Mechanistic insights into the non-equilibrium thermodynamics of nitrogen fixation via acoustic cavitation

Domain: neuroscience
Published: 2026-02-12
Editorial outcome: minor_revision

Abstract
Non-equilibrium reaction environments offer a route to bypass the thermodynamic constraints that limit conventional nitrogen fixation, yet such conditions remain inaccessible in traditional thermal systems. Here, we show that rapid activation-quenching chemistry inside cavitation bubbles provides a viable non‑equilibrium pathway for nitrogen fixation. The violent collapse of ultrasound-driven bubbles generates an intense temperature pulse that enables direct nitrogen activation and subsequent redox chemistry within a transient gas phase microreactor. Nitrogen-containing products are produced with tuneable rates and selectivity controlled by feed gas composition, cavitation dynamics, and solution properties. Introduced cavitation nuclei lower the cavitation threshold and improve collapse reproducibility, while noble‑gas doping modulates collapse temperatures and shifts nitrate-nitrite distributions through enhancing the involvement of water‑derived species. Isotopic labelling and single‑bubble modelling indicate that nitrogen reaction proceeds predominantly through gas‑phase pathways during collapse, which can be described by a dynamic thermodynamic model within a temperature pulse. These findings establish cavitation‑driven non-equilibrium thermal cycling as a distinct mechanism for nitrogen fixation and underscore the broader potential of transient thermal microenvironments for chemical synthesis.

Introduction
Nitrogen fixation, the conversion of inert atmospheric nitrogen (N2) into reactive nitrogen compounds, underpins global agriculture and chemical manufacturing1–3. Artificial nitrogen fixation is predominantly achieved through the Haber–Bosch process4,5, which produces ammonia from nitrogen and hydrogen under high temperatures and pressures. In the industrial nitrogen cycle, ammonia is further oxidised to produce nitrate6, a key component of fertilisers and other nitrogen-based chemicals7. Despite nitrate being a major form of industrial nitrogen products8, the direct oxidation of nitrogen molecules remains a fundamental challenge in chemistry and catalysis7,9,10. The primary difficulty lies in overcoming the high dissociation energy of the nitrogen triple bond11 (≈9.8 eV at 298 K). Direct oxidation typically requires temperatures exceeding 1500 K, yet the reaction rate remains low12, and further increases in temperature are not practical due to material instability under such conditions. In contrast, nitrogen reduction is thermodynamically exothermic, meaning high temperatures do not favour the forward reaction due to the constraints imposed by chemical equilibrium, which leads to the high-pressure system13. Therefore, the central challenge in nitrogen fixation lies in reconciling the conflicting requirements of achieving sufficient activation energy while maintaining reaction conditions that favour nitrogen product formation. This delicate balance between chemical kinetics and thermodynamic limitations remains a major bottleneck in the development of efficient and sustainable nitrogen fixation technologies.

Recently, programmable heating and quenching strategies have been developed to regulate reaction pathways, aiming to facilitate nitrogen activation while preserving catalyst stability14. These electrothermal systems offer controlled temperature modulation, with ramping and cooling rates reaching up to 104 Ks−1. While this represents a significant advance over conventional heating methods, such rates are only sufficient to influence reactions on the millisecond timescale. Consequently, they are unable to selectively control sequences of elementary reaction steps that occur on much shorter timescales. Achieving selective control, therefore, requires both fast temperature oscillation and access to high temperatures that are inaccessible to conventional reactors.

Acoustic cavitation provides such conditions. Under ultrasound irradiation, gas–vapour bubbles nucleate, expand, and undergo inertial collapse in liquids15,16. The collapse of these cavitation bubbles generates localised “hotspots” with transient high temperature and pressure pulse17,18. These non-equilibrium conditions enable molecular activation and product formation steps to occur in distinct temporal regimes, offering a fundamentally different route to nitrogen fixation. A schematic illustration of the nitrogen fixation process via cavitation is shown in Fig. 1a. The cavitation bubbles behave as confined microreactors. Upon violent inertial collapse, the temperature and pressure inside the bubbles rise dramatically, driven by the nearly adiabatic compression of the gas. These conditions trigger the thermolytic dissociation of gas-phase molecules and generate a range of reactive radical species (e.g., N, O, H, OH). Subsequent recombination reactions yield nitrogen-containing products, which are rapidly quenched and transferred into the surrounding liquid, allowing accumulation in solution. This phenomenon represents the chemical effects of ultrasound, collectively referred to as sonochemistry.

Although nitrogen fixation via acoustic cavitation has been previously observed19–23, the mechanistic basis and controllability remain elusive24. As a result, this phenomenon has often been regarded as a secondary effect of sonochemistry rather than a viable pathway for nitrogen fixation25. Early pioneering studies reported the formation of nitrite and nitrate in air-saturated water under ultrasound, with most attributing the process to a high-temperature combustion-like pathway26, namely, the Zeldovich mechanism27. However, this explanation fails to account for the observed non-stoichiometric product distributions and the significant role of water in the sonochemical reaction system. Critically, no systematic strategies have been proposed to modulate the reaction pathway or control the product distribution. In contrast, the production of ammonia via cavitation has been scarcely reported in the literature23, likely due to the assumption that ammonia synthesis is incompatible with high-temperature combustion conditions.

In this work, we establish a dynamic thermodynamic framework to elucidate the chemistry occurring during bubble collapse. We identify the physical origin of inertial cavitation as the key factor governing nitrogen activation and demonstrate that nitrogen oxidation and reduction pathways can coexist under the same sonochemical conditions. This behaviour contrasts with the disproportionation mechanisms recently proposed for microdroplets28. We attribute this unique reactivity to the combination of transient high temperatures, sufficient to activate molecular nitrogen, followed by rapid quenching that selectively stabilises reaction intermediates and products. This rapid thermal cycling plays a decisive role in directing the reaction pathway. Furthermore, the gas-phase reaction products formed within the collapsing bubbles diffuse into the surrounding liquid phase, effectively shifting the chemical equilibrium and enabling continued product accumulation.

Results
Direct gas phase reaction in collapsing cavitation bubbles
To model the chemistry in cavitation bubbles, we consider the direct radical reaction pathway, where molecular nitrogen undergoes direct dissociation. The associated free energy landscape reveals that nitrogen dissociation is strongly endothermic, while subsequent steps, such as the formation of nitrous acid or ammonia, are energetically downhill (Fig. 1b). At 5000 K, N≡N bond dissociation becomes accessible, whereas nearly all steps, including product formation, become thermodynamically uphill. Stable nitrogen products, therefore, require a rapidly oscillating thermal profile: transient high temperature to activate N2, followed by fast quenching to stabilise intermediates. This dynamic temperature cycling is intrinsic to inertial bubble collapse and cannot be achieved in conventional steady-state thermal systems. For example, the collapse of nitrogen–water vapour bubbles can produce peak temperatures approaching 5000 K or higher (Fig. 1c). Importantly, this thermal pulse occurs within ≈3 ns, corresponding to a heating/cooling rate on the order of 1012 Ks−1. Herein, different elementary reaction steps are initiated at distinct stages of this transient thermal cycle. By enabling these processes to occur sequentially under optimised thermal conditions, cavitation offers an opportunity to overcome both kinetic and thermodynamic constraints that limit conventional nitrogen fixation technologies.

To evaluate nitrogen fixation under these conditions, we investigated two closed reaction systems (Supplementary Fig. 1): water saturated with pure nitrogen or air. The measured UV-vis spectra of nitrogen products after 30 min are shown in Supplementary Fig. 3 (Calibration curves present in Supplementary Fig. 2). Pure N2 produced only trace amounts of fixed nitrogen, whereas air led to substantially higher yields (42 μM), indicating that oxygen is essential for initiating efficient N–O chemistry (Fig. 1d). However, the air-saturated system showed variability due to stochastic cavitation behaviour.

To stabilise cavitation, talc (magnesium silicate, 10 μm particle size, see structural characterisation in Supplementary Fig. 4) was introduced as an inert cavitation agent. The cavitation activity with talc is due to the transition from stochastic nucleation to controlled nucleation of bubbles. As shown in Supplementary Fig. 5, adding talc to water lowers the cavitation threshold and enables controllable bubble collapse. As a result, talc increased the total nitrogen fixation for both pure nitrogen and air compared to the pure water system. For reaction with gas, the incorporation of talc specifically increased nitrate production without decreasing nitrite production. We also found that by adjusting the pH with sulphuric acid, nitrate became the dominant product for both cases, while total nitrogen fixation decreased for the air reaction. This indicates that liquid properties also play a role in the nitrogen fixation reaction.

These comparative results suggest that the primary reaction mechanism is driven by gas-phase interactions inside the cavitation bubbles, rather than reactions between dissolved gases and water in the bulk liquid. This is mainly concluded from the low nitrogen fixation of pure nitrogen reaction, which lacks reactive oxygen-containing species required to initiate efficient radical chemistry. Although ref. 29 has proposed that hydroxyl (OH) radicals generated from water contribute significantly to liquid-phase nitrogen fixation, our findings indicate that gas-phase reactions during bubble collapse are the dominant pathway in this system. This interpretation is further supported by the enhanced nitrogen fixation observed upon the addition of talc particles. Talc acts as a cavitation nucleus source, increasing the number of stable bubble nucleation sites and thereby promoting more frequent and intense bubble collapse events. This leads to increased hotspot formation and radical generation, resulting in higher nitrogen fixation yield.

Conversely, introducing sulphuric acid leads to a decrease in total nitrogen fixation when air is used as the feed gas. This behaviour is attributed to the salting-out effect, in which the presence of ionic species reduces the solubility of both N2 and O2 in water, thereby lowering the gas content within bubbles and reducing reaction yield30. Because the air-based system relies more strongly on gas incorporation and radical oxidation pathways, its reaction rate is more sensitive to this reduction in gas solubility. The relative increase of nitrate concentration suggests that nitrate formation is influenced by solution-phase oxidation processes occurring after bubble collapse19. Taken together, these results reinforce the conclusion that the microenvironment inside collapsing cavitation bubbles determines both the extent and the selectivity of nitrogen fixation, while subsequent solution chemistry modulates the relative distribution of oxidised nitrogen products.

Reaction regulated by cavitation and gas–liquid conditions
Following the above analysis, it is evident that the amount of ammonium produced remains consistently low, even under pure nitrogen conditions. This contradicts conventional nitrogen fixation pathways due to the more moderate reaction conditions required for nitrogen reduction compared to nitrogen oxidation. However, this observation suggests that the direct reaction between nitrogen and water vapour is not a favourable pathway for ammonium synthesis. Motivated by these findings, we further explored nitrogen fixation using different gas mixtures, focusing on two closed reaction systems: water saturated with either nitrogen–oxygen or nitrogen–hydrogen gas mixtures. We then studied product distributions as a function of nitrogen concentration, acoustic pressure of ultrasound, and reaction time (UV-vis spectra are shown in Supplementary Figs. 6, 7).

For nitrogen–oxygen mixtures, the optimal nitrogen fixation was observed at a nitrogen concentration of ≈79% (air) (Fig. 2a). Interestingly, a 50% nitrogen concentration did not show the highest yield, despite being stoichiometric for NO formation if a direct 1:1 reaction between nitrogen and oxygen were assumed. Previous studies, including computational analyses based on the Zeldovich mechanism, have shown that the maximum NOx production occurs at around 70% nitrogen, while experimental results are different22. According to the Zeldovich mechanism, the initial step involves oxygen molecule dissociation to form O radicals, which then readily react with N2 to produce NO and N radicals. This explanation aligns with our observations, as the equilibrium formation of reactive O species is favoured at specific nitrogen-to-oxygen ratios. Nevertheless, few studies have conducted in-depth investigations into this deviation under non-equilibrium conditions such as those created by acoustic cavitation. This intriguing phenomenon will be discussed in greater detail in subsequent sections.

After identifying the optimal nitrogen-to-oxygen ratio, we examined product distributions under varying acoustic pressures. When air was used as the feed gas (Fig. 2b), the nitrite concentration initially increased almost linearly with increasing acoustic pressure and then reached a plateau. By contrast, the nitrate concentration continued to rise more sharply across the entire pressure range. This divergence suggests that higher acoustic pressures not only enhance primary nitrogen activation but also increasingly favour nitrate formation. Such nitrate enhancement may arise from direct oxidation pathways inside the collapsing bubble or post-collapse liquid-phase oxidation of nitrite. To further test this hypothesis, we monitored time-dependent nitrogen fixation in a closed, air-saturated system (Supplementary Fig. 8). The total amount of fixed nitrogen exhibited a linear increase with reaction time, indicating effective reaction kinetics in a closed system, not limited by dissolved gas concentration. Notably, while the accumulation rate of nitrite gradually slowed over time, the nitrate concentration continued to rise steadily. This temporal divergence supports a sequential mechanism in which nitrite serves as a precursor to nitrate, with nitrate formation partially governed by secondary oxidation processes occurring after bubble collapse.

To better visualise this trend, the nitrate-to-nitrite ratio was calculated and plotted. A nitrogen–oxygen mixture containing 79% nitrogen yielded the highest nitrate-to-nitrite ratio of 0.72, which further increased to 0.99 with prolonged reaction time (Supplementary Fig. 8h). More significantly, the nitrate-to-nitrite ratio exhibited a clear positive correlation with acoustic pressure, rising sharply from 0.11 to 0.72. This behaviour may be attributed to two main factors: first, stronger cavitation activity directly enhances nitrate formation during bubble collapse; second, increased reaction time in the closed system leads to accumulation of OH radicals, which facilitates the secondary oxidation of nitrite to nitrate in water. OH radicals are from the pyrolysis of water and can form H2O2 in water. Supplementary Fig. 9 presents the H2O2 concentrations under different feed gases. As a benchmark, pure argon yielded the highest concentration of H2O2, while significantly lower concentrations were observed with nitrogen and nitrogen-containing mixtures. Although differences in thermal conductivity among the gas mixtures may influence hotspot temperatures, the substantial reduction in H2O2 suggests that OH radicals are being consumed by reactions with nitrogen species.

