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

Ammonia (NH₃) is indispensable to global agriculture via its use in fertilizers and is a target for more sustainable synthesis routes than the energy-intensive Haber–Bosch process. Plasma-activated NH₃ formation could enable N₂ fixation from air at lower temperatures and pressures, yet reported energy yields remain far below Haber–Bosch. Improving yields requires molecular-level understanding of formation mechanisms, including quantum-state-resolved information to capture non-thermal populations that can alter state-specific reaction rates. In non-thermal plasmas, different molecular degrees of freedom (translational, rotational, vibrational) can have distinct temperatures, affecting kinetics. Existing laser diagnostics for NH₃ in plasmas typically scan few transitions, limiting state-resolved insight. Frequency-comb methods offer broader coverage, but prior demonstrations have not provided a quantum-state-resolved picture of non-thermal plasmas for challenges like N₂ fixation. This study applies mid-IR QCL dual-comb spectroscopy near 9.4 µm to resolve translational, rotational, and vibrational populations of NH₃ formed in low-pressure N₂–H₂ plasmas, aiming to elucidate energy transfer dynamics and formation pathways.

Prior active laser diagnostics for NH₃ in plasmas include cavity-enhanced absorption spectroscopy, tunable diode laser absorption spectroscopy, and quantum-cascade laser absorption spectroscopy, generally limited to a few scanned lines with CW lasers. External-cavity QCLs broaden coverage but still target subsets of transitions. Frequency-comb Fourier transform spectroscopy has detected multiple species in discharge effluents, and dual-comb spectroscopy has captured time-resolved spectra in electric discharges and detected atomic species after laser-induced breakdown in the visible. However, previous comb-based studies have not delivered quantum-state-resolved analyses of non-thermal plasmas for NH₃ synthesis. Non-thermal effects are also reported in laser-induced plasmas, combustion, and exoplanetary atmospheres, where laser diagnostics support quantitative sensing, motivating broadband, high-resolution methods like QCL-DCS to probe complex energy distributions.

QCL dual-comb spectroscopy was implemented near 1060 cm⁻¹ (λ≈9.4 µm) using two mid-IR QCL frequency combs (IRsweep IRis-core). Comb 1 provided probe and reference beams with repetition rate frep,1 = 7.417 GHz; comb 2 acted as a local oscillator with frep,2 = frep,1 + Δfrep, Δfrep = 2.1 MHz. Probe light traversed a multipass cell (path length L = 3.16 m) attached to an industrial stainless-steel plasma reactor; the reference bypassed the reactor. Probe and reference interferograms were recorded on separate detectors for normalization. High-resolution spectra were obtained by step-sweep interleaving: both comb currents were stepped to acquire 600 interleaved, normalized transmission spectra over 50 cm⁻¹ bandwidth, yielding an effective point spacing of 4.6 × 10⁻³ cm⁻¹ (14 MHz) in 7 minutes. Frequency axes were calibrated to HITRAN2020 NH₃ lines with correction of interleaving-step drifts. Background offsets and phase slopes varying from seconds to hours were removed per step by masking absorption, subtracting median transmission, and removing a linear phase baseline; residual fringes were modeled by polynomial baselines. The plasma was a DC discharge (355 W ± 50 W) sustained on a stainless-steel mesh at the top of the reactor. A stainless-steel workload was negatively biased to stabilize and increase discharge power. N₂/H₂ precursor mixtures were fed at total 500 ± 5 sccm with pressure held at 100 ± 1 Pa. Reactor outer wall was water-cooled to ~295 K; inner wall (Twall) and workload temperatures (Tload) were monitored. The spectral window contains transitions from NH₃ ν₂ fundamental (01000000), 2ν₂+ν₄ hot band (02000100), and ν₂+ν₄ hot band (01010001). A two-zone line-of-sight transmission model was used: a non-thermal region (between hot inner walls) allowing distinct translational (Ttrans), rotational (Trot), and vibrational (Tvib) temperatures; and a thermal region beyond the inner walls with a single temperature Tth applied to all degrees of freedom. The Beer–Lambert law with Voigt profiles was applied, using Doppler half-widths set by Ttrans and Lorentzian widths from pressure (100 Pa) and HITRAN2020 air-broadening parameters. For the non-thermal region, 86 targeted lines (20 ν₂ fundamental, 15 2ν₂ hot, 51 ν₂+ν₄ hot) were modeled with band-specific Trot and Tvib; all other weaker lines above an intensity threshold were included assuming Ttrans = Trot = Tvib = Ttrans. Partition functions Qrot and Qvib were constructed from literature statistical weights and energy levels (up to J=43), with small bias corrections (<6%) applied relative to HITRAN temperature-dependent intensities. Thermal and non-thermal number densities were computed via the ideal gas law using Tth and Ttrans, respectively, with a fixed fractional thermal path length fth = 0.190 (single-pass path lengths estimated from reactor drawings: 64.0 cm non-thermal, 15.0 cm thermal, total 79.0 ± 0.5 cm). Transmission spectra T(ν̃) were formed from squared ratios of sample to background multiheterodyne beat intensities, normalized by the reference channel, appropriate for the phase-sensitive configuration where one comb traverses the sample. Uncertainties were evaluated with Monte Carlo propagation: input parameters (e.g., line intensities with HITRAN error codes, pressure, path length) were randomly drawn from normal distributions; for spectra with sufficient SNR across three bands, 100 simulations were fit; for one/two-band SNR cases, 10 simulations were used. When band SNR < 4, Trot and Tvib for that band were fixed to values drawn from weighted means of other spectra meeting SNR ≥ 4. Preliminary line-by-line analyses (Voigt fits, Boltzmann plots) provided initial guesses and identified hot-band frequency adjustments relative to HITRAN; adjustments are listed in supplementary data.

