Dual-comb spectroscopy of ammonia formation in non-thermal plasmas

Plasma-activated chemical transformations promise the efficient synthesis of salient chemical products. However, the reaction pathways that lead to desirable products are often unknown, and key quantum-state-resolved information regarding the involved molecular species is lacking. Here we use quantum cascade laser dual-comb spectroscopy (QCL-DCS) to probe plasma-activated NH3 generation with rotational and vibrational state resolution, quantifying state-specific number densities via broadband spectral analysis. The measurements reveal unique translational, rotational and vibrational temperatures for NH3 products, indicative of a highly reactive, non-thermal environment. Ultimately, we postulate on the energy transfer mechanisms that explain trends in temperatures and number densities observed for NH3 generated in low-pressure nitrogen-hydrogen (N2–H2) plasmas.


Introduction
Through its use in industrial fertilisers 1 , ammonia (NH3) makes an indispensable contribution to global agriculture by helping to feed about 50 % of the world's population 2 .Because of its critical place within our food supply chain, current research into plasma-activated NH3 formation aims to reduce costs, improve distribution and increase efficiency as compared to the energy-intensive and ubiquitous Haber-Bosch process 3 .Ideally, plasma activated NH3 production would be achieved by nitrogen (N2) fixation from air, preferably at lower temperatures and pressures than are currently required.However, despite significant efforts, the energy yields reported for plasma-activated NH3 formation remain more than one order-of-magnitude lower than that of the conventional Haber-Bosch process 4 .To overcome this deficit, it is crucial to improve our understanding of formation processes at the molecular level.Beyond its application to addressing the challenges of a global food supply chain, improved knowledge of plasmaactivated NH3 formation mechanisms could also impact our future energy needs by improving mitigation strategies applied to gas reprocessing in tokamak fusion reactors 5 .
Because plasmas comprise high-energy electrons, ions, radicals and neutral molecules together in a confined environment, there exist myriad pathways that may lead to the breaking and formation of chemical bonds, and therefore a large number of possible chemical transformations.Generally, NH3 formation in plasma reactors is ascribed to the stepwise hydrogenation of adsorbed nitrogen atoms (N), imidogen radicals (NH) and amino radicals (NH2) found at various reactor surfaces 6,7 .If correct, this mechanism should yield NH3 molecules in non-thermal equilibrium, an environment characterized by different temperatures being ascribed to different degrees of freedom of the molecule (translational, rotational and vibrational).Consequently, molecules in non-thermal equilibrium can exhibit enhanced or reduced rate constants for state-specific, vibrationally mediated reactions 8 .Therefore, to better understand the pathways to plasma-activated NH3 formation, we require quantum-state-resolved information on the NH3 molecule in operando.Although we focus on NH3 in this work, quantum-stateresolved information and its impact on reaction pathways is of high importance to other plasma driven chemical syntheses 9 .This information is essential to develop and optimise new catalytic materials, which no longer have to enhance the dissociation of N2, now taken care of by the plasma, but have to be tailored for maximum NH3 production.
To date, several active laser diagnostics have been used to probe NH3 molecules in plasma reactors.They are cavity-enhanced absorption spectroscopy 7,10 , tuneable diode laser absorption spectroscopy 7,11 and quantum-cascade laser absorption spectroscopy [11][12][13] .These techniques rely upon stepwise scanning or sweeping the wavelength of a continuous-wave (CW) laser to measure the molecular absorption.Only a few absorption features are generally accessible to any one CW laser, limiting the scope of their application to only a sub-set of the complex plasma processes that occur between species within a nonthermal environment.To increase the spectral coverage and hence the number of quantum states that can be probed, external cavity diode lasers have been used.External cavity diode lasers, however, require in situ wavelength calibration to achieve the necessary spectral accuracy 14,15 , and are often plagued by mode-hops.The overall measurement time to scan the single wavelength over a large range in fine increments presents another experimental challenge.