In the nitrogen–hydrogen mixture system (Fig. 2c, d), the main product was ammonium, while negligible nitrate was detected. The maximum nitrogen fixation was achieved at 80% nitrogen concentration (Fig. 2c). Compared to the nitrogen–oxygen system, where ammonium production was minimal, the clear production of ammonium in the nitrogen–hydrogen mixture suggests direct N–H coupling in the gas phase. Interestingly, the stoichiometric ratio for ammonia synthesis (25% nitrogen and 75% hydrogen) exhibited much lower ammonium production, indicating that the reaction does not simply follow a stoichiometric mechanism but is governed by the complex processes inside the collapsing bubbles. For time-dependent experiments with 80% nitrogen, ammonium concentration increased linearly with reaction time (Supplementary Fig. 8i). A similar trend was observed in acoustic pressure-dependent experiments (Fig. 2d), further confirming the high selectivity of ammonium production under these conditions. It is noteworthy that the total nitrogen fixation in the nitrogen–hydrogen system was less than half that observed for the nitrogen–oxygen system, which reflects differences in the reaction kinetics between nitrite and ammonium formation.

To further evaluate system performance, we compared the production normalised to the energy input (Supplementary Fig. 10). In the nitrogen–oxygen system, nitrogen fixation continuously increases with the pulse energy (100 cycles), reaching a maximum yield of 0.18 μmol J−1. Nitrite formation plateaued at a pulse energy of 11.09 μJ, corresponding to a yield of 0.098 μmol J−1, whereas nitrate yields continued to increase with higher pulse energy. In the nitrogen–hydrogen system, ammonium formation exhibited a maximum at 12.38 μJ per pulse, giving a peak yield of 0.048 μmol J−1, while nitrite concentrations decreased progressively with increasing pulse energy.

In addition to varying the acoustic pressure, we also investigated the role of cavitation agents in sonochemical nitrogen fixation (Supplementary Fig. 11). As previously demonstrated, the addition of talc enhances cavitation activity. To systematically assess its impact, we monitored product distributions across a range of talc concentrations (0–4 mg mL−1). In the nitrogen–oxygen system, reactions conducted without talc showed large fluctuations in total nitrogen fixation, comparable to those observed at 1 and 2 mg mL−1 talc. Interestingly, nitrate production decreased with increasing talc concentration, while nitrite levels remained relatively constant. This suggests that cavitation activity affects not only the overall extent of nitrogen fixation but also the selectivity between nitrite and nitrate formation. In the nitrogen–hydrogen system, maximum ammonium production was achieved at a talc concentration of 1 mg mL−1. In the absence of talc, nitrogen fixation was significantly lower, and increasing the talc concentration beyond 1 mg mL−1 did not lead to further improvement in ammonium yield. These findings indicate that both nitrate and nitrite production can be modulated by tuning bubble dynamics via cavitation agents. The addition of talc promotes inertial collapse by reducing the inertial cavitation pressure threshold. This alters bubble‑collapse dynamics, thereby suppressing direct nitrate formation, which requires longer sequential gas‑phase reaction pathways. These results support the notion that nitrate can be formed directly within the bubbles during collapse, in addition to subsequent reactions in the liquid phase.

Overall, these findings highlight the complex interplay between primary gas-phase reactions occurring within collapsing cavitation bubbles and secondary liquid-phase reactions driven by reactive oxygen species. They underscore the critical role of cavitation activity, gas-phase composition, and transient thermal dynamics in modulating nitrogen fixation pathways under sonochemical conditions.

In the closed reaction system, our primary focus was on analysing liquid-phase products; however, gas-phase species are also critically important, particularly under closed conditions where accumulation and secondary reactions may occur. It is well-established that ultrasound treatment leads to the production of hydrogen through the recombination of H generated by water splitting. Using argon as the feed gas, hydrogen production was confirmed via mass spectrometry (Supplementary Fig. 12). Similar hydrogen formation was also observed in nitrogen-saturated systems (Fig. 3a), validating that water splitting occurs regardless of the feed gas composition. When a mixed H2O/D2O solution was employed, the detection of HD and D2 signals further confirmed active radical recombination and water splitting.

These results indicate that sonication always induces water splitting, contributing H2 and O2 to the system. These gaseous products may influence the local reaction environment inside cavitation bubbles, potentially altering product selectivity and formation rates. To further examine this, we performed reactions under continuous gas flow conditions (Fig. 3b, c, Supplementary Fig. 13). The continuous introduction of gas nuclei into the liquid helps maintain stable and efficient cavitation. With pure nitrogen as the feed gas, nearly equal amounts of nitrite and nitrate were produced, accompanied by a gradual increase in ammonium concentration over time (Supplementary Fig. 14a). In this setup, nitrogen can only react with water-derived radicals, indicating that OH and H participate in nitrogen fixation, although their reaction rate (0.27 μM min−1) is substantially lower than that observed for reactions involving oxygen or hydrogen gas. Interestingly, the ratio of nitrate to nitrite is around 1.0 (Fig. 3b), which shows different behaviour to direct reaction with oxygen.

When air was used as the feed gas (Fig. 3b), the total nitrogen fixation rate increased significantly to 1.69 μM min−1. Both nitrite and nitrate concentrations showed strong linearity over time, while ammonium remained negligible (Supplementary Fig. 14b). We find that the ratio of nitrate to nitrite slightly increases from 0.32 to 0.53. The continuous refreshment of the gas stream helped stabilise the system and maintain the nitrate to nitrite ratio, which otherwise might be suppressed by secondary reactions in a closed system. In contrast, nitrogen fixation rate in the closed system is 1.38 μM min−1 and nitrate to nitrite ratio is around 0.7 (Supplementary Fig. 8g, h), which demonstrates that the flow system delivers stable reaction kinetics. We further explored the possibility of the involvement of the products in further reaction. We flowed hydrogen gas into 10 mM potassium nitrate, and the reduction products are negligible (≈1 μM after 30 min reaction), which can be attributed to the sluggish radical reaction in liquid (Supplementary Fig. 15).

Herein, we further investigated strategies to selectively promote the formation of nitrogen‑containing products. In Fig. 3c, Supplementary Fig. 16, we show that in the continuous-flow system, nitrogen–oxygen mixtures selectively produced nitrate in acidic solution at an average rate of 1.03 μM min−1, with nitrite remaining negligible. In contrast, selective ammonia formation requires the introduction of hydrogen gas. Nitrogen–hydrogen mixtures produced ammonium as the dominant product, with a rate of 0.45 μM min−1. This ammonium production rate is comparable to that obtained in the closed system (0.41 μM min−1) (Supplementary Fig. 8i) but exhibits substantially improved linearity with reaction time under continuous-flow operation, indicating enhanced stability and reproducibility. We also measured the ammonium concentration in the acid trap at downstream remained below the detection limit (<0.05 ppm) even after 2 h of continuous operation indicating that no measurable ammonia is released into the gas phase during the reaction (Supplementary Fig. 17). In both cases, product concentrations were linearly dependent on time, further confirming the validity and selectivity of the sonochemical nitrogen fixation reactions. These findings demonstrate that by altering the feed gas composition, our system can selectively synthesise either nitrate or ammonium. We also checked the morphology of talc after 2 h reaction (Supplementary Fig. 4c) and observed no changes to the original structure. The element mapping of talc before and after a 2 h reaction shows similar element distribution and Si/Mg ratio (Supplementary Fig. 18), demonstrating its stability as a cavitation agent.

We then employed 15N isotopic labelling to confirm the involvement of molecular nitrogen in the reaction. In the oxidation pathway using a 15N2 gas mixture, mass spectrometry clearly revealed a signal at m/z = 63, corresponding to 15NO3− (Fig. 3d). For the reduction pathway, 1H NMR spectra showed characteristic doublet peaks at 7.05 and 7.16 ppm, consistent with 15NH4+ (Fig. 3e). These results verify that the observed nitrogen-containing products originated directly from molecular nitrogen.

From the above experiments, we draw three principal conclusions: First, gas-phase reactions dominate sonochemical nitrogen fixation, occurring within collapsing cavitation bubbles where high temperatures favour molecular activation. Second, radicals generated from water, such as OH and H, can participate in nitrogen fixation, but their contribution is significantly less effective than that of molecular oxygen interactions. However, it influences the pathway and results in product distributions that deviate from expected stoichiometric ratios. Third, the primary reaction only happens in the gas phase, making the products separate in liquid, which inhibit the products’ decomposition.

Reaction kinetics analysis
Having established the general trends in nitrogen fixation rates, we next investigated the reaction kinetics associated with bubble collapse. We first investigated reactions with both nitrogen–oxygen and nitrogen–hydrogen mixtures using different ultrasound burst periods (Supplementary Fig. 19). Optimal nitrogen fixation was observed at a 122 μs burst period (100 cycles), with the nitrate-to-nitrite ratio remaining constant at ≈0.4. The optimal fixation likely corresponds to the optimal operating state of the transducer, as previously reported in hydrogen production studies31. The invariance of the nitrate-to-nitrite ratio across burst periods strongly suggests that product formation occurs within a single bubble collapse event, on the scale of just a few acoustic cycles, and that changes in the burst period do not significantly affect the cavitation dynamics. Therefore, in evaluating the reaction mechanism, we should focus on the conditions during a single temperature spike.

To further probe the role of collapse temperature, we introduced noble gas argon (Ar), which is known to enhance hotspot temperatures during cavitation by reducing heat capacity within bubbles. Increasing the Ar fraction in air mixtures led to a pronounced rise in total nitrogen fixation, reaching a maximum at 50% Ar (Fig. 4a, Supplementary Fig. 20a). Simultaneously, the nitrate-to-nitrite ratio steadily increased from 0.32 to 0.62 with increasing Ar content. In contrast, ammonium concentrations in N2–H2 mixtures remained nearly constant upon Ar addition (Supplementary Fig. 20b). Meanwhile, both nitrate and nitrite concentrations continued to rise. However, when the Ar proportion reached 80%, nitrite became the dominant product, accompanied by a noticeable decrease in ammonia production.

This confirms that the nitrate-to-nitrite ratio is a sensitive indicator of the reaction mechanism tuned by cavitation conditions, particularly the collapse temperature. The shift in product distribution in the Ar-containing nitrogen–hydrogen system suggests a competitive interaction between hydrogen gas and water vapour. At elevated collapse temperatures, enhanced thermolysis of water vapour generates reactive OH/O radicals, which can outcompete molecular hydrogen in reacting with nitrogen species. Consequently, oxidised nitrogen products are favoured even in the absence of an external oxygen source. A similar effect can thus be inferred in the Ar-containing nitrogen–oxygen system, where the monotonically increasing nitrate-to-nitrite ratio with rising Ar content suggests increased participation of water-derived species in the reaction. This shift in mechanism likely leads to reduced overall nitrogen fixation yield, as more reactive nitrogen is diverted toward different pathways. The results thus indicate that Ar not only raises the collapse temperature but also alters the relative contribution of competing reactants, modulating both product selectivity and total yield.

In the long-term reaction (Fig. 4b, Supplementary Fig. 21), the air–argon mixture maintained strong reaction kinetics, achieving a total nitrogen fixation rate of 2.42 μM min−1, corresponding to a yield rate of 5.95 μmol h−1 in a 2.5 mL vial. Both nitrate and nitrite concentrations increased linearly, with individual fixation rates of 0.89 and 1.51 μM min−1, respectively. The nitrate-to-nitrite ratio stabilised around 0.6, slightly higher than that observed in the pure air reaction, indicating enhanced kinetics for nitrate production. However, a distinct trend was observed in the nitrogen–argon reaction system. As shown in Supplementary Fig. 22, the total nitrogen fixation rate reached 0.77 μM min−1, nearly three times that of pure N2. Meanwhile, the nitrate-to-nitrite ratio increased from 0.3 to 0.6 over 120 min, which remained notably lower than that for pure N2 (ratio ≈ 1). This shift suggests a change in the underlying reaction mechanism, likely due to the direct formation of O radicals from H2O rather than through OH radical-mediated oxidation of nitrogen species, a similar case in reaction with nitrogen-oxygen mixtures (dissociation of O2).

To correlate these observations with thermal dynamics, we employed a single-bubble model to simulate peak temperatures during a 50 μs ultrasound period under different gas compositions (Fig. 4c, Supplementary Fig. 23a). Because the system operates in the high-frequency high-intensity focused ultrasound regime with sub-micrometre talc nuclei, bubble collapse remains close to spherical, validating the applicability of single-bubble kinetic modelling. Pure Ar yielded the highest average collapse temperature (>15000 K), followed by pure nitrogen (≈7300 K), while nitrogen–oxygen and nitrogen–hydrogen mixtures showed even lower values (≈5500 K). When 50% Ar was added, the temperatures increased significantly above 7500 K, explaining the observed enhancement in nitrogen fixation and the increased nitrate-to-nitrite ratio. In simulations varying nitrogen percentages in mixtures (Supplementary Fig. 23), the peak temperature remained relatively constant. However, a clear dependence of peak temperature on acoustic pressure was observed, aligning with experimental trends in pressure-dependent nitrogen fixation. These results collectively indicate that higher spike temperatures favour nitrate formation and shift product selectivity under sonochemical conditions.

Ultrasound frequency provides a second, independent control parameter. At lower frequencies, such as 530 kHz, the resonant bubble size increases, leading to more violent collapse events with higher peak temperatures but lower bubble population density. Under these conditions, we observed distinct shifts in nitrogen fixation behaviour. Comparing air and air–argon mixtures as feed gases (Supplementary Fig. 24), the total nitrogen fixation rates were 1.16 and 2.15 μM min−1, respectively. The nitrate-to-nitrite ratio was below 0.2 for air and increased slightly above 0.2 with the addition of Ar, both significantly lower than the values obtained with the 820 kHz transducer. This indicates that lower-frequency ultrasound favours nitrite formation, consistent with a reaction environment dominated by strong but less frequent bubble collapses, where rapid quenching limits secondary oxidation steps leading to nitrate. These observations highlight that acoustic pressure and ultrasound frequency influence cavitation along two independent axes: acoustic pressure primarily affects bubble population density, altering the number of reactive microreactors; ultrasound frequency primarily affects collapse intensity, altering the temperature and radical production profile within each bubble. Together, these two parameters modulate both the rate and selectivity of nitrogen fixation through distinct and complementary mechanisms.