• High-resolution, broadband QCL-DCS resolved NH₃ rovibrational transitions from ν₂ fundamental, ν₂+ν₄, and 2ν₂+ν₄ bands in N₂–H₂ plasmas at 100 Pa, with 14 MHz point spacing across 50 cm⁻¹.
• Broadband fitting with a two-zone model revealed distinct non-thermal populations: Ttrans, Trot, and Tvib differ, confirming non-local thermal equilibrium for product NH₃.
• Representative fitted parameters (for the spectrum in Fig. 2a) with 1σ combined uncertainties (Table 1): • Tth = 310 ± 20 K • Ttrans = 456 ± 10 K • Trot(ν₂) = 390 ± 40 K; Trot(ν₄) = 460 ± 30 K; Trot(v₆ label in table likely ν₂+ν₄) = 530 ± 40 K • Tvib(ν₂) = 419 ± 13 K; Tvib(ν₄) = 454 ± 10 K • Non-thermal NH₃ number density nn-th = (3.6 ± 0.2) × 10¹⁴ cm⁻³
• Residuals away from saturated lines had a standard deviation ~0.0036, yielding a maximum SNR of ~280:1; minor systematics appeared near saturated lines.
• Assuming a single global temperature (e.g., 450 K) for line-by-line analysis would bias inferred nn-th by up to a factor of six across different bands, underscoring the need for broadband, state-resolved modeling.
• NH₃ number density nn-th as a function of H₂ mass flow fraction φH₂ showed a pronounced asymmetry with maximum yield on the H₂-deficient side; densities spanned more than two orders of magnitude, demonstrating wide dynamic range.
• Tvib values generally 400–500 K with Tvib > Trot on average; Trot typically ≤ Ttrans. Trends of Ttrans vs φH₂ mirror those of nn-th, peaking near maximum NH₃ yield.
• No systematic difference in Doppler widths between hot- and fundamental-band lines at given power and SNR, consistent with absence of external heating.
• Energy transfer interpretation: rapid V–T, V–R, R–R, and R–T processes in NH₃ dominate over V–V along vibrational ladders (contrasting with CO₂), leading to relatively modest Tvib and Trot ≤ Ttrans.
• Collisions with NH₃ are posited as the dominant relaxation pathway for vibrationally excited NH₃; electron-induced processes have much lower dissociation rates (at Te ≈ 0.31 eV, roughly three orders of magnitude lower than predicted V–T rates).