More broadly, in the mid-infrared wavelength region, direct frequency-comb Fourier transform spectroscopy has been used to detect multi-species in the effluent of a dielectric barrier discharge 16 and dual-comb spectroscopy has studied time-resolved spectra from a CH4/He electric discharge 17 .In the visible wavelength region, dual-comb spectroscopy has also been used to detect trace amounts of the atomic species Rb and K after ejection from a laser-induced breakdown of a solid target 18 .But no previous demonstrations of comb spectroscopy have revealed a quantum-state-resolved picture of non-thermal plasmas applied to grand societal challenges like N2 fixation to NH3.
Here, we apply quantum cascade laser dual-comb spectroscopy (QCL-DCS) 19 at a wavelength near  = 9.4 μm to study NH3 formation in a low-pressure, nitrogen-hydrogen (N2-H2) plasma.This study highlights several advantages of QCL-DCS as a diagnostic tool for probing complex environments like a non-thermal plasma, including high spectral resolution (4.5×10 −4 cm −1 or 14 MHz) and broad spectral coverage (50 cm −1 ).Previously, QCL-DCS has been applied to jet-cooled molecular expansions 20 and thermally populated gas samples at ambient temperature 21 to demonstrate high-resolution, and to condensedphase biological systems to demonstrate fast (μs) acquisition rates 22 .Here we combine these two inherent advantages to rapidly perform high-resolution molecular spectroscopy of a complex, non-thermal environment inside of a research-grade industrial plasma reactor.

Plasma-activated NH3 generation probed by dual-comb spectroscopy.
We probe plasma-activated NH3 generation via line-of-sight laser absorption spectroscopy in the longwave infrared, near  ̃ = 1060 cm −1 ( ̃= / in units of cm −1 and c is the speed of light).A schematic of the experimental set-up is shown in Fig. 1a.Briefly, the output from the first QCL comb with a repetition rate, frep,1, of 7.417 GHz propagates along two distinct free-space beam paths, creating a probe beam and a reference beam.The probe beam is coupled to a multi-pass cell (path length of  = 3.16 m) attached to the plasma reactor, and the reference beam bypasses the reactor.A second local-oscillator QCL comb with slightly different repetition rate (frep,2 = frep,1 + Δfrep, where frep = 2.1 MHz) is spatially overlapped with the probe and reference beams, respectively, at two different photodetectors, thus creating both probe and reference down-converted DCS signals (interferograms) for spectral analysis and optical power normalization.Additional details are provided in the Methods section.
The result is a transmission spectrum of NH3, sampled at the frequencies of the first QCL comb.To perform high-resolution spectroscopy, both QCL combs are scanned by increasing the laser currents using a "stepsweep" approach 23 , creating a set of 600 interleaved and normalized transmission spectra of NH3 which together yield a composite transmission spectrum with an ultimate resolution of 4.5×10 −4 cm −1 (14 MHz) achievable in seven minutes of total acquisition time.
The spectral region near  ̃ ≈ 1060 cm −1 includes transitions from three different vibrational bands of NH3.Using a labelling scheme which indicates the number of quanta excited in each of the  1  2  3  4 normal vibrational modes of NH3, the transitions are described as (i) the fundamental  2 ←  0 band, corresponding to the 0100 ← 0000 transition, (ii) the 2 2 ←  2 hot band, corresponding to the 0200 ← 0100 transition and (iii) the  2 + 4 ←  4 hot band, corresponding to the 0101 ← 0001 transition.Figure 1b shows a schematic of the vibrational levels probed here, with transition energies 24 listed in wavenumbers.Shown are the energy values of both the symmetric (grey) and antisymmetric (black) states with respect to molecular inversion.In the case of the symmetric states, the  4 and 2 2 levels interchange their positions within the energy level diagram, as do the  2 + 4 and 3 2 levels.Overall, the accessible vibrational states represent the first steps on a molecular vibrational ladder -or a series of energy levels which is useful for the study of overpopulation in non-thermal environments.