To quantitatively assess production, we normalised nitrogen production rates to both the effective reaction time and acoustic energy, which enables the direct comparison with other ultrasonic reactors and other nitrogen fixation methods. Based on the focused cylindrical reactor design, acoustic energy is confined within the reaction vial, improving energy utilisation. A precise 3D measurement of the acoustic pressure field was developed (Supplementary Figs. 25–27), from which the effective reaction volume was determined to be 6.16 mm3 (Supplementary Fig. 26). The energy delivery into the reaction vial was then precisely calculated by a potential energy density approximation (see details and calculation examples in Supplementary Note 2).

We also calculated the energy cost per mole of fixed nitrogen and compared it with other well-developed nitrogen fixation technologies (Fig. 4d, Table 1 and Supplementary Table 3). Under optimised conditions, our energy cost is comparable to that of the classical Birkeland–Eyde process32, ranging from 2.4 to 3.1 MJ mol−1. While this remains higher than the highly optimised Haber–Bosch process (0.5–0.6 MJ mol−1). In comparison, plasma-based nitrogen fixation methods33, often exceed 5 MJ mol−1 at ambient conditions, even with catalysts. Relative to other nitrogen‑fixation technologies, particularly industrial processes, sonochemical methods currently exhibit moderate selectivity toward nitrogen products, and improvements in energy efficiency and yield remain necessary. It is important to emphasise that the present study employs an experimental‑scale reactor designed primarily to elucidate mechanistic principles rather than to optimise performance or demonstrate scalability. Further optimisation of product selectivity, reactor design, and energy efficiency based on large-scale reactor systems needs to be explored to advance cavitation-driven nitrogen fixation toward practical implementation.

Notably, in both plasma and our ultrasound-based systems, the energy cost for ammonia production is considerably higher than for NOx production. The reduction pathway to ammonium in our system requires 20.14 MJ mol−1, consistent with the greater sensitivity of ammonia formation to the peak collapse temperature and pulse duration. These observations reinforce that direct oxidative nitrogen fixation is energetically more favourable12, although the sluggish kinetics under mild conditions limit its application. We also note that co-products such as H2, O2 (gas) and H2O2 (aqueous) are also generated from water splitting during cavitation, similar to what is commonly observed in photochemical and electrochemical nitrogen fixation systems (Supplementary Table 3). While these pathways divert a portion of the input energy, the products themselves are energy-bearing species and separable, suggesting opportunities for integrated fertiliser–fuel co-production strategies.

Dynamic reaction mechanisms
Despite the high temperature spikes during cavitation bubble collapse, reaches values sufficient to dissociate the nitrogen triple bond, nitrogen compounds such as ammonia and nitrate are stably formed. This raises a mechanistic question: how do these products survive, and how is chemical thermodynamics established under such transient conditions?

To elucidate these mechanisms, we performed density functional theory (DFT) calculations to assess the thermodynamics of nitrogen fixation under sonochemical conditions. As shown in Supplementary Fig. 28, under static high-temperature conditions, direct gas-phase reactions producing these nitrogen-containing species (NO, NO2, and NH3) are generally thermodynamically unfavourable. Therefore, the reaction energy landscape must be interpreted within a dynamically evolving thermal environment, where transient conditions can open otherwise inaccessible reaction pathways.

In classical nitrogen oxidation (e.g., combustion), the reaction proceeds via the Zeldovich mechanism (O + N2 → NO + N) at temperatures around 1500 K. However, cavitation bubble collapse can reach temperatures higher than 5000 K, making direct N2 dissociation feasible. As shown in Fig. 5a, at temperatures below 2000 K, indirect pathways are thermodynamically favoured, while direct dissociation is hindered by a high activation barrier (>6 eV). At 5000 K, the Gibbs free energy changes for both direct and indirect pathways converge, enabling multiple parallel reaction routes. In subsequent steps (e.g., NO to HNO2 or HNO3), the oxidation becomes increasingly endogenic, particularly for HNO3, which requires additional oxygenation. This supports the observation that HNO2 is the dominant nitrogen oxide product formed directly within collapsing bubbles. Furthermore, NO appears as a stable intermediate even at high temperatures, indicating its favourable formation. Its high reactivity with OH radicals or H2O can result in fixed nitrogen compounds.

This thermal behaviour also governs NH3 synthesis. As shown in Fig. 5b, the free energy for forming intermediates such as N2H2 increases with temperature, eventually becoming less favourable than direct N2 dissociation. However, the subsequent hydrogenation steps are highly exothermic and require much lower temperatures. Because NH3 decomposes above ≈773 K, continuous high temperatures would prevent its accumulation. Therefore, product formation is only viable if the system undergoes temperature quenching (dashed lines in Fig. 5b), as in cavitation collapse. This rapid quenching stabilises the products and inhibits reverse reactions, enabling the preservation of NH3 and other species.

To further validate this concept, we modelled some possible oxidation and reduction pathways at both room and elevated temperatures (Supplementary Fig. 29). At low temperatures, indirect mechanisms dominated due to the high dissociation energy of N2. At 5000 K, however, multiple pathways become thermodynamically accessible, supporting the notion that transient high-temperature spikes facilitate N2 activation, while subsequent cooling allows product stabilisation. This dynamic separation of activation and stabilisation steps is what distinguishes sonochemical nitrogen fixation from steady-state thermal systems.

To summarise, the key advantage of cavitation chemistry lies in its ability to generate transient high temperatures (Fig. 5c). Conventional thermal systems can ramp to moderate temperatures (≈1500 K) over milliseconds to minutes, enabling only indirect dissociation pathways or catalytic reactions. Even a system capable of maintaining constant high temperatures (e.g., ≈5000 K) would not enable product formation, due to the unfavourable thermodynamics of stabilising nitrogen-containing species. Instead, cavitation enables nanosecond-scale heating and cooling, matching the timescale of sequential reaction steps and decoupling the thermodynamic and kinetic limitations. Thus, short-pulse, transient high-temperature environments promote energy utilisation and selective nitrogen product formation.

Another critical aspect is the dynamic behaviour of the cavitation bubbles, which act as microscale, transient reactors. These gas-phase domains are temporarily isolated from the liquid phase but maintain continuous mass exchange. During bubble expansion, dissolved gases are rapidly taken up; upon collapse, the newly formed reaction products are expelled into the surrounding liquid. This cyclical exchange allows for the dynamic progression of chemical reactions that are otherwise inaccessible under static conditions, further enhancing the nitrogen fixation.

Methods
Materials
Commercial talc powder (average particle size ≈ 10 μm) was purchased from Sigma-Aldrich. HPLC-grade water for gradient analysis was obtained from Fisher Chemical. Gases, including argon (99.998%), nitrogen (99.998%), hydrogen (99.99%), oxygen (99.6%), and compressed air (21% ± 0.5% O2 in N2), were supplied by BOC. Prior to use, all gases were purified through a double-trap system consisting of a first trap containing 0.1 M sodium hypochlorite solution (5% active chlorine, Thermo Scientific) in 0.1 M sodium hydroxide solution (≥98%, Sigma-Aldrich), followed by a second trap containing 0.05 M sulphuric acid solution (95%–97%, Sigma-Aldrich). Nitrite concentrations were determined using a commercial modified Griess reagent (Sigma-Aldrich). Nitrate measurements involved the use of hydrochloric acid (≈37%, Fisher Chemical) and sulphamic acid (≥99%, Sigma-Aldrich) solutions. Ammonium concentrations were measured via the salicylate method, utilising salicylic acid (Scientific Lab Supply), sodium citrate tribasic dihydrate (≥99%, Sigma-Aldrich), sodium nitroprusside dihydrate (≥99%, Sigma-Aldrich), sodium hypochlorite (5% active chlorine, Thermo Scientific), and sodium hydroxide (≥98%, Sigma-Aldrich). For isotopic labelling experiments, deuterium oxide (D2O, 99.9 at.% D), was purchased from Sigma-Aldrich, and 15N2 gas (>98%) was purchased from Cambridge Isotope Laboratories.

Characterisation
The powder X-ray diffraction was measured by Bruker D8 Advance Eco Cu sourced diffractometer with a fluorescence filtering LYNXEYE XE-T detector, the voltage is 40 kV, and current is 25 mA. The morphology was characterised by a Zeiss Merlin Compact Field Emission Gun (FEG)-SE, accelerating voltage is 3 kV. The EDX mapping was performed by the Oxford Instruments Ultim Xtreme X-ray detector.

Sonochemical reaction system
In the sonochemical reactor34, a cylindrical tube piezoelectric ceramic transducer operating at 820 kHz was used to generate ultrasound. A waveform generator (Wavestation 2052, Teledyne LeCroy) was employed to produce a pulsed sine wave, which was subsequently amplified by a radio frequency amplifier (AR 125A250 RF Amplifier). In a typical experiment, the ultrasound parameters were set to 100 cycles per burst with a burst period of 2 ms, corresponding to a duty cycle of 6.1% (see details in Supplementary Note 1). The transducer and the reaction vial are cooling down by circulating cooling water (10 °C). This temperature is chosen to balance the gas solubility and reaction rate in the bulk of the solution.

Cavitation probability measurement
Cavitation probability as a function of peak negative acoustic pressure was quantified at two driving frequencies, 820 kHz and 530 kHz, for three sample media: a 1 mg mL−1 talc suspension in air-saturated water, air-saturated water alone, and degassed water. At each pressure level, a 100-cycle tone burst was delivered repetitively to the sample (N = 1000). The burst-repetition period was 2 ms at 820 kHz and 3 ms at 530 kHz. Acoustic emissions resulting from each burst were recorded using an immersion transducer (Olympus, Japan VU-V384, centre frequency 3.5 MHz) operated as a Passive Cavitation Detector (PCD) and positioned beneath the sample. The PCD signal was pre-amplified (Stanford Research Systems SR445A) and digitised using a TiePie Handyscope HS5 oscilloscope at a sampling rate of 100 MHz.

Acoustic potential energy method
Acoustic waveforms were measured using a calibrated Fibre-optic Hydrophone Systems sensor (FOHSv2, Precision Acoustics), with a fibre and active element diameter of 125 µm and 10 µm, respectively. The Fibre-optic Hydrophone (FOH) was mounted onto a 3D positioning system (3-Stepping Motor Controller, Velmex VXM) and used to scan in 0.2 mm increments along the x and y axes (normal to waveform propagation), and either 0.5 mm or 1 mm increments along z (constrictor radially converging field) for the 530 kHz and 820 kHz fields, respectively.

Nitrogen fixation experimental details
In a typical nitrogen fixation experiment, 2.5 mL HPLC-grade water containing the desired concentration of talc was loaded into a polyethylene tube (11 mm diameter) and sealed with a PTFE tee connector. The talc suspension was prepared at least one day in advance to allow any potential soluble impurities to leach into the solution prior to use. Blank control samples were collected and analysed, confirming that ammonium, nitrite, and nitrate remained below the detection limit, indicating that talc does not introduce detectable nitrogen-containing contaminants. The schematic diagram is shown in Supplementary Fig. 1. A double three-way valve arrangement allows switching between a continuous flow mode, in which the feed gas passes through the reactor and into an acid trap, and a closed mode, in which the feed gas first saturates the liquid and is then isolated for sonication. The feed gases were purified using two gas scrubbers connected in series. For the continuous flowing reaction, a 1/16-inch PTFE tube is inserted into water to keep gas purging in water (flow rate: 10 mL min−1). The minimal flow ensures stable and reproducible cavitation due to the cavitation activity is strongly localised in the focal zone. Upon completion of the sonochemical reaction, the liquid was retrieved and filtered using a syringe filter (Fisherbrand, Nylon, 25 mm, 0.2 µm pore size) to remove talc particles. The filtered liquid was then analysed using specific colourimetric reagents. For gas-phase product analysis, a quadrupole mass spectrometer (HPR-20, Hiden Analytical Ltd) with a secondary electron multiplier detector was used (ionisation energy 70 eV).

Quantification of nitrogen-containing products and hydrogen peroxide
Standard solutions were prepared by serial dilutions. The 100 ppm-N ammonia solution was purchased from Thermal Scientific (Orion 100 ppm Ammonia as Nitrogen (N) Standard). The standard nitrite and nitrate solution was prepared from homemade 1000 ppm solutions. Potassium nitrite (ACS reagent, ≥96.0%, Sigma-Aldrich) and potassium nitrate (ACS reagent, ≥99.0%, Sigma-Aldrich) were used for the standard solution preparation. The hydrogen peroxide standard solutions (1000 ppm) were prepared from a standard 35% solution (stabilised, SAFC). Then, measuring specific volumes of solutions and using volumetric flasks to prepare ammonium, nitrate, nitrite and hydrogen peroxide solutions from 1 to 0.05 ppm. The concentrations of nitrogen‑containing products were quantified using a UV-vis spectrometer (Shimadzu UV‑2600) equipped with a multicell sample compartment. Three soluble nitrogen species, ammonium, nitrite, and nitrate, were detected in this study, and their corresponding calibration curves are provided in Supplementary Fig. 2. Nitrate measurements were performed using a quartz micro‑cuvette, whereas ammonium and nitrite were analysed using polystyrene micro‑cuvettes, each with a standard 10 mm optical path length.

Ammonium concentrations were determined using the salicylate method35. In a typical procedure, 100 μL 0.55 M sodium hydroxide colouring solution (5.0 wt.% salicylic acid and 5.0 wt.% sodium citrate), 20 μL 0.01 g mL−1 sodium nitroprusside dihydrate aqueous solution, and 20 μL oxidising solution (0.75 M sodium hydroxide in sodium hypochlorite solution) were sequentially added to 2 mL sample solution. After mixing, the reaction mixtures were allowed to stand for 1 h at room temperature, and the absorbance was measured at 680 nm.