The study addresses the need for quantum-state-resolved insight into plasma-activated NH₃ formation by directly measuring translational, rotational, and vibrational temperatures and number densities across multiple bands with high spectral resolution and broad coverage. The observation that Tvib and Trot differ from Ttrans demonstrates non-thermal populations, validating the hypothesis that plasma-formed NH₃ exhibits distinct energy partitioning across degrees of freedom. The asymmetric dependence of nn-th on φH₂ and the correlation of Ttrans with NH₃ density indicate that NH₃ itself serves as an efficient energy sink, with rapid V–T relaxation channeling vibrational energy into translation. The finding that Trot ≲ Ttrans supports a relaxation sequence where initial vibrational excitation (from surface association reactions or electron impacts) is quickly redistributed via V–R/R–R and then V–T, rather than via V–V up-pumping along vibrational ladders. These results clarify energy transfer mechanisms in non-thermal NH₃ plasmas, providing constraints for plasma-chemistry models and informing optimization of plasma catalysis conditions (e.g., gas composition, reactor materials, and pressures) to enhance NH₃ yield and energy efficiency. While uncertainties in Trot and Ttrans overlap for many conditions, the consistent trends and quantitative fits across ~125,000 spectral elements strengthen the interpretation. Further improvements in SNR and complementary modeling would refine parameter estimates and deepen mechanistic understanding.

This work demonstrates that mid-IR QCL dual-comb spectroscopy, with fast interleaving for 14 MHz resolution over 50 cm⁻¹, can quantify state-specific number densities and non-thermal population distributions (Ttrans, Trot, Tvib) of NH₃ in reactive, low-pressure N₂–H₂ plasmas. The broadband, multi-line approach avoids biases inherent to single-line analyses and reveals that V–T, V–R, R–R, and R–T relaxation processes dominate NH₃ energy redistribution, with NH₃ acting as a principal energy sink. These quantum-state-resolved observations advance mechanistic understanding of plasma-activated NH₃ formation and provide benchmarks for plasma-chemistry models. Looking ahead, DCS with other chip-scale sources (interband cascade and THz QCLs, electro-optic combs) could extend diagnostics across 1–100 µm, enabling simultaneous, high-resolution monitoring of multiple vibrational bands and species without sacrificing speed. Future studies may explore water-enhanced NH₃ synthesis, CO₂ conversion to fuels, and broader plasma-driven syntheses, integrating measurements with detailed modeling to close knowledge gaps in plasma catalysis.

• Measurement precision is limited by SNR; many cases have overlapping 1σ uncertainties between Trot and Ttrans, constraining definitive ordering. Improving SNR would reduce parameter uncertainties and strengthen mechanistic conclusions.
• The two-zone line-of-sight model assumes a fixed fractional thermal path and uniform properties within each zone; spatial gradients and non-uniformities are not directly resolved.
• Baseline drifts (amplitude offsets, phase slopes) and optical fringes required post-processing and baseline modeling, which may introduce small systematic uncertainties.
• Line-shape modeling used Voigt profiles with air-broadening parameters; potential non-Voigt effects and precise collisional parameters at 100 Pa were not explored due to lack of systematic residuals at current SNR.
• Transition intensity uncertainties (often 10–20% in HITRAN2020) and incomplete partition sums necessitated bias corrections; hot-band line frequencies required manual adjustments for some lines.
• The step-sweep interleaving over 7 minutes trades temporal resolution for frequency resolution, limiting access to fast plasma dynamics.
• Results are specific to one reactor geometry, materials, and operating point (100 Pa, 355 ± 50 W); generalizability to other reactors and pressures may require additional validation.