Here we generate the plasma in a research-grade, industrial reactor made of stainless steel by direct current (DC) discharge at a total power of 355 W ± 50 W.The discharge was located on a metal mesh of stainless steel in the top of the reactor.A workload made of stainless steel was also used to increase the discharge power and the stability of the plasma, and it was negatively biased relative to the reactor wall.A schematic of the plasma reactor is shown in Fig. 1a.Different mixtures of N2 and H2 gas precursors are delivered to the reactor at a constant mass flow rate of (500 ± 5) standard cubic centimeters per minute (sccm).The pressure inside the reactor is maintained at a constant value of 100 Pa ± 1 Pa using a back pressure controller and vacuum pump.The outer wall of the reactor is cooled to near room temperature at 295 K ± 1 K by a recirculating flow of water at 293.0 K ± 0.1 K, and the temperature of the inner wall ( wall ) is recorded by two temperature probes.Additionally, the temperature within the plasma at a blank stainless-steel working load ( load ) is also recorded using a third temperature probe.Figure 2a shows the broadband transmission spectrum of NH3, measured for a plasma generated with precursor mass flow rates of 200 sccm of H2 and 300 sccm of N2.The strong absorption lines of the NH3  2 ←  0 fundamental band are saturated at mixing ratios of H2/N2 ≈ 1 where the highest NH3 yield is observed.The fitted spectral model, calculated using the HITRAN2020 database 25 and Voigt line shape functions, reveals absorption from the three different vibrational bands of NH3 illustrated in Fig. 1b.We determine an NH3 number density in the non-thermal region (the distance between the inner walls of the reactor), n-th, by fitting a spectroscopic model that accounts for possible non-thermal distributions by floating the translational temperature,  trans , as well as the rotational temperature,  rot , and vibrational temperature,  vib , for the different vibrational bands.More details regarding the spectral model and fit are available in the Methods section.For the spectrum plotted in Fig. 2a, the resulting fit parameters and their estimated combined and relative uncertainties are listed in Table 1.Table 1.Fitted values for temperature () and non-thermal number density (n-th) parameters, derived from fitting the NH3 transmission spectrum plotted in Fig. 2. Combined standard uncertainty and relative uncertainty are reported at the 1σ confidence level.The transitions shown in Fig. 2b-d also serve to highlight an advantage of our broadband approach.As an example, if we assume an average global temperature for the non-thermal region of  trans =  rot =  vib = 450 K, a line-by-line analysis of these respective transitions would yield significantly different NH3 number densities, n-th, when fitted for each respective spectral region.In such a scenario, singletransition fits of n-th would differ between the spectral regions shown in Fig. 2b-d by a factor of six -potentially biasing conclusions on the efficiency of NH3 formation in non-thermal plasmas and impeding a quantitative comparison between different reactors.

NH3 number densities measured for different H2 mass flow fractions.
In Figure 3 we show the number density of NH3 in the non-thermal region (n-th), obtained from our broadband spectral fits and plotted as a function of the H2 mass flow fraction.The H2 mass flow fraction is defined as  H 2 = ̇H 2 /(̇H 2 + ̇N 2 ), where ̇ is the mass flow of each precursor gas.The figure comprises data retrieved from the fitting of 27 unique spectra measured at different values of  H 2 .The spectra were collected in two series, proceeding from either low to high values of  H 2 (left-to-right, blue circles) or high to low values of  H 2 (right-to-left, red triangles).The highest NH3 yield is observed on the H2-deficient side of the data set agrees with measurements performed on similar plasma reactors 12 .However, the maximum NH3 yield has also been observed in other types of reactors to be on the opposite, H2-abundant side 6,7,10,11 .The position of the maximum and the observed asymmetry with respect to  H 2 is influenced by the reactor wall material and process pressure, as well as the plasma electron energy and density 7,26,27 .The reported NH3 number densities span more than two orders of magnitude (see insets in Fig. 3), illustrating the wide dynamic range capabilities of QCL-DCS as a laser-based plasma diagnostic technique.Non-thermal population of NH3 states.