Nitrite concentrations were measured using a modified Griess method (following Sigma-Aldrich kit protocols). For each measurement, 2 mL sample solution was mixed with 1 mL Griess reagent. After standing for 15 min at room temperature, the absorbance was recorded at 540 nm.

Nitrate concentrations were determined by direct absorbance measurement after chemical pretreatment28. Specifically, 2 mL sample solution was mixed with 40 μL 1 M hydrochloric acid solution and 40 μL 0.8 wt.% sulphamic acid solution. The absorbance at 220 nm (A1) and 275 nm (A2) was recorded, and the final absorbance was calculated by A = A1 − 2A2.

Hydrogen peroxide concentrations were determined by the potassium titanium oxide oxalate (PTO) method28. To prepare the reagent, 1.5 g PTO was dissolved in 40 mL water to obtain a 0.1 mol L−1 PTO solution. For the sample measurement, take 2 mL the sample, and add 100 μL reagent. After standing for 5 min, the absorbance at 385 nm was measured.

Isotopic products measurement
The ammonium products from 15N2 were measured by Bruker Avance III 700 with a 1H inverse TCI cryoprobe equipped with a 16.44 T magnet; the frequency for 1H spectra is 699.9 MHz. The solution is prepared by mixing 50 μL 0.05 M H2SO4, 50 μL 2% 3-(trimethylsilyl)−1-propanesulfonic acid sodium salt aqueous solution, with 900 μL solution filtered after reaction. The nitrate products were measured by the BioAccord LC-MS System. Reversed-phase chromatography was performed on an ACQUITY I-Class PLUS UPLC System (Waters, Milford, MA, USA) coupled to an ACQUITY RDa mass spectrometer (Waters, Milford, MA, USA) equipped with an ESI probe, in negative ion mode.

DFT calculations of free energy profile
The computations for molecules were performed by means of spin-polarised density functional theory (DFT) methods using the DMol3 code36,37. The meta-generalised gradient approximation (m-GGA) and the M06-L exchange-correlation functional38 were employed. The All Electron core treatment was adopted, in which all electrons are included in the calculation. The double numerical plus polarisation (DNP)36 was chosen as the basis set for calculation. The convergence criteria are: (1) a self-consistent field (SCF) tolerance of 10−6 arb. u.; (2) an energy change of 10−6 Ha; (3) a max force tolerance of 0.002 Ha Å−1; (4) a maximal displacement tolerance of 0.005 Å. To ensure high-quality results, the real-space global orbital cutoff radius was chosen as high as 3.1 Å and thermal smearing with a width of 0.005 Ha was applied to the orbital occupation to speed up convergence. The Multiplicity was set according to the specific spin state of radicals.

