependent reactions such as thermal dissociation and recombination of species.Previous modeling studies of CH 4 /N 2 plasmas have identified the predominant reactions that lead to methane dissociation and recombination.These reactions are highly dependent on the operating conditions of the plasma, specifically temperature, and if they produce CH 4 would lead to a decrease in CH 4 conversion.One of these modeling studies was of a DBD at atmospheric pressure and room temperature (approximately 300 K) [11] and attributed the main formation of methane to a (10) 9 The initial conversion of CH 4 as a function of a average charge per filament and b average filament lifetime for a CH 4 /N 2 plasma with a total flow rate of 50 mL/min and a one-to-one gas composition ratio reaction, where M is a third body involved in the reaction and most likely CH 4 in this case.Another study also modeled CH 4 /N 2 plasmas at atmospheric pressure in a gliding arc resulting in much higher temperatures upwards of 1000 K [13].They attributed the predominant formation of methane to a reaction.If we assume the concentration of reactants stay the same, we expect that changes in the reaction rate constants should increase as the temperature is increased.
Figure 10 shows the reaction rate constants for both Eq. 10 (Fig. 10a) and Eq.11 (Fig. 10b), as determined from the rate expressions for Eq. 10 [43], and, for Eq.11 [44].(Note that temperature is in units of Kelvin for both expressions.)Fig. 10a from Eq. 12 shows a non-monotonic trend in the reaction rate constant as a function of temperature, decreasing at temperatures greater than 300 °C whereas we would expect it to increase and inhibit conversion.However, Fig. 10b for Eq. 13 shows an exponential increase in the reaction rate constant, indicating that as temperature increases, we would achieve more re-combination of dissociated products, producing additional CH 4 and inhibiting conversion.Notably, the magnitudes of the reaction rate constants for Eq.11 are also much higher than Eq. 10.This supports that the reaction in Eq. 11 may contribute to inhibiting methane conversion due to gas-phase recombination as temperatures increase.Another possible reaction that could occur, besides reactions involving CH 3 species, is CH 2 + H 2 → CH 4 .Thermal kinetic studies from both [11] and [13] indicate that this reac- tion is not a predominant path that leads to methane formation, possibly due to a low CH 2 concentration.That being said, the rate constant for this reaction up to temperatures of 400 K [45] are appreciably larger than those of reactions 10 and 11, but there are limited  studies on the kinetics at temperatures closer to our experimental conditions.We cannot conclusively determine the predominant methane formation mechanism in our system without detailed kinetic modeling.However, it is clear that there are temperature effects on the kinetics of the reaction independent of the changes to the plasma operating conditions that could lead to the conversion trends we observe in our experiments.

Conclusions and Final Thoughts
In this study, we reacted methane with a mixture of other gases, focusing particularly on nitrogen, in a DBD plasma reactor in order to understand the role of plasma-phase chemistry in potential plasma-catalysis systems.We observed that increasing temperatures led to a decrease in methane conversion and that this could be potentially attributed to two effects.First, the temperature increase reduces the gas density, allowing the gas to be ionized and decreasing the resistance of the gas gap prior to plasma initiation.This reduction in density transitions the plasma from a filamentary to a more glow-like mode, decreasing the intensity of filaments (total charge, average charge, and lifetime) and thus the dissociation and conversion of methane.Second, a bulk reaction between CH 3 and H 2 consumes intermediates in the plasma, recombining to produce methane such that any methane dissociation that does occur is driven back to methane formation.Together, these plausibly explain the very low conversions measured at high temperatures, and likely do so independently.Still, it is difficult to distinguish between the effects of temperature on the reaction kinetics and the plasma properties, and thus this explanation is not conclusive.With a better understanding of these temperature effects, one particularly interesting use will be reacting methane with nitrogen to produce high value and transportable products [4], especially at relatively modest reaction temperatures where methane conversion is high.Implementing this process of coupling wasted natural gas to abundant nitrogen on-site at flaring locations would then both reduce a source of greenhouse emissions and produce value-added chemicals.

1 Fig. 1
Fig. 1 Schematic of the reactor setup to investigate the effects of temperature on methane conversion in DBD plasma systems

Fig. 3 a
Fig. 3 a Lissajous (charge-voltage) curves showing a change in shape from more parallelogram to almond shape with increasing temperature for CH 4 /N 2 plasmas at 10 W, a total flow rate of 50 mL min −1 , and a one-to-one gas composition ratio.Simplified schematics of the equivalent electric circuits showing b the capacitance of the gas C gas , and the dielectric C diel in series prior to plasma initiation, where the combined capacitance is called C cell , and c an additional resistive component added due to the plasma, R pl , after breakdown, where the combined capacitance is called ζ diel

Fig. 4 a
Fig. 4 a Extracted discharge cell capacitance C cell showing an increase in the capacitance during the plasma-off phase and b extracted effective capacitance ζ diel also showing an increase in the capacitance during the plasma-on phase of the discharge

Fig. 6 a
Fig. 6 a Experimental charge-voltage curves below the plasma initiation threshold (applied voltage of 1.25 kV) at varying temperatures.And simulated charge-voltage curves with varying resistive elements b parallel to the gas capacitance, c parallel to the dielectric capacitance, and d in series with the gas and dielectric capacitance

Fig. 8
Fig.8Initial conversion of CH 4 plotted against increasing power for a CH 4 /N 2 plasma with a total flow rate of 50 mL min −1 and a one-to-one gas composition ratio.Environment temperature was kept constant at 500 °C.An increase in Q avg with increasing power is observed