In Figure 4 we show the fitted temperatures that partition population amongst the translational, rotational and vibrational states of NH3 found within the non-thermal region of the plasma reactor.Plotted in Fig. 4a  Plotted in Fig. 4c are the fitted values for NH3 translational temperatures in the non-thermal ( trans ) and thermal ( th , in regions beyond the inner walls of the reactor) regions of the line-of-sight.In the thermal region, we assume a single temperature for all degrees of freedom (i.e.,  th =  rot =  vib ), and the fitted results reveal a temperature for the thermal region that is consistent with the room temperature and the outer plasma-reactor walls,  th ≈ 300 K.The non-thermal region, where NH3 is formed, shows a similar trend in  trans vs.   2 to that observed for the NH3 number density, n-th, in Fig. 3.

Discussion
The N2-H2 plasmas generated here are a case-study of plasma-activated N2 fixation to NH3.Therefore, it is instructive to postulate on the energy transfer dynamics that yield the non-thermal populations of rotational and vibrational states observed for NH3 products.
We partially attribute the measured non-thermal population of excited states -observed in the gas phase -to surface association reactions of radicals and atoms adsorbed on the reactor walls.These surface association reactions then release NH3 into the gas phase in vibrationally excited states.In addition to direct NH3 formation, surface association reactions can also form rovibrationally excited H2, as has already been reported in expanding plasmas 29 , and electron impact reactions can yield other vibrationally excited molecules, such as NH3 30 .
Regardless of the formation mechanism, vibrationally excited NH3 in the gas phase is not likely to undergo rapid population redistribution through a vibrational-vibrational (V-V) energy transfer mechanism.Instead, and somewhat unique to NH3, experimental evidence suggests that vibrational-translational (V-T), vibrational-rotational (V-R), rotational-rotational (R-R) and rotational-translational (R-T) relaxation mechanisms are more likely [31][32][33][34][35][36] .This picture is consistent with the relatively low vibrational temperatures observed for NH3 in Fig. 4a, where we find  vib <  rot for both the  4 and  2 progressions.Indeed, NH3 behaves differently than other molecules like CO2 which exhibit rapid V-V relaxation processes along a vibrational ladder, leading to higher vibrational temperatures observed for CO2 formed in non-thermal plasmas 37 than are observed here for NH3.
In the following discussion, we focus on two more key observations: (i) The rotational temperature of the  0 state is lower than the translational temperature, and (ii) The translational temperature appears to follow the same trend vs.  H 2 as the non-thermal NH3 number density.
Together, these observations further point to the role of rapid V-T, V-R, R-R and R-T energy transfer mechanisms in dictating the non-thermal population distribution of NH3 products.Initially, vibrationally excited NH3 is rapidly deactivated to translational and rotational degrees of freedom.Following V-V relaxation which takes place on longer time scales, any remaining vibrational energy in the lowest vibrational level of a given mode -here,  2 or  4 -is further dissipated into translational energy via V-T relaxation.If the translational degree of freedom is taken to be the main sink for excess vibrational energy contained in the initial NH3 products, this qualitatively explains observation (i), where  rot  0 <  trans .
Furthermore, NH3 is proposed as the major sink for excess vibrational energy found in all the plasmaactivated molecules, due to relaxation via near-resonant V-V energy transfer between NH3 and a vibrationally excited N2 or H2 collider.Once the excess energy is transferred to NH3, the above-mentioned mechanisms of V-T, V-R, R-R and R-T relaxation dominate.In such a scenario, energy is most efficiently dissipated into translation motion through NH3 relaxation channels.Ammonia is a polar molecule with a steep intermolecular potential energy curve for collisional processes, leading to efficient relaxation of internal energy into heat 31,32 .This suggests that differences in buffer gas composition would affect efficiency, and hence chemical reactivity within N2-H2 plasmas.Indeed, we anticipate that vibrationally excited N2 ( ̃ = 2311 cm −1 ) and H2 ( ̃ = 4160 cm −1 ) are both formed in the plasma, and could transfer their energy via rapid V-V mechanisms into NH3 rather than dissipating it by self-collision and internal V-T processes.The number of collisions required to achieve self-deactivation via V-T for NH3, H2 and N2, respectively, is approximately 5, 10 7 and 10 9 at a temperature of 300 K 33 .For comparison, the deactivation of NH3 by collision with N2 is measured to require only 670 collisions 32 .From these values, we would expect that deactivation of NH3 by collision with H2 would take greater than 670 collisions, as could also be inferred from looking at the respective vibrational frequencies of H2 and N2 (which differ by almost a factor of two).Therefore, the most efficient route to deactivation of vibrationally excited molecules in the plasma appears to be through collisions with NH3.This hypothesis is consistent with the following observation (ii), that  trans appears to follow an asymmetry trend vs.  H 2 that is qualitatively like that of NH3 number density.As the energy sink molecule in our N2-H2 plasmas, greater number densities of NH3 result in a higher  trans .