Single bubble collapse simulation
The temperature of single spherical collapsing bubbles in water saturated with different dissolved gas mixtures was numerically investigated with the Keller-Miksis model39. The Keller-Miksis equation was solved with a fourth-order Runge-Kutta method. The initial radius of the bubble was set to 5 μm in thermal, mechanical, and chemical equilibrium with the liquid. The heat capacity ratio of the gas mixture was computed using the following: γN2 = 1.47, γO2 = 1.4, γAr = 1.67, γH2 = 1.41. The acoustic pressure at the focal point was obtained experimentally. Simulations required further inputs such as the water vapour pressure at 11 °C (liquid temperature) of 2065 Pa, water density of 997 kg m−3, water viscosity of 0.89 mPas−1, water surface tension of 0.07275 Nm−1, and speed of sound in water of 1480 ms−1.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript by Pan et al reports a novel sonochemical approach to nitrogen fixation by exploiting the transient extreme conditions generated during acoustic cavitation. The authors demonstrate that both oxidative (nitrate/nitrite) and reductive (ammonium) products can be obtained without catalysts, with selectivity tuned by feed gas composition, cavitation agents, and solution conditions. They combine experimental results, isotopic labelling, and thermodynamic modelling to propose that ultrafast thermal cycling during bubble collapse enables pathways otherwise inaccessible in conventional steady-state systems. Energy-normalized yields approach those of historical electric arc methods, offering potential for decentralized, low-carbon fertiliser production.\n\nThe concept is very interesting and could be highly impactful for sustainable nitrogen chemistry, especially given the interest in green ammonia and nitrate production. On this basis, the work seems suitable for Nature Communications. I reviewed this paper along with a couple of my research group members, and here are our collated recommendations for revisions to the paper:\n\n1. Line 130: could more details on the construction of this “closed system” be provided?\n2. Line 138: The authors claim that the introduction of talc particles lowers the cavitation threshold. It would be useful if more evidence could be supplied to support this. What effect do the talc particles have on the number of nucleating sites within the samples? Perhaps acoustic data on the bubbles would shed more light?\n3. Line 148: “…the ratio of nitrate to nitrite was found to depend on the pH of the solution, implying that nitrate is likely formed through a secondary oxidation of nitrite in the liquid phase, rather than being a direct product of bubble collapse”. The data in Figure 1d seem to imply that the primary outcome of switching to acid is to reduce the yield of nitrite, whereas the amount of nitrate produced remains unchanged within error of the amounts with talc or with no additive. Therefore, although the ratio of nitrite to nitrate is changing, this is more to do with less nitrite forming than giving any clues as to how nitrate forms. Therefore, we think this part of the paper needs revision.\n4. In lines 195–196, the authors attribute the increase in nitrogen fixation to stronger cavitation activity during bubble collapse. This explanation is somewhat vague. It is generally known that increasing the acoustic pressure increases the bubble population, while the intensity of collapse depends majorly on the frequency (which is directly related to bubble size) — a parameter that is constant in this study. Therefore, the authors should reconsider their explanation by accounting for bubble populations. Regarding the second factor mentioned in the paper here, would tests to directly measure OH concentration support the authors’ claims (although the concentration of H₂O₂ was reported, it does not directly translate to OH concentration under these conditions)?\n5. In lines 219–222, the authors claim that nitrate yields continued to increase with higher pulse energy, whereas nitrite production plateaued at ~6 mJ. No reason was provided for this observation. Is this the result of acoustic saturation?\n6. In lines 224–232, the introduction of talc, in addition to its effect on the nucleating sites for bubble formation, could also modify the nature of bubble propagation. In fact, bubble jetting is highly possible due to the potential non-uniform collapse of bubbles in the presence of talc. Also, relating jetting bubble collapse to the peak temperature inside the bubbles would shed more light.\n7. Line 248: The H2O/D2O ratio would be useful to know.\n8. Line 273-275: No \"before\" image of the talc has been provided in Supplementary Figure 16, only the images of the talc after sonication. Some EDX mapping would also be nice to see if chemical composition as well as morphology remains unchanged.\n9. Lines 262-263: do the authors mean nitrite to nitrate, instead of the other way round?\n10. Line 524: It is unclear whether the methods presented in this section are standard or if they are taken from other research articles. Either way, they should be appropriately referenced.\n11. The information summarised in Table 2 in the Supplementary information seems central to the paper’s claims. It would therefore be useful we think to put this table in the main text and discuss the results in comparison to the examples in the table in more detail in the main text.", "reviewer_2": "The authors would like to report nitrogen fixation via acoustic cavitation, a non-equilibrium technique that balances kinetics and thermodynamics for nitrogen fixation. In this work, rapid temperature ramping and quenching contribute to the production of ammonium, nitrate, and nitrite. While this is a systematic work, its originality is not strong enough. The concept of bubble collapse, which provides high transient temperatures and cooling rates to drive nitrogen activation and conversion, has been well developed in many literatures (e.g., J. Am. Chem. Soc. 2024, 146, 14765-14775). In addition, the lack of appropriate performance evaluation (such as production yield, product selectivity, and so on) makes it difficult to demonstrate the potential for practical application of this technology. The detailed comments are as follows:\n\n1. The catalytic activities are mostly determined in the form of “concentration (μM)”. It seems “Yield (mmol/h)” is a more appropriate form to reflect the activity, because it can be directly used for comparison with other methods. Therefore, the comparison of production yield between this method and other methods (including thermochemical, photochemical, electrochemical, mechanochemical, and laser-powered nitrogen fixation) is necessary. It is crucial to understand its potential for practical application.\n2. The detailed analysis of gas composition is lacking. The authors verify the existence of H2 in the gas product. What about other possible by-products such as O2, NO, and NO2? It is clear that nitrogen fixation via acoustic cavitation is complex and not readily controllable, many unexpected side reactions may happen. Furthermore, the generated gaseous by-products would reduce the product selectivity. Therefore, product selectivity should be accurately determined based on all liquid and gaseous products, not just considering ammonium, nitrate, and nitrite. Likewise, does this method have an advantage over other methods (thermochemistry, photochemistry, electrochemistry, and so on) in terms of product selectivity?\n3. The ammonium was detected in solution. Is gaseous NH3 detected in the gas product?\n4. For the optimization experiments, Air and N2 flow rates may have a significant influence on the catalytic activity. They should also be detailed studied.\n5. Bubble collapse could provide high transient local temperatures, but the bulk temperatures of the solution seem controlled by the cooling water system. Thus, the setting temperatures are important for the experimental detail, which is, however, missing in the manuscript. In addition, do the setting temperatures affect the catalytic activity?\n6. The authors set up the closed and continuous systems. Generally, industrialization requires a continuous process rather than a batch process, due to the high yield and low energy consumption. However, it is not clear whether the continuous system is superior to the closed system in this work. A detailed table comparing these two processes is necessary.\n7. In the continuous process, the stability of the catalytic activity is a vital parameter. In Fig. 3, it is hard to observe its stability. Appropriate exhibition of stability is necessary, yield (mmol/h), rather than total amount, as a function of reaction time is recommended.\n8. The usage of talc indeed improved the catalytic activity, but also resulted in the contamination issue. Is there a method to separate talc and N-containing products after the reaction?\n9. When conducting the mechanism study, the authors rely solely on the theoretical models. The in situ characterization (such as FTIR) is necessary to determine the formation of NO*, NH* intermediates.\n10. In Fig. 2c, the concentration of ammonium is much higher than the total concentration of nitrate and nitrite for some points. Considering it is under an acidic condition (i.e., [H+] concentration is higher than [OH-] concentration), how can it balance the excessive positive charges in the solution? Please explain this phenomenon.", "reviewer_3": "This manuscript presents a systematic investigation of nitrogen fixation driven by acoustic cavitation, emphasizing the gas-phase chemistry occurring during ultrasonic bubble collapse. The authors combine experimental observations with DFT calculations to demonstrate that transient high-temperature conditions (>5000 K) enable N₂ activation and formation of nitrite, nitrate, and ammonium in the absence of a catalyst. The study provides a mechanistic picture of sonochemical nitrogen fixation, identifying key factors such as gas composition, acidity, and cavitation agents in controlling product selectivity.\n\nThe results are noteworthy in that they integrate mechanistic insights with tunability of product formation, supported by isotopic labeling and modelling. However, the concept of sonochemical nitrogen fixation is not new.\n\nThe methodology is sound and well executed, with appropriate use of spectroscopic and computational tools. The data and analysis appear to support the proposed conclusions, though the extent of quantitative validation (e.g., yield comparison, radical quantification) could be clarified. The mechanistic interpretation is plausible and well argued. The methods seem sufficiently detailed to allow reproduction.\n\nRecommendations:\n1) It is not clear why the very high energy costs of nitrogen fixation by acoustic cavitation, as conducted in this study, are discussed mainly in relation to historical electric arc processes—this comparison is made three times in the manuscript. The appropriate benchmark, as noted on line 372, should instead be the Haber–Bosch process, which requires approximately 0.5 MJ mol⁻¹, compared to about 20 MJ mol⁻¹ for the acoustic cavitation process. Along these lines, a comparison of production rates and energy costs with recent developments in ammonia synthesis by electrochemically assistance using proton-conducting ceramic cells as well as by in-liquid plasma catalysis would also be of interest to the reader.\n2) The manuscript is somewhat difficult to read due to the very long captions accompanying rather small figures, as well as the large number of figures placed in the Supplementary Information. A full research article format, offering more space, would likely result in a more reader-friendly layout.\n\nIn summary, the work revisits an established but fascinating phenomenon and refines our mechanistic understanding of sonochemical nitrogen fixation. While the study is of clear scientific merit, its scope and degree of novelty make it more appropriate for a specialized journal in physical chemistry or sonochemistry rather than Nature Communications.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Response letter to reviewers' comments\nManuscript ID: # NCOMMS-25-58387A-Z\nGeneral Response to Reviewers\nWe sincerely thank the editor and reviewers for their careful evaluation of our manuscript entitled\n\"Efficient Nitrogen Fixation via Non-Equilibrium Thermodynamics Induced by Acoustic Cavitation\".\nWe fully appreciate the time and effort invested in the review process and acknowledge the\nconstructive feedback provided. A detailed point-by-point response follows.\nReviewers' comments:\nReviewer #1 (Remarks to the Author):\nThis manuscript by Pan et al reports a novel sonochemical approach to nitrogen fixation by exploiting\nthe transient extreme conditions generated during acoustic cavitation. The authors demonstrate that\nboth oxidative (nitrate/nitrite) and reductive (ammonium) products can be obtained without catalysts,\nwith selectivity tuned by feed gas composition, cavitation agents, and solution conditions. They\ncombine experimental results, isotopic labelling, and thermodynamic modelling to propose that\nultrafast thermal cycling during bubble collapse enables pathways otherwise inaccessible in\nconventional steady-state systems. Energy-normalized yields approach those of historical electric arc\nmethods, offering potential for decentralized, low-carbon fertiliser production.\nThe concept is very interesting and could be highly impactful for sustainable nitrogen chemistry,\nespecially given the interest in green ammonia and nitrate production. On this basis, the work seems\nsuitable for Nature Communications. I reviewed this paper along with a couple of my research group\nmembers, and here are our collated recommendations for revisions to the paper:\nResponse: We thank Reviewer #1 for their thoughtful and constructive comments, as well as their\npositive assessment. We appreciate the detailed technical questions regarding cavitation behaviour,\npH influence, and the effect of talc on nucleation. In response, we provide expanded details and\nschematic diagrams for the closed reactor system and acoustic field characterisation; Include new\nacoustic measurements and optical observations to quantify bubble populations and nucleation\ndynamics; Clarify the role of acidity and talc on product distribution, with updated data and discussion\nsupported by additional EDX mapping. We are confident these additions will resolve all specific\nqueries while reinforcing the mechanistic interpretation of bubble dynamics and nitrogen fixation\nselectivity.\n1. Line 130: could more details on the construction of this “closed system” be provided?\nResponse: We thank the reviewer for this helpful suggestion. We agree that the description of the\nclosed and continuous reaction configurations should be made clearer. In the revised manuscript, we\nwill expand the Methods section and include a labelled schematic illustrating both systems.\nAs shown in Fig. R1, the reaction cell consists of a PTFE fitting with one gas inlet and one outlet.\nThe inlet is connected to a 1/16-inch PTFE capillary tube that extends into the reactor solution to\nintroduce gas. A double three-way valve arrangement allows switching between (i) a continuous flow\nmode, in which the feed gas passes through the reactor and into an acid trap, and (ii) a closed mode,\nin which the feed gas first saturates the liquid and is then isolated for sonication. The acid trap uses\nthe same PTFE configuration to capture any gaseous nitrogen species formed under continuous\noperation. This arrangement enables precise control of gas composition while preventing\ncontamination or escape of reactive gas-phase products.\nWe have added a schematic diagram and corresponding description to the revised Supplementary Fig.\n1 and added a brief reference to this figure in the main text (page 5 and Methods).\nFigure R1. (new Supplementary Fig. 1 b,c) (a) Schematic illustration of the closed and continuous\nflow configurations. Red lines indicate gas lines. The system incorporates two three-way valves that\nswitch between continuous flow (gas passing through the reactor and into the acid trap) and closed\nmode (gas is first introduced to saturate the liquid, after which the reactor is isolated for ultrasound\nirradiation). The reactor cell contains a PTFE gas inlet/outlet assembly, the inlet is connected to a\n1/16 inch PTFE capillary tube submerged in the solution to ensure controlled bubble introduction and\nuniform gas dissolution. (b) The photography of sonoreactor system.\n2. Line 138: The authors claim that the introduction of talc particles lowers the cavitation threshold.\nIt would be useful if more evidence could be supplied to support this. What effect do the talc particles\nhave on the number of nucleating sites within the samples? Perhaps acoustic data on the bubbles\nwould shed more light?\nResponse: We thank the reviewer for this insightful suggestion. We agree that clarifying the role of\ntalc in controlling cavitation activity will strengthen the manuscript. Fig. R2 shows the cavitation\nprobability as a function of the peak negative pressure reached during the rarefaction phase of the\nultrasonic wave (820 and 530 kHz), both in degassed water, air saturated water and water containing\n1 mg/mL talc. In pure water, cavitation occurs randomly because it depends on the presence of\npersistent microbubbles or impurities that act as cavitation nuclei. Previous studies have reported that,\nin pure water, cavitation requires more than 30 MPa of negative pressure to take place (Phys. Rev. E,\n2015, 92, 023019). Consequently, relying on such a purely stochastic process makes sonochemical\nreactions difficult to control and predict.\nAdding talc helps initiate cavitation by introducing a fixed number of nuclei that serve as carriers of\ngas impurities. This lowers the cavitation threshold and reduces the energy needed for cavitation to\noccur. The number of bubbles generated depends directly on the number of added nuclei, which in\nturn is determined by the concentration of talc particles in the solution, a parameter kept constant in\nour experiments. When enough talc is present, the cavitation probability approaches unity, meaning\nthat cavitation occurs with every ultrasonic pulse. Under these conditions, cavitation is no longer\nrandom, energy losses are minimised, and the results become highly reproducible. Moreover, the size\ndistribution of the introduced nuclei is also more controlled compared to the random impurities or\nmicrobubbles naturally present in water, further enhancing the consistency and predictability of the\nprocess.\nIn the revised manuscript, we included a discussion in the main text (page 6) and added new data and\nreference in the supplementary information.\nFig. R2. (new Supplemnetary Fig. 5) Cavitation probability as a function of peak negative acoustic pressure\nin degassed water (green), air saturated water (blue) and water containing 1mg/mL talc (red), at driving\nfrequencies of (a) 820 kHz and (b) 530 kHz. (c) Example of power density spectra used for estimating\ncavitation probability, averaged over 1000 bursts at 820 kHz and 6.3 MPa peak negative pressure.\n3. Line 148: “…the ratio of nitrate to nitrite was found to depend on the pH of the solution, implying\nthat nitrate is likely formed through a secondary oxidation of nitrite in the liquid phase, rather than\nbeing a direct product of bubble collapse”. The data in Figure 1d seem to imply that the primary\noutcome of switching to acid is to reduce the yield of nitrite, whereas the amount of nitrate produced\nremains unchanged within error of the amounts with talc or with no additive. Therefore, although the\nratio of nitrite to nitrate is changing, this is more to do with less nitrite forming than giving any clues\nas to how nitrate forms. Therefore, we think this part of the paper needs revision.\nResponse: We thank the reviewer for this thoughtful observation. We agree that the original wording\nsuggested a mechanistic conclusion that was not sufficiently supported by the data and therefore\nrequires clarification. Upon re-examination, we confirm that nitrite concentration decreases\nsignificantly under acidic conditions, whereas nitrate remains approximately constant within\nexperimental uncertainty, resulting in an increased nitrate-to-nitrite ratio. At first glance, this may\nappear as if acidification solely suppresses nitrite formation. However, the total fixed nitrogen\ndecreases in both pure water and talc-assisted systems when the solution is acidified (Fig. R3).\nThis behaviour is consistent with the well-established salting-out effect, in which the solubility of\ngases decreases in the presence of ionic species (Ultrason. Sonochem., 2022, 82, 105860). In our case,\nthe addition of H SO reduces the dissolved concentrations of both N₂ and O , lowering the total\n2 4 2\nextent of nitrogen fixation. The key point is therefore selectivity rather than absolute concentration.\nUnder acidic conditions, nitrite formation is more strongly suppressed than nitrate. Although nitrate\nincreases only slightly (within error), its fractional contribution increases, leading to a higher nitrate-\nto-nitrite ratio, demonstrate the selectively production of nitrate.\nAs discussed in the manuscript, nitrogen activation occurs primarily inside cavitation bubbles, where\nNO is formed as a key intermediate. Nitrite and nitrate may then form either: (i) via sequential gas-\nphase oxidation during collapse, or (ii) through post-collapse aqueous-phase oxidation pathways. The\nobserved pH-dependent shift is therefore best interpreted as modulation of post-collapse liquid-phase\nchemistry, rather than evidence of nitrate forming exclusively through secondary oxidation of nitrite.\nWe have modified the relevant discussion in revised manuscripts, and added a new reference #29.\nFig. R3. The comparison of products from pure nitrogen and air in water, acidic solution (0.05 M\nH SO ) and water with talc (1 mg /mL).\n2 4\n4. In lines 195–196, the authors attribute the increase in nitrogen fixation to stronger cavitation\nactivity during bubble collapse. This explanation is somewhat vague. It is generally known that\nincreasing the acoustic pressure increases the bubble population, while the intensity of collapse\ndepends majorly on the frequency (which is directly related to bubble size) — a parameter that is\nconstant in this study. Therefore, the authors should reconsider their explanation by accounting for\nbubble populations. Regarding the second factor mentioned in the paper here, would tests to directly\nmeasure OH concentration support the authors’ claims (although the concentration of H O was\n2 2\nreported, it does not directly translate to OH concentration under these conditions)?\nResponse: We thank the reviewer for this insightful comment. We agree that the relationship between\nacoustic pressure, bubble population, and collapse intensity requires clearer explanation.\nIn our study, the acoustic pressure was varied while the frequency was held constant at 820 kHz.\nUnder fixed frequency, the collapse intensity of individual bubbles does not significantly change, but\nthe number of active cavitation events increases with acoustic pressure, due to the pressure-dependent\ngrowth and activation of cavitation nuclei (ChemPhysChem, 2010, 11, 1680-1684, Ultrasonics, 2006,\n44, e407-e410). Therefore, the observed increase in nitrogen fixation yield is attributed primarily to\nan increased bubble population rather than a change in the collapse strength of each bubble.\nTo demonstrate the role of collapse intensity independently, we performed comparison using a lower-\nfrequency (530 kHz) transducer, which generates larger resonant bubble size and thus a stronger\ncollapse event. As shown Fig. R4, the lower frequency selectively enhances nitrite production\nefficiency, resulting in only 0.2 for nitrate-to-nitrite ratio. These results suggest that lower ultrasound\nfrequency alters the selectivity of nitrogen products, favouring nitrite formation under more intense\ncavitation conditions. This indicates that lower-frequency ultrasound favours nitrite formation,\nconsistent with a reaction environment dominated by strong but less frequent bubble collapses, where\nrapid quenching limits secondary oxidation steps leading to nitrate. These two trends, frequency\ncontrolling collapse intensity and pressure controlling bubble population, are mechanistically\ncomplementary but tuneable along different axes. Acoustic pressure primarily affects bubble\npopulation density, altering the number of reactive microreactors. Ultrasound frequency primarily\naffects collapse intensity, altering the temperature and radical production profile within each bubble.\nThe relevant description has been added to revised manuscript (page 16).\nRegarding direct measurement of OH radicals: we agree that H O concentration does not directly\n2 2\nreflect OH radical concentration under these conditions. However, quantitative OH radicals probing\nin cavitating systems is challenging, because both the formation and consumption of OH radicals\noccur within the collapsing bubble, and the surviving fraction that escapes into the liquid phase is not\nrepresentative of the reactive concentration that participates in nitrogen fixation. In particular, when\nair is used, OH radicals are rapidly consumed through reactions forming nitrite and nitrate, making\nthe net measurable aqueous OH radicals misleading. Therefore, bulk-phase OH radicals detection\ncannot reliably reflect the bubble-phase radical chemistry relevant to nitrogen activation.\nFig. R4. Comparison of nitrogen fixation products with 820 and 530 kHz transducers (feed gas 50%\nair and 50% Ar. (a) Experiments using the 820 kHz transducer were conducted with a burst period of\n2 ms and a duty cycle of 6.1%, the maximum acoustic pressure is 6.77 MPa. (b) Experiments using\nthe 530 kHz transducer were conducted with a burst period of 3 ms and a duty cycle of 6.3%, the\nmaximum acoustic pressure is 6.24 MPa.\n5. In lines 219–222, the authors claim that nitrate yields continued to increase with higher pulse\nenergy, whereas nitrite production plateaued at ~6 mJ. No reason was provided for this observation.\nIs this the result of acoustic saturation?\nResponse: We thank the reviewer for raising this important point. Nitrite and nitrate originate from\ndifferent stages of the nitrogen oxidation pathway. In particular, nitrite is formed predominantly via\nthe intra-bubble reaction of NO with OH, while nitrate can be formed either directly in the gas phase\nthrough further oxidation of NO or through post-collapse oxidation of nitrite in the liquid phase. At\nlow to moderate pulse energies, nitrite formation increases because both NO and OH radicals\nproduction increase with bubble collapse intensity.\nHowever, at higher pulse energy, two effects become dominant: (i) Enhanced oxidation inside the\nbubble: The concentration of reactive oxygen radicals reaches a regime where intra-bubble oxidation\nenhances the direct production of nitrate. This limits further growth in nitrite yield. (ii) Enhanced\nsecondary oxidation outside the bubble: Higher pulse energy produces more OH radicals, shifts the\npost-collapse aqueous chemistry to favour further oxidation of nitrite to nitrate (e.g., NO ⁻ + H O →\n2 2 2\nNO ⁻ + H O).\n3 2\nThus, the plateau in nitrite and continued increase in nitrate are consistent with a shift from primary\nintra-bubble formation to secondary oxidation pathways at higher pulse energies, rather than acoustic\n\"saturation\" per se.\nWe have revised the manuscript to clarify this mechanistic interpretation (page 8).\n6. In lines 224–232, the introduction of talc, in addition to its effect on the nucleating sites for bubble\nformation, could also modify the nature of bubble propagation. In fact, bubble jetting is highly\npossible due to the potential non-uniform collapse of bubbles in the presence of talc. Also, relating\njetting bubble collapse to the peak temperature inside the bubbles would shed more light.\nResponse: We appreciate this point. We agree with the reviewer that bubble deformation and non-\nuniform collapse inevitably lead to bubble jetting towards the mentioned particles. However, as\nshown by Supponen et al. (Phys. Rev. E, 2017, 96, 033114), the collapse temperature does not show\nany clear trend as a function of the bubble deformation. Therefore, we do not expect a particular\nchange in bubble temperature, neither in turn on the development of all cited chemical reactions.\nHowever, we do believe that the energy at collapse is affected, as suggested by Supponen et al. in the\narticle above. As reported, the energy at collapse decreases with the anisotropy parameter (indicative\nof the bubble deformation).\nIn our case, given the small size of the cavitating agents (talc particles) and the relatively high driving\nfrequency (> 500 kHz), we expect the occurrence of small bubbles with resonance diameters in the\norder of 10’s of microns. These eventually detach and depart from the particles, as shown by Kwan\nat al. in a similar work (Phys. Rev. E, 2015, 92, 023019). Consequently, the bubble anisotropy\nparameter remains small (J. Fluid Mech. 2016, 802, 263-293). The bubble then collapses in the weak\njets regime, whereby the collapse energy is similar to the case of a spherically collapsing bubble.\nFinally, we could imagine a decrease in process efficiency and chemical conversion related to energy-\nrelated matter at bubble collapse, but temperature there is expected to remain stable.\nWe have added description to clarify this point (page 15).\n7. Line 248: The H O/D O ratio would be useful to know.\n2 2\nResponse: We appreciate this suggestion. Specifically, we used a 3:2 volume ratio of H O to D O. In\n2 2\na typical experiment, 1.0 mL of 99.9 atom% D O was added to 1.5 mL of H O to form the reaction\n2 2\nmedium. This ratio ensures sufficient deuterium incorporation for isotopic tracing while maintaining\nsimilar cavitation dynamics and gas solubility to the H O-only system. The exact ratio and preparation\n2\nsteps are now reported in the caption of Fig. 3.\n8. Line 273-275: No \"before\" image of the talc has been provided in Supplementary Figure 16, only\nthe images of the talc after sonication. Some EDX mapping would also be nice to see if chemical\ncomposition as well as morphology remains unchanged.\nResponse: We thank the reviewer for this helpful clarification. The SEM image of talc before\nsonication was previously included in Supplementary Fig. 4, but we agree that presenting it alongside\nthe post-sonication image would facilitate clearer comparison. We have therefore moved both\n\"before\" and \"after\" SEM images into a single comparative panel in the revised Supplementary Fig.\n4.\nIn addition, following the reviewer’s suggestion, we have conducted EDX elemental mapping of talc\nbefore and after sonication. As shown in Fig. R5, the elemental distributions of Mg, Si, and O remain\nuniform, and the Si/Mg ratios are unchanged, confirming that talc retains its chemical composition\nand morphology during sonication. No nitrogen signals were detected in the spectra or mapping,\nruling out the possibility of nitrogen contamination. These results confirm that talc functions purely\nas a physical cavitation nucleation agent rather than as a chemically active or catalytic species.\nFig. R5. (new Supplementary Fig. 18) Energy-dispersive X-ray spectroscopy (EDX) of pristine talc\n(a-c) and after 2 h sonication (d-f). For the pristine talc, element atomic ratios are N 0%, O 61.32%,\nMg 16.05%, Si 19.89%, Cu (Substrate) 2.74%. For the talc after 2h sonication, N 0%, O 54.37%, Mg\n15.35%, Si 17.83%, Cu (Substrate) 12.45%.\n9. Lines 262-263: do the authors mean nitrite to nitrate, instead of the other way round?\nResponse: We thank the reviewer for noting this ambiguity. We confirm that the intended expression\nis the nitrite-to-nitrate ratio, not the reverse. We have corrected it in the manuscript. In the continuous-\nflow configuration, the continuous refreshing of dissolved gases reduces the accumulation of gas\nproducts, which stabilises the nitrite-to-nitrate ratio by limiting back-conversion or secondary\noxidation pathways.\n10. Line 524: It is unclear whether the methods presented in this section are standard or if they are\ntaken from other research articles. Either way, they should be appropriately referenced.\nResponse: We appreciate this request for clarification. We clarify that the colorimetric assays used\nfor quantifying ammonium, nitrite, nitrate, and hydrogen peroxide follow standard analytical\nprotocols, and we have now added new references (#35 and #38) to the Methods section to explicitly\nacknowledge their established origins.\n11. The information summarised in Table 2 in the Supplementary information seems central to the\npaper’s claims. It would therefore be useful we think to put this table in the main text and discuss\nthe results in comparison to the examples in the table in more detail in the main text.\nResponse: We thank the reviewer for this constructive suggestion. We agree that the benchmarking\ndata summarised are central to positioning this work within the broader nitrogen fixation landscape.\nDue to the limitation of pages, we choose to only present our results in main text accompanying by\nthe comparison between different industrial nitrogen fixation methods. Nevertheless, we have\nexpanded the discussion to directly compare our energy-normalised yields and selectivity against\nrepresentative nitrogen fixation systems (pages 16-18).\nReviewer #2 (Remarks to the Author):\nThe authors would like to report nitrogen fixation via acoustic cavitation, a non-equilibrium\ntechnique that balances kinetics and thermodynamics for nitrogen fixation. In this work, rapid\ntemperature ramping and quenching contribute to the production of ammonium, nitrate, and nitrite.\nWhile this is a systematic work, its originality is not strong enough. The concept of bubble collapse,\nwhich provides high transient temperatures and cooling rates to drive nitrogen activation and\nconversion, has been well developed in many literatures (e.g., J. Am. Chem. Soc. 2024, 146, 14765-\n14775). In addition, the lack of appropriate performance evaluation (such as production yield,\nproduct selectivity, and so on) makes it difficult to demonstrate the potential for practical application\nof this technology. The detailed comments are as follows:\nResponse: We thank Reviewer #2 for the thoughtful comments. While we agree that transient high\ntemperatures generated during bubble collapse are well established, our work introduces a\nmechanistically distinct kinetic pathway for nitrogen fixation. Previous work only emphasised the\nrole of \"extreme\" temperature, our findings emphasise that the rate of temperature ramping and\nsubsequent rapid quenching is a key determinant of nitrogen activation under non-equilibrium\nconditions, and that cavitation provides a highly suitable environment for exploring chemical\nreactions that operate on comparable timescales. Moreover, although frameworks such as the\nZeldovich mechanism are widely used to rationalise nitrogen chemistry at high temperature, the\ncritical role of water in modulating reaction pathways during bubble collapse has not previously been\nelucidated. Our results demonstrate that the reaction proceeds primarily through gas-phase activation\ninside collapsing bubbles, rather than through bulk aqueous radical oxidation or catalyst-assisted\nroutes commonly assumed in earlier sonochemical nitrogen fixation studies. This conclusion is\nsupported by isotopic labelling, systematic variation of gas composition /cavitation-agents/solutions,\nsingle-bubble modelling, and energy-scaling behaviour. Therefore, our study not only establishes an\nenergy-efficient reaction system but also provides a systematic mechanistic analysis from a non-\nequilibrium chemistry perspective.\nWith regard to the study cited by the reviewer (J. Am. Chem. Soc. 2024, 146, 14765–14775), we agree\nthat both works are conceptually grounded in the thermodynamic requirement of high temperature\nfor N≡N bond activation. However, the physical origin of the transient high-temperature state in that\nstudy is fundamentally different. Laser-induced bubble chemistry is dominated by plasma formation\nand optical ionisation, where chemical activation is driven by photophysical excitation rather than\nchemistry during inertial collapse. Furthermore, although the laser pulse width is on the nanosecond\nscale, the effective bubble environment persists for ~100–400 μs due to plasma and thermal relaxation,\nproducing reaction conditions that differ significantly from the adiabatic, rapidly quenched, high-\npressure gas-phase environment generated in acoustic cavitation. In contrast, our ultrasound-driven\nsystem relies solely on inertial collapse, enabling precise adjustment of collapse intensity and product\nselectivity through acoustic pressure, duty cycle, and gas composition, and does not involve direct\nplasma effects.