The observation of similar trends in  trans and n-th when plotted vs.  H 2 provides additional support for the argument that V-T processes are largely responsible for depleting the anticipated initial population of excited vibrational states that occurs immediately following NH3 formation at the reactor surfaces.Contrast this trend with the impact that collisions between plasma-generated vibrationally excited NH3 and electrons would have on the observed steady-state populations: If processes such as scattering, momentum transfer, dissociation, and excitation of rotational and vibrational degrees of freedom were induced by electron-NH3 collisions, we would expect a monotonic change in  trans vs.  H 2 . 30Additionally, the rate coefficient for the dissociation of NH3 by electrons -calculated at an electron temperature of 0.31 eV observed for similar plasma reactors 38 -is roughly three orders of magnitude lower than the predicted V-T relaxation rate 26 .Thus, V-T is likely the dominant relaxation process for NH3 once generated in N2-H2 plasma.

Outlook
We demonstrate that quantum cascade laser dual-comb spectroscopy (QCL-DCS) can provide precision measurements of number densities and non-thermal population distributions across the translational, rotational and vibrational degrees of freedom of molecules confined to a reactive plasma environment.This is achieved here for a broad optical bandwidth by a combination of rapid spectra acquisition and high spectral resolution.With other chip-based laser sources like the long-wave infrared QCLs used here, DCS could also be employed as a plasma diagnostic in the mid-wave infrared using interband cascade lasers 39 or in the THz regime using QCLs 40 .When combined with injection-locked electro-optic comb generators in the short-wave infrared 41 , it may become possible to use DCS as a plasma diagnostic anywhere across the wavelength range of 1 μm to 100 μm, choosing between a series of distinct yet compact instruments.This would advance the field of laser-based plasma diagnostics beyond the current state-of-the-artwhere only a few pre-selected rovibrational transitions of a single molecular species are observed -by enabling observations of several vibrational bands of multiple species, without sacrificing spectral resolution or measurement speed.
In this demonstration, we begin to unravel the complex energy transfer mechanisms that result from a non-thermal population of energy levels in plasma-activated ammonia.Specifically, we highlight the role of various energy transfer mechanisms in partitioning population densities amongst quantized states, a process which significantly affects chemical reactivity.This opens the door to further systematic studies of plasma-activated processes involving NH3 generation, water-enhanced NH3 synthesis 42 , or the conversion of carbon dioxide to high value-added chemical products like renewable fuels.Furthermore, such a quantum-state-resolved picture of molecules within reactive environments will be of high importance for understanding other plasma driven chemical syntheses and transformations.

Methods
Quantum cascade laser dual-comb spectroscopy setup.
The dual-comb source (IRsweep IRis-core) emitted in the spectral range from 1035 cm −1 to 1085 cm −1 with repetition rates of frep ≈ 7.417 GHz, a difference in repetition rates of Δfrep = 2.1 MHz and average output optical powers ≥100 mW.The QCL outputs were attenuated by approximately tenfold using neutral density filters and aligned to create two dual-comb paths: reference and probe.Polarizers were used in each recombined QCL beam path to match interferogram intensities, and the dual-comb beams were focused onto photodetectors using off-axis parabolic mirrors with focal lengths of 25.4 mm.
Transmission spectra, T( ̃) were calculated by squaring the ratio   ( ̃)/ 0  ( ̃), where   ( ̃) is the intensity of the multi-heterodyne beat notes measured after passing through a plasma containing both N2 and H2 (the sample spectrum) and  0  ( ̃) is the intensity measured in a pure N2 or H2 plasma (the background spectrum) where no NH3 is formed.The squaring of the ratio is required when only one of the two interfering combs in the sample channel passes through the sample, thus creating a phase-sensitive configuration 43 .To suppress laser intensity noise and frequency noise, all measured intensities are normalized by the simultaneously measured intensities in the reference channel where both combs bypass the reactor.