\nTo our knowledge, this work provides the first experimental evidence that nitrogen activation in\nacoustic cavitation proceeds predominantly through gas-phase collisions inside the bubble, and that\nproduct selectivity can be tuned by controlling bubble collapse dynamics. In response to the\nreviewer's suggestion regarding performance evaluation, we now include expanded discussion and\nbenchmarking of production yield and energy cost, comparing our method with other methods. These\ncomparisons demonstrate that our method is competitive among non-thermal fixation strategies,\nparticularly for oxidative nitrogen fixation under ambient conditions.\n1. The catalytic activities are mostly determined in the form of “concentration (μM)”. It seems “Yield\n(mmol/h)” is a more appropriate form to reflect the activity, because it can be directly used for\ncomparison with other methods. Therefore, the comparison of production yield between this method\nand other methods (including thermochemical, photochemical, electrochemical, mechanochemical,\nand laser-powered nitrogen fixation) is necessary. It is crucial to understand its potential for practical\napplication.\nResponse: We thank the reviewer for this important point. Our initial choice to report concentrations\n(μM) rather than yields (mmol/h) was motivated by the observation that nitrogen fixation under\nacoustic cavitation does not always proceed linearly with reaction time, particularly during the first\n10-20 minutes of operation, where gas dissolution, bubble nucleation dynamics, and initial radical\nequilibria are still stabilising. Under these conditions, directly converting concentration to production\nrate by simply scaling to mmol/h could lead to misleading or overestimated yield values (especially\nwhen we only run the reaction for short durations). Another point we need to emphasise is that the\ntime we use is the total time for reaction, which ultrasound only irradiates for a 6.1% of the total time\n(pulse mode). When comparing with other technologies, we also need to take it into account.\nFor this reason, our standard methodology uses a fixed reaction duration of 30 minutes for condition\ncomparison, and we only report the product concentration. For production rates, we only report these\nvalues in our long-duration experiments (0-2 h), where the system reaches a time-invariant steady\nstate. We use linear fitting to get the average yield value. In these cases, the rates are reported in\nμM/min, which can be directly converted to mmol/h because the liquid volume (2.5 mL) is constant\nand explicitly stated. We also note that yield-normalised metrics commonly used in catalytic ammonia\nsynthesis (e.g., mmol/g/h or mmol/cm2/h) (Nat. Rev. Methods Primers, 2021, 1, 56) are not directly\napplicable here, as the talc added in our experiments does not act as a catalyst but rather as a cavitation\nagent, and therefore does not influence reaction energetics through surface-mediated pathways. So,\nyield normalised to catalyst loading are not applicable here, as talc functions solely as a cavitation\nnucleus rather than as an active catalyst.\nImportantly, because the underlying energy input mechanism is electrical driving of ultrasound rather\nthan catalytic turnover, we use energy-normalised nitrogen fixation metrics (MJ/mol, mol /kWh) for\ncross-technology benchmarking. These metrics allow direct performance comparison with industrial–\nHaber Bosch process and other emerging processes. We note that the precise quantification of acoustic\nenergy is challenging and we use established industry standards for defining the acoustic beam\nintensity from measured 3D scans of the acoustic field to calculate the acoustic potential energy. All\nthese data can be found in Table 1 in the manuscript and notes in supplementary information. The use\nof acoustic energy is to account for potential innate inefficiencies in our prototype reactor that may\nnot be present in commercial systems (e.g., electrical and acoustic impedances, attenuation loses,\netc.).\nIn response to the reviewer's request, we now additionally report the steady-state yield rates in μmol/h\nin Table 1 and have expanded the discussion in the revised manuscript (page 15) to explicitly compare\nproduction rates across nitrogen fixation strategies, which will favour the direct comparison between\nbroad fields.\n2. The detailed analysis of gas composition is lacking. The authors verify the existence of H in the\n2\ngas product. What about other possible by-products such as O , NO, and NO ? It is clear that nitrogen\n2 2\nfixation via acoustic cavitation is complex and not readily controllable, many unexpected side\nreactions may happen. Furthermore, the generated gaseous by-products would reduce the product\nselectivity. Therefore, product selectivity should be accurately determined based on all liquid and\ngaseous products, not just considering ammonium, nitrate, and nitrite. Likewise, does this method\nhave an advantage over other methods (thermochemistry, photochemistry, electrochemistry, and so\non) in terms of product selectivity?\nResponse: We thank the reviewer for raising this important point. We have now expanded and\nclarified our gas-phase product analysis. During bubble collapse, water undergoes pyrolysis,\ngenerating H, OH, and O radicals that can recombine to form H , H O , and O . To quantify gaseous\n2 2 2 2\nproducts, we analysed the gases products after reaction using quadrupole mass spectrometry (QMS).\nAs shown in Fig. R6, a clear signal at m/z = 32 confirms the presence of O . H was observed as\n2 2\npreviously reported. We did not detect NO or NO in the gas phase, this is consistent with their known\n2\nhigh solubility and rapid hydrolysis under aqueous conditions. Thus, nitrogen oxides are retained in\nthe liquid phase rather than released as gases.\nTo ensure that additional nitrogen-containing intermediates were not overlooked, we quantified\nhydrazine (N H ) and hydroxylamine (NH OH) using established colourimetric methods: the 8-\n2 4 2\nquinolinol assay for hydroxylamine (Nat. Commun. 2024, 15, 1535) and the Watt–Chrisp method for\nhydrazine (Commun. Chem. 2021, 4, 10). In both cases, the concentrations were below the detection\nlimit (<0.05 ppm). We therefore confirm that ammonium, nitrite, and nitrate constitute the nitrogen-\ncontaining products under our reaction conditions. Importantly, the sum of concentrations of these\nproducts increase linearly with reaction time, demonstrating both steady-state operation and accurate\ncollection of all nitrogen-derived products.\nRegarding selectivity, we agree that gas-phase H and O formation reflects parallel radical chemistry.\n2 2\nHowever, these species arise from the same radical pool (H, OH, O) that drives nitrogen activation\ninside collapsing bubbles, and therefore represent mechanistically coupled rather than purely\ncompetitive pathways. In other words, water-derived radicals are not side-reactions to be suppressed,\nbut necessary participants enabling both oxidative (NO formation) and reductive (NH ) nitrogen\nx x\nfixation pathways.\nFinally, in response to the reviewer's question about selectivity relative to other nitrogen fixation\nroutes, we now include in the revised manuscript a comparative table (Table R1, Supplementary\nTable 3) summarising yield, selectivity, reaction pathway (oxidative or reductive), and operational\nchallenges across thermochemical, electrochemical, photochemical, mechanochemical, plasma, and\nsonochemical systems. This comparison highlights that our system uniquely achieves selective\nnitrogen oxidation directly from air under ambient bulk temperature and without catalysts, in contrast\nto electrochemical and photochemical systems which typically needs reactive intermediates and show\nlimited selectivity and low reaction rate in water-based environments.\nFigure R6. Mass spectroscopy results of gas products after 30-minute reaction in closed. The water\nis saturated by the feed gas (N , H , and Ar), run the reaction for 30 minutes and open the valve\n2 2\nconnected to capillary sampling inlet connected to quadruple mass spectrometry.\nTable R1 (new Supplementary Table 3.) Comparison between nitrogen-fixation approaches (In addition to Haber-Bosch, other methods are\naqueous solutions based)\nReaction\nProcess Typical Conditions Typical Selectivity Yield/Rate Challenges Reference\nType\n400–500 °C, 150–300 Very high (tonne-scale Extremely energy-intensive, centralised\nHaber–Bosch Reduction to\n(industrial) NH3 a\nfr\nt\no\nm\nm\n, F\nfo\\e\ns\\c\ns\\a\nil\nt a\\s\nl\no\ny\nu\ns\r\nts\\c\n,\ne\nH\ns\nc\no\no\nn\nn\nt\nv\ni\ne\nn\nr\nu\ns\rio\nu\ns\n), 15% per-pass i\nC\nn\nO\nfr\n2\na s\ne\nt\nm\nru\ni\nc\ns\nt\ns\nu\nio\nre\nn\n,\ns\nr\n. eliance on fossil H2, 1,2\nElectrocatalytic\nVery low selectivity (NH3 vs.\nN (a 2 q u re e d o u u c s t ) i on R N e H d 3 u ction to A tra m n b si i t e i n o t n c m on e d ta i l t i c o a n t , a lysts H lo 2 w e v fa o r l a u d ti a o ic n e c f o f m ici p e e n t c it y io ( n < ) ~ , 1– L μm ow ol r /c a m te 2 1 /s 0 −5–10−3 P st o a o b r i l s it e y l e o c f t i c v a i t t a y l y d s u t e s . t o competing HER, 3,4\n20%)\nPhotocatalytic N2\nReduction to\nAmbient condition, Weak N2 activation, low quantum\nreduction semiconductor Very low selectivity Low rate < 1–1000 μmol/g/h efficiency, poor light 5\n(aqueous)\nNH3\nphotocatalysts + light absorption/utilisation.\nPlasma reduction Ambient condition, non- Competition between reduction and\n(gas-phase or Reduction to thermal plasma Moderate, NH3 often mixed mg-g/h NH3 scale depending oxidation, NH3 decomposition in\n6,7\nplasma-liquid NH3 activating N2 + hydrogen with NOx on reactor plasma, efficiency strongly reactor-\nhybrid) source (H2 or H2O) dependent.\nBall milling with metal Moderate selectivity Gram-scale reported but Scale-up limited, mechanical wear,\nMechanochemical Reduction to\nN2 activation NH3 c\nso\na\nl\nta\\id\\ly\nc\ns\no\nt\ns\nn t\nu\na\nn\nc\nd\nt\ne\na\nr\nc\nt\niv\na\nt\ns\nio\nl\nn\n– (\nc\nd\nta\np\nl\ne\ny\nn\nd\nt/\ns\nt\no\no\nn\nic hiometry)\nf\nd\nr\ni\no\ns\nm\nco n\nb\nt\na\ni\nt\nn\nc\nh\no\nr\nu\ne\ns\na ction, e\nh\nn\na\ne\nn\nr\nd\ng\nl\ny\nin\nc\ng\no\nc\ns\no\nt\nm\npe\np\nr\nl e\nm\nx\no\nit\nl\ny\ne\n.\noften high, solid 8\nOur sonochemical\nHigh selectivity, tuneable by Up to ~0.18 mol N fixed per Mechanism control still developing,\nreaction (N2-H2 Reduction to Ambient conditions,\ngas composition and catalyst kWh, linear energy scaling requires optimisation of bubble This work\nmixtures, NH3 high-intensity ultrasound\nsurface observed dynamics and gas–liquid transfer.\naqueous)\nOxidation to\nExtremely electricity-intensive,\nBirkeland–Eyde N\nco\nO\nn\nx\nv e\na\nr\nn\ns\nd\nio n to\nE\nat\nl\nm\nec\no\nt\ns\nr\nt\np\nh\na\ne\nr\nr\nc\nic\na\nt\ni\na\nr\nc\na\nt\ni\nr\na\nt\ni\nr\n> 3000 K, Moderate selectivity (HNO3) L\nM\no\nW\nh\ne n\np\ne\ne\nr\nr\nt\ny\no n\nen\nff\ne\ni c\nH\nie\nn\nn\nc\ny\ng\nr\ne\nh\nas\nis\no\nt\nn\no\ns\nr\n. i cally 9\nHNO3\nElectrochemical Oxidation to Moderate selectivity (indirect Requires strong oxidising potentials,\nO\n(a\nx\nq\ni\nu\nd\ne\na\no\nt\nu\nio\ns\nn\n) of N2 n\ns\nit\nr\nu\nit\nt\ni\ne\no\nn\n/n\ni trate in A\nca\nm\nta\nb\\ly\ne\ns\nt/\nt\nr a\nc\nd\no\ni\nc\nd\na\ni\nl\nt i\np\no\na\nn\nth\ns\n, w ays\nr\nf\ne\na\nra\nc\nti\na\no\ni\nc\ne\np\nf\na\nf\nt\ni\nh\nc\nw\nie\na\nn\ny\nc\n)\ny\n, l\n(\no\n<w\n20 %)\n3\no\n5\nft\n-\ne\n6\nn\n0\nm\ni\nμ\nx\nm\ned\no l\nN\n/h\nO\n/g\n2\nc\n−\n/\nN\nO\n3\ng\n−\n, c\nc\no\no\nnt\np\nro\ne\nl\nt\n.\ni ng OER, poor selectivity 10,11\nPlasma oxidation\nOxidation to Ambient conditions, Wide range (ppm to % scale) Competing radicals, product\n(gas-phase or Moderate selectivity (mixture\nnitrate/nitrite in plasma discharge in air depending on reactor and overoxidation, unstable discharge 12,13\nplasma-liquid\nsolution or on water interface\nof NO2 −, NO3 −, etc) absorption conditions.\nhybrid)\nOur sonochemical Up to ~0.67 mol N fixed per\nOxidation to Moderate selectivity (mixture Further mechanistic quantification\noxidation system Ambient conditions, kWh, energy-normalised\n(air / Air–Ar\nnitrate/nitrite in\nhigh-intensity ultrasound\nof NO2 −, NO3 −, etc), suitable\nyield significantly exceeds\nneeded to improve energy efficiency This work\nmixtures)\nsolution for liquid fertiliser\nprior ultrasound reports\nand H2O2 competition.\nReferences for Table R1\n1. Humphreys, J., Lan, R. & Tao, S. Development and recent progress on ammonia synthesis catalysts\nfor Haber–Bosch process. Adv. Energ. Sust. Res. 2, 2000043 (2021).\n2. Jennings, J. R. Catalytic ammonia synthesis: fundamentals and practice. (Springer Science &\nBusiness Media, 1991).\n3. Ren, Y. et al. Strategies to suppress hydrogen evolution for highly selective electrocatalytic\nnitrogen reduction: challenges and perspectives. Energ. Environ. Sci. 14, 1176–1193 (2021).\n4. Qing, G. et al. Recent advances and challenges of electrocatalytic N reduction to ammonia. Chem.\n5. Tang, X. C. et al. Recent advances in photocatalytic nitrogen fixation based on two‐dimensional\nmaterials. ChemCatChem 16, e202401355 (2024).\n6. Sakakura, T., Murakami, N., Takatsuji, Y. & Haruyama, T. Nitrogen fixation in a plasma/liquid\ninterfacial reaction and its switching between reduction and oxidation. J. Phys. Chem. C 124, 9401–\n9408 (2020).\n7. Zhao, X. & Tian, Y. Sustainable nitrogen fixation by plasma-liquid interactions. Cell Rep. Phys. Sci.\n4, 101618 (2023).\n8. Han, G.-F. et al. Mechanochemistry for ammonia synthesis under mild conditions. Nat.\nNanotechnol. 16, 325–330 (2021).\n9. Rouwenhorst, K. H., Jardali, F., Bogaerts, A. & Lefferts, L. From the Birkeland–Eyde process\ntowards energy-efficient plasma-based NO synthesis: a techno-economic analysis. Energ. Environ.\nx\nSci. 14, 2520–2534 (2021).\n10. Chen, S. et al. Direct electroconversion of air to nitric acid under mild conditions. Nat. Syn. 3, 76–\n84 (2024).\n11. Wan, H., Bagger, A. & Rossmeisl, J. Limitations of electrochemical nitrogen oxidation toward\nnitrate. J. Phys. Chem. L 13, 8928–8934 (2022).\n12. Bradu, C., Kutasi, K., Magureanu, M., Puač, N. & Živković, S. Reactive nitrogen species in\nplasma-activated water: generation, chemistry and application in agriculture. J. Phys. D Appl. Phys.\n53, 223001 (2020).\n13. Bruggeman, P. J. et al. Plasma–liquid interactions: a review and roadmap. Plasma Sources Sci. T.\n25, 053002 (2016).\n3. The ammonium was detected in solution. Is gaseous NH detected in the gas product?\nreleased in the gas phase during sonication, we incorporated an acid trap downstream of the\nreaction vessel in the continuous-flow configuration (Fig. R7a). The trap contained 0.05 M\nH SO , such that any volatilised NH (g) would be quantitatively captured and converted to\n2 4 3\nNH + (aq). After reaction, the contents of both the reaction vial and the acid trap were analysed\n4\nusing the indophenol blue method.\nAs shown in Fig. R7b, the ammonium concentration in the acid trap remained below the\ndetection limit (<0.05 ppm) even after 2 hours of continuous operation, whereas the reaction\nvial exhibited clear accumulation of ammonium. This indicates that no measurable NH is\n3\nreleased into the gas phase during the reaction. Instead, ammonia formed inside cavitation\nbubbles dissolves rapidly upon bubble collapse due to its high Henry's law constant and strong\nacid–base buffering in the aqueous phase. The absence of NH in the gas phase is consistent\n3\nwith prior reports of sonochemically generated NH in water.\nammonium represents the total NH produced. We added related description in revised\n3\nmanuscript (page 12).\nFigure R7. (part of new Supplementary Fig.17) (a) Schematic of the continuous-flow\nsonochemical system with downstream acid trap for capturing gaseous NH . (b) UV–vis\n3\nabsorbance curves from ammonium assays of the reaction vial (solid line) and acid trap (dashed\nline), showing detectable ammonium only in the reaction solution. Conditions: feed gas is 80%\nN and 20% H , frequency is 820 kHz, and duty cycle is 6.1%.\n2 2\n4. For the optimization experiments, Air and N flow rates may have a significant influence on\n2\nthe catalytic activity. They should also be detailed studied.\nResponse: We thank the reviewer for this important point. We agree that gas flow rate is a key\nparameter in large-scale acoustic reactors where gas–liquid mass transfer and bubble seeding\ncan significantly influence cavitation dynamics. In the present work, our aim was to establish\nintrinsic reaction behaviour under controlled and reproducible conditions within a small\nreaction volume (2.5 mL). For this reason, the gas flow rate was intentionally minimised to\nmaintain a steady saturated state while avoiding turbulence and bubble coalescence effects that\nwould disrupt the focused acoustic field.\nOur reactor employs a high-intensity focused ultrasonic beam (Fig. R8a–b), and the cavitation\nactivity is strongly localised in the focal zone. When gas flow rates were increased beyond the\nminimal saturation rate, we observed that large bubbles introduced by sparging scattered and\ndefocused the acoustic energy field, resulting in reduced nitrogen fixation efficiency and\ndecreased reproducibility. Therefore, we saturated the solution prior to sonication and\nmaintained only a low, constant flow rate to preserve gas composition without disturbing the\nacoustic field.\nWe agree, however, that gas flow becomes a major optimisation parameter for larger-scale or\nnon-focused reactors, where the bubble population distribution interacts differently with the\nacoustic field. Indeed, previous work (Ultrason. Sonochem. 2022, 90, 106214) has\ndemonstrated that controlled gas sparging can increase cavitation activity in large reactors by\nmodifying the spatial extent of the active zone. We would like to clarify that: (i) In the present\nfocused microreactor, minimal flow ensures stable and reproducible cavitation. (ii) In larger\nreactors, gas flow optimisation is expected to be beneficial and will be a key focus of future\nscale-up work.\nWe have added a schematic of the reactor geometry and focal region (Fig. R8) and clarified the\ngas saturation procedure and flow conditions in the Methods section (page 23).