High-resolution spectra were obtained by spectral interleaving of 600 measurements following the "stepsweep" approach 23 , yielding a spectral point spacing of 4.6×10 −4 cm −1 (14 MHz) in a total measurement time of seven minutes.The absolute frequency axis was calibrated by matching the offset frequency, foff and frep of the first measurement step to a pair of NH3 line positions retrieved from the HITRAN2020 database 25 .To correct for a residual drift of the measured wavenumber axis with interleaving step number, the measured changes in foff in every step were corrected by a constant factor of 0.9942 and 0.9972, respectively, for measurements taken with two slightly different stabilization times on different days.These factors were determined as the linear slope in the difference between measured and reference absorption peak positions of NH3 from the HITRAN2020 database 25 , plotted against the step number at which the absorption peak was measured.Hence, three fitting parameters (frep, foff, and foff) were used to assign approximately 125 000 spectral datapoints.After such calibration, the difference between found peak positions and those listed in the HITRAN2020 database 25 were < 4.3×10 −4 cm −1 (or 13 MHz).
The interleaved spectra of plasma samples showed a constant offset (>5 % transmission) in amplitude and linear slope in phase.These background signals varied on timescales from minutes to hours, as well as on a timescale of seconds, or between interleaving steps.The slower variations are likely due to thermal drifts.Since the spectrometer and the reactor are not mechanically connected, thermal expansion in the plasma reactor can change detector alignment and therefore signal levels.The origin of the fast drifts could not be identified.The constant offset in amplitude and linear slope in phase were both removed in post-processing from every interleaving step.To this end, absorption features were first masked out.Then, the median value of transmission of the remaining spectral datapoints was subtracted, as well as a linear function fitted to the phase.This procedure reduced the root-mean-square noise on the measured transmission to 0.0045, with the remaining noise dominated by optical fringing in the multi-pass cell, which was further fitted by a series of polynomial baseline functions.
Broadband spectral model and analysis.
(1), and includes a total number density of absorbers, , a spectral line intensity,   , for a transition connecting a lower state, , with an upper state, , and an area-normalized line shape function, ( ̃): Above,  ̃ is frequency in wavenumbers.The transition intensity,   , is related to the difference in number density between the lower and upper states 44 by the following equation: In Eq. ( 2),  a is the isotopic abundance of the species involved in the specific transition,   is the lowerstate number density,   is the upper-state number density,   and   are the Einstein -coefficients for induced absorption and emission, respectively, ℎ is the Plank constant,  ̃ is the transition frequency, and  is the speed of light.Note that     =     and   = 8ℎ ̃ 3   , where   is the lower-state statistical weight,   is the upper-state statistical weight, and   is the Einstein -coefficient for spontaneous emission.
Following the procedure of Klarenaar et al. 37 , we write the number density  for each energy level ,   , where  =  or  = , as: Above,  is the rotational quantum number and  is the index of vibrational modes (  = 1, 2, 3, or 4).The fraction of molecules,   /, in both rotational state ,  rot, , and vibrational mode   ,  vib,  , is normalized by the total internal partition sum,  tot =  rot  vib .Here, the internal partition sums for rotation and vibration are [44][45][46] In Eqs. ( 4)-( 5),  rot is the rotational temperature,  vib is the vibrational temperature,  s and  in are the state-dependent and state-independent weights,    is the degeneracy for the fundamental vibration   , and    is the term symbol for vibration   .To calculate  rot for ammonia (NH3), we use values for  s and  in from Šimečková et al. 44 and sum over all rotational states listed in ExoMol 47,48 , up to Jmax = 43.
To calculate  vib for NH3, we use values for    from Polyansky et al. 49 and degeneracy factors    derived from the D3h point group 50 .At values of  < 1000 K, when letting  =  rot =  vib , our calculation of   using Eq. ( 2) has a relative deviation from the temperature-dependent values calculated from HITRAN2020 parameters 25 of <6 %.This bias was corrected for each vibrational band and is ascribed to the use of an incomplete list of energy levels in our total partition function summations.
For the line shape function, ( ̃), we use a Voigt function with a Doppler-broadened half-width at halfmaximum of: where   is the Avogadro constant,  trans is the translational temperature, and  is the molecular molar mass.Here we assume a single, shared value for  trans across all transitions.The Lorentzian term for the Voigt function was calculated using the measured gas pressure and the air-broadening coefficients for NH3 from HITRAN2020 22 .
For the non-thermal region of the plasma reactor, we use the above equations to model and fit the absorption by 86 total transitions belonging to the  2 ←  0 fundamental band (20 transitions), the 2 2 ←  2 hot band (15 transitions), and the  2 + 4 ←  4 hot band (51 transitions).All other transitions meeting an intensity threshold criterion of (5 × 10 −5 ) ×  ,max ( rot ,   ), where  ,max is the maximum temperature-dependent transition intensity generated from within the list of the 86 targeted lines, are simulated assuming  =  trans =  rot =  vib at a temperature equal to the fitted value of  trans .
Based on machine drawings of the physical dimensions of the plasma reactor, we estimate the single-pass path length of the non-thermal region along the line-of-sight to be 64.0 cm -equivalent to the physical distance between the hot inner walls of the reactor.For a single-pass total optical path length of 79.0 cm ± 0.5 cm, we estimate a thermal region beyond the hot inner walls to be 15.0 cm in length, resulting in a fractional thermal path length of  th = 0.190.Again, following the procedure of Klarenaar et al. 37 , we fit a single thermal temperature,  th , for the thermal region with a lower bound equal to the observed room temperature of 295 K and an upper bound equal to the translational temperature of the non-thermal region,  trans .The combined model for the observed transmission signal is then the product of the respective transmission models for the thermal and non-thermal regions.Thermal and non-thermal number densities are calculated assuming the ideal gas law, using either  th or  trans .

Uncertainty analysis.
We adopt a probabilistic approach to the uncertainty propagation 51 , using Monte Carlo simulation methods and fitting to produce a distribution of output values that are the result from models generated by randomly drawn inputs.Components of the spectral reference data used to model NH3 absorption are Tables of initial parameters and drawing distributions used for each fitted spectrum, along with the mean values and standard deviations that resulted from the Monte Carlo simulation and fitting routine, are provided as Supplementary Information.
Preliminary line-by-line spectral analysis.
Prior to the broadband spectral modelling and fitting described above and reported in the Results section, a preliminary line-by-line analysis was useful in estimating initial guesses for parameters like  trans and  rot , and for identifying transitions -particularly hot-band transitions -that required manual adjustments to their HITRAN2020 25 frequencies to accommodate our assigned wavenumber axis.A list of transition frequency adjustments applied to our broadband model is provided as Supplementary Information.
Here we focus on a Boltzmann plot analysis to determine initial values of  rot .By plotting the natural logarithm of the lower-state number density,   , normalized by the lower-state statistical weight,   (i.e., the quantity ln(  /  )), versus the lower-state energy,   , rotational temperatures could be estimated from the band-specific Boltzmann plot slopes.The Boltzmann plot analysis is presented here in Fig. 5.To create Fig. 5, individual lines were fit with a Voigt line shape function, with the fit parameters including the Doppler-broadened half-width at half-maximum and the line center.The translational temperature (Ttrans) was evaluated from the Doppler width using Eq. ( 6), while   was determined from the integral of the absorption profile and the HITRAN2020 parameters   and  ̃ .
More detailed Boltzmann plot expressions are introduced below.The statistical-weight-normalized number density in state  is described by the Boltzmann law:

Fig. 1 |
Fig. 1 | Quantum cascade laser dual-comb spectroscopy (QCL-DCS).a Schematic of the experimental setup.The probe beam from QCL comb 1 is coupled to a multi-pass cell attached to the plasma reactor, whereas the reference beam bypasses the reactor.Probe and reference combs are combined with copies of the local-oscillator QCL comb 2 at two different photodetectors.Dashed lines indicate electronic connections.Reactor temperatures  wall and  load were measured where indicated by the black arrows, and the non-thermal region (distance between the inner walls) of the reactor is indicated by the left-right arrow.b Energy level diagram for NH3 at the 2 vibration, as probed by QCL-DCS (vertical arrows).The transition energies (in wavenumber) of both the antisymmetric (black, horizontal) and symmetric (grey, horizontal) states are shown.

Fig. 3 |
Fig. 3 | NH3 number density in the non-thermal region, n-th, as a function of the H2 mass flow fraction,    .Mixed precursor gases were maintained inside the plasma reactor at a fixed pressure of 100 Pa ± 1 Pa.Measurements for the two data series (Data 1 and Data 2; blue circles and red triangles) proceeded in two distinct  H 2 directions (blue and red arrows).A modified Akima interpolation model 25 (Interp.;black dashed line) is shown to illustrate the asymmetry in the observed data set, and zoomed-in traces near  H 2 = 0 and  H 2 = 1 are plotted as grey insets (linear y-axis).Error bars are combined standard uncertainty.

Fig. 4 |
Fig.4| Distinct temperatures for plasma-activated NH3 generation.a Vibrational temperatures ( vib ) for the  4 (yellow triangles) and  2 (red squares) progressions, plotted vs.  H 2 .b Rotational temperatures ( rot ) for the transitions beginning in  4 (yellow triangles),  2 (red squares) and  0 (blue diamonds) states, plotted vs.  H 2 .c Translational temperatures in the non-thermal ( trans , black circles) and thermal (th, gray filled circles) regions, plotted vs.  H 2 .Also plotted in a-c are the smoothed values of  load (blue dashed line) and  wall (magenta dashed lines).The smoothed values of  load are only visible in b, where higher temperatures are shown.

Fig. 5 |
Fig. 5 | Boltzmann plot to estimate band-specific rotational temperatures.Rotational temperatures,  rot , were estimated for three rovibrational bands of NH3, including the 2 ← 0 fundamental band (black dots), the 22 ← 2 hot band (black squares), and the 4+2 ← 4 hot band (black diamonds).Linear fits are also shown (red lines).Two data sets for each vibrational band are presented, each of which was collected at  H 2 = 0.6 and recorded on successive days.Error bars represent 1σ fit precision in the area of the line profile (type-A evaluation only).

Fitted Value Combined Uncertainty Units Relative Uncertainty Units
H 2 .The observed rotational temperatures reveal a general trend, where  rot  4 >  rot  2 >  rot  0 .Two smoothing splines appear in Fig. 4b, each fitted to the average values of  load and  wall , respectively.No external heating was applied to the plasma reactor, and  load >  wall is due to the negative bias applied to the working load.For the 2 2 ←  2 and  2 + 4 ←  4 hot bands, values of  vib and  rot are only reported for spectra with an observed signal-to-noise ratio (SNR) greater than or equal to four for the strongest rovibrational transition within each respective hot band.The choice of SNR > 4 is rather arbitrary, but roughly corresponds with the minimum SNR required for the fitting of band temperatures to converge.
are the fitted values of  vib vs.  H 2 .Generally, values of  vib are between 400 K and 500 K, and we observe  vib  4 >  vib  2 .Also plotted is a smoothing spline fitted to the average measured value of  wall .Figure4bshows the fitted values of  rot plotted vs.
Vibrational temperatures ( vib ) for the  4 (yellow triangles) and  2 (red squares) progressions, plotted vs.  H 2 .b Rotational temperatures ( rot ) for the transitions beginning in  4 (yellow triangles),  2 (red squares) and  0 (blue diamonds) states, plotted vs.  H 2 .c Translational temperatures in the non-thermal ( trans , black circles) and thermal (th, gray filled circles) regions, plotted vs.  H 2 .Also plotted in a-c are the smoothed values of  load (blue dashed line) and  wall (magenta dashed lines).The smoothed values of  load are only visible in b, where higher temperatures are shown. :