\nFig. R8. (a) Schematic of the focused ultrasound reactor showing transducer geometry and gas\ninlet configuration. (b) 3D acoustic field mapping of the focal region, illustrating localisation\nof cavitation activity.\n5. Bubble collapse could provide high transient local temperatures, but the bulk temperatures\nof the solution seem controlled by the cooling water system. Thus, the setting temperatures are\nimportant for the experimental detail, which is, however, missing in the manuscript. In addition,\ndo the setting temperatures affect the catalytic activity?\nResponse: We thank the reviewer for raising this point. As noted in the Methods section, the\nreactor is water-jacketed at 10 °C, and direct thermocouple measurement inside the reaction\nvial shows a stable bulk liquid temperature of ~11 °C during sonication. We will include the\nexact measured temperature in the revised manuscript.\nThe effect of temperature can be considered from two perspectives: (i) Gas solubility: Lower\nbulk temperature increases the solubility of both N and O , increasing their concentration in\n2 2\nthe bubbles prior to collapse. Since nitrogen activation occurs inside the bubbles, higher\ndissolved gas concentration favours nitrogen fixation. Therefore, low bulk temperature is\nbeneficial. (ii) Bulk-phase reaction kinetics: Bulk temperature influences only post-collapse\nreactions involving longer-lived species (e.g., OH recombination, nitrite oxidation). These\nreactions occur after bubble collapse and do not determine the primary N activation pathway.\nmicroreactors (the bubbles), and is not governed by bulk heating. We have clarified this\nexplicitly in the Methods section (page 23).\n6. The authors set up the closed and continuous systems. Generally, industrialization requires\na continuous process rather than a batch process, due to the high yield and low energy\nconsumption. However, it is not clear whether the continuous system is superior to the closed\nsystem in this work. A detailed table comparing these two processes is necessary.\nResponse: We thank the reviewer for the comments. I agree that industrialisation requires a\ncontinuous process, so we only reported reaction rate data with flow system, which is related\nto comment 1. Herein, we didn't directly compare the closed and flow systems, as there is no\npotential to apply a batch mode for practical applications. In sonochemical reactions, gas\nbubbles as nuclei are necessary to get efficient cavitation, which can be created by continuously\nsparging gases. In our work, we reported some reactions in batch mode, is to use it as a model\nto investigate the reaction mechanism, which help us identify the relationship between nitrite\nand nitrate. We do not think closed system could be an option for practical applications as it\nwill be degassed after certain time of sonication. The comparison is shown in Table R2. The\ncontinuous flow system is the configuration relevant for scalable operation, and therefore all\nreported reaction rates and energy-efficiency benchmarks are based on the continuous system.\nTable R2 Comparison table summarising the differences between closed system and\ncontinuous flow system.\nFeature Closed System (Batch) Continuous Flow System\nPurpose Mechanistic investigation Practical operation & rate quantification\nGas Supply Static, pre-saturated Constant gas refresh, controlled composition\nCavitation Stability Limited, degas easily Stable due to continuous bubble seeding\nSuitability for Scale-Up Not suitable Suitable and preferred\nWe clarified this distinction in the revised manuscript (page 11).\n7. In the continuous process, the stability of the catalytic activity is a vital parameter. In Fig.\n3, it is hard to observe its stability. Appropriate exhibition of stability is necessary, yield\n(mmol/h), rather than total amount, as a function of reaction time is recommended.\nResponse: We agree that demonstrating stability is important. While our system does not\ninvolve a \"catalyst\", stability here refers to whether the cavitation intensity and bubble\npopulation remain constant over time. To address this explicitly, we performed new\ncavitation‐probability measurements (new Supplementary Fig. 5), which confirm that talc\neffectively enhances cavitation activity and renders it stable and controllable throughout\noperation. We also conducted additional material characterisation (new Supplementary Fig. 18),\ndemonstrating that talc maintains both structural and chemical integrity under sonication,\nconfirming that it functions solely as a cavitation agent rather than as a reactive or degradable\nspecies.\nUnlike heterogeneous catalytic systems, where continuous product sampling can be performed\nduring a single run, our approach involves independent experiments conducted for different\nreaction durations. The product concentrations obtained from each experiment were then\nplotted as a function of reaction time.\nThis stability of the process is evidenced by the linear time-dependent accumulation of total\nfixed nitrogen, as shown in Figs. 3 and 4. Across all 2-hour continuous-flow experiments (Air\nand N –H systems), the summed nitrogen product concentrations increase linearly with\n2 2\nreaction time, with coefficients of determination R2>0.998. This confirms that the reaction rate\nremains constant throughout the experiment and that the measured nitrogen products are\ncomplete and accurately quantified.\nIn the revised manuscript, we added R2 results for all the linear fitting (Caption of Figs. 3, 4).\n8. The usage of talc indeed improved the catalytic activity, but also resulted in the\ncontamination issue. Is there a method to separate talc and N-containing products after the\nreaction?\nResponse: We confirm that no nitrogen-containing species are introduced by the talc. A blank\ntalc suspension was prepared under identical sonication-free conditions and analysed.\nAmmonium, nitrite, and nitrate were all below detection limit. We have provided this\nclarification in revised manuscript (page 23).\nAdditionally, talc is insoluble and is removed after reaction by a 0.2 μm PTFE syringe filter, as\nstated in the Methods. No talc components were detected in the filtrate.\n9. When conducting the mechanism study, the authors rely solely on the theoretical models.\nThe in situ characterization (such as FTIR) is necessary to determine the formation of NO*,\nNH* intermediates.\nResponse: We appreciate the reviewer's interest in intermediate identification. We note that the\nreaction pathway in this system proceeds via gas-phase radical chemistry inside collapsing\ncavitation bubbles, rather than through surface-bound intermediates (NO*, NH*) that are\ncharacteristic of heterogeneous catalytic systems. The relevant species (N, O, H, NO, NH, OH)\nare formed under transient high-temperature conditions (>5000 K) and have lifetimes on the\nsub-nanosecond scale, making direct in situ spectroscopic detection in the bulk liquid infeasible.\nNevertheless, the formation of NO radicals under ultrasonic cavitation has been experimentally\ndemonstrated in previous work using spin-trapping methods such as the sodium N-methyl-D-\nglucamine dithiocarbamate iron(II) complex ((MGD) Fe2+), (J. Phys. Chem. 1996, 100, 17986-\n2\n17994).\nWe performed ex-situ ATR-FTIR on post-reaction solutions and observed bands corresponding\nto NO − and NO −, which supports the proposed reaction network but does not allow direct\n2 3\ndetection of radicals.\nFig. R9. The FT-IR spectra of products after 2h reaction with N -H and N -O mixtures, the\n2 2 2 2\nconcentration of N is 80%.\n2\n10. In Fig. 2c, the concentration of ammonium is much higher than the total concentration of\nnitrate and nitrite for some points. Considering it is under an acidic condition (i.e., [H+]\nconcentration is higher than [OH-] concentration), how can it balance the excessive positive\ncharges in the solution? Please explain this phenomenon.\nResponse: We thank the reviewer for noting this. The primary nitrogen species formed during\nbubble collapse are neutral molecules (NH , HNO , HNO ). These species are protonated or\n3 2 3\ndeprotonated only after dissolution in water, e.g., NH + H+ → NH +, HNO → NO − + H+,\n3 4 2 2\nHNO → NO − + H+. Thus, electroneutrality is maintained because the acid–base reactions in\n3 3\nthe solution provide the corresponding counterions, no net charge imbalance occurs.\nReviewer #3 (Remarks to the Author):\nThis manuscript presents a systematic investigation of nitrogen fixation driven by acoustic\ncavitation, emphasizing the gas-phase chemistry occurring during ultrasonic bubble collapse.\nThe authors combine experimental observations with DFT calculations to demonstrate that\ntransient high-temperature conditions (>5000 K) enable N activation and formation of nitrite,\n2\nnitrate, and ammonium in the absence of a catalyst. The study provides a mechanistic picture\nof sonochemical nitrogen fixation, identifying key factors such as gas composition, acidity, and\ncavitation agents in controlling product selectivity.\nThe results are noteworthy in that they integrate mechanistic insights with tunability of product\nformation, supported by isotopic labeling and modelling. However, the concept of\nsonochemical nitrogen fixation is not new.\nThe methodology is sound and well executed, with appropriate use of spectroscopic and\ncomputational tools. The data and analysis appear to support the proposed conclusions, though\nthe extent of quantitative validation (e.g., yield comparison, radical quantification) could be\nclarified. The mechanistic interpretation is plausible and well argued. The methods seem\nsufficiently detailed to allow reproduction.\nResponse: We thank Reviewer #3 for their positive assessment of the mechanistic framework,\nexperimental execution, and isotopic and modelling support. We also appreciate the\nrecommendations regarding benchmarking and manuscript presentation. We agree that\nsonochemical nitrogen fixation has been studied before, however, we respectfully clarify that\nthe mechanistic basis underlying the process has remained unresolved. Prior studies have\ngenerally interpreted nitrogen fixation under ultrasound through analogy to high-temperature\ncombustion (e.g., the Zeldovich mechanism), without accounting for the ultrafast thermal\ncycling and non-equilibrium kinetics unique to cavitation.\nOur study systematically investigated the reaction steps in the cavitation system and emphasise\nthe role of the short pulse, which really distinguishes sonochemical nitrogen fixation from any\nother methods, which also represents a new non equilibrium chemistry mechanism. Our work\nestablishes and validates a gas-phase non-equilibrium activation–quenching route inside\nindividual cavitation bubbles, which provide new understanding of nitrogen fixation through\nboth reduction and oxidation pathway. To our knowledge, this direct radical chemistry pathway\nhas not been described previously and addresses major mechanistic uncertainty in the field.\nRecommendations:\n1) It is not clear why the very high energy costs of nitrogen fixation by acoustic cavitation, as\nconducted in this study, are discussed mainly in relation to historical electric arc processes—\nthis comparison is made three times in the manuscript. The appropriate benchmark, as noted\non line 372, should instead be the Haber–Bosch process, which requires approximately 0.5 MJ\nmol⁻¹, compared to about 20 MJ mol–1 for the acoustic cavitation process. Along these lines, a\ncomparison of production rates and energy costs with recent developments in ammonia\nsynthesis by electrochemically assistance using proton-conducting ceramic cells as well as by\nin-liquid plasma catalysis would also be of interest to the reader.\nResponse: We thank the reviewer for raising this important benchmarking point. Our system\noperates mainly via the oxidation pathway (N → NO −) with air as feed gas, whereas Haber–\n2 x\nBosch proceeds via reductive hydrogenation (N → NH ). Because these two processes differ\n2 3\nfundamentally in both thermodynamics and product form, the mechanistically appropriate\nindustrial analogue is the Birkeland–Eyde (BE) electric arc process, which also forms NO\nx\ndirectly from air under high-temperature nonequilibrium conditions. This is why BE was used\nas our primary benchmark.\nWe acknowledge that the Haber–Bosch process is currently the most optimised nitrogen\nfixation technology, operating close to its thermodynamic and practical limits. In contrast, the\nsonochemical nitrogen fixation approach reported here is still at an early stage of development\nand far from being fully optimised. The system involves a large multidimensional parameter\nspace, including ultrasonic frequency, acoustic pressure, focal zone geometry, gas composition,\nreaction temperature, gas flow rate and reactant delivery, among others. These parameters\nrequire systematic investigation to approach higher efficiency. We also recognise that side\nreactions such as water splitting and hydrogen peroxide formation divert part of the energy\ninput away from nitrogen fixation. However, we note that such competing reactions are\ncommonly observed in other aqueous nitrogen reduction systems, including electrochemical\nand photocatalytic processes. To provide a clearer contextual comparison, we have now\nincluded a new comparison table in the Supplementary Information (Supplementary Table 3),\noutlining key differences among major nitrogen fixation approaches, including the referred\nelectrochemical methods and in-liquid plasma catalysis.\nOverall, while our current energy efficiency does not yet match the level of the industrial\nHaber–Bosch process, the sonochemical pathway remains promising, with substantial room for\noptimisation. Importantly, the ability to drive the process using clean electricity and to produce\nliquid nitrogen fertilisers directly from air and water presents a compelling opportunity for\ndecentralised, small-scale, and distributed fertiliser production. We believe that highlighting\nthis broader context, including both oxidative and reductive nitrogen fixation pathways, will\nbe beneficial to readers given the relevance to sustainable fertiliser manufacturing.\n2) The manuscript is somewhat difficult to read due to the very long captions accompanying\nrather small figures, as well as the large number of figures placed in the Supplementary\nInformation. A full research article format, offering more space, would likely result in a more\nreader-friendly layout.\nResponse: We thank the reviewer for this practical and constructive suggestion. In the revised\nmanuscript, we have enlarged the main figures to improve clarity. We acknowledge that the\nmanuscript contains substantial information, as our aim is to present a systematic study. To\nmaintain a clear narrative in the main text, we have retained the essential results in the main\nfigures and moved supporting but potentially distracting details to the Supplementary\nInformation. We have also carefully revised the manuscript to streamline the logic and improve\nreadability, including shortening and reorganising some sections.\nIn summary, the work revisits an established but fascinating phenomenon and refines our\nmechanistic understanding of sonochemical nitrogen fixation. While the study is of clear\nscientific merit, its scope and degree of novelty make it more appropriate for a specialized\njournal in physical chemistry or sonochemistry rather than Nature Communications.\nResponse: We thank the reviewer for their constructive evaluation and for recognising the\nscientific merit of our study. We respectfully clarify that the contribution of this work goes\nbeyond revisiting a known sonochemical phenomenon. We clarify that our work demonstrates\na direct, non-equilibrium gas-phase activation mechanism inside collapsing bubbles. This\nmechanistic distinction is supported by isotopic tracing, gas-composition-dependent product\ntuning, single-bubble cavitation modelling, DFT calculation and spatially resolved acoustic\nenergy quantification.\nTo summarise the contribution of the study: (i) Resolves a longstanding mechanistic\ncontroversy in sonochemistry. (ii) Establishes a generalisable non-equilibrium activation\nprinciple with relevance beyond nitrogen. (iii) Enables direct and meaningful cross-technology\nenergy benchmarking by developing a model to quantify acoustic energy.\nBecause the study combines elements of reaction engineering, sonochemistry, nitrogen\nactivation chemistry, mechanistic modelling, and sustainable fertiliser production, we believe\nthe work will be of broad interest to readers across catalysis, energy materials, non-equilibrium\nchemistry, and agricultural sustainability. For these reasons, we respectfully maintain that the\nmanuscript aligns well with the interdisciplinary scope of Nature Communications.\nReviewer #4 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This\nis part of the Nature Communications initiative to facilitate training in peer review and to\nprovide appropriate recognition for Early Career Researchers who co-review manuscripts.\nResponse: We appreciate Reviewer #4's participation and their acknowledgement of the joint\nreview process."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have fully addressed my comments. Therefore, from my perspective, I see no reason not to publish the paper in its current form in Nature Communications. The work is interesting and it will be of considerable import to the community in my view.", "reviewer_2": "Regarding the revised manuscript entitled “Efficient Nitrogen Fixation via Non-Equilibrium Thermodynamics Induced by Acoustic Cavitation”, the reviewer appreciates the authors’ efforts to improve the manuscript quality. However, the reviewer still considers the level of innovation to be insufficient, and technology lacks convincing prospects for practical application.\n1. In the authors’ explanation of the innovation of their work on Page 9, although the authors claimed the physical origin of the transient high-temperature state is different between their work and the previously reported literatures, these distinctions cannot be regarded as significant conceptual innovation or advancement sufficient to meet the standards of Nat. Commun.\n2. In Table R1, it is apparent that the authors selectively highlight the limitations of other methods regardless of their strengths, which is not an objective practice from a scientific perspective.\n3. In response to comment 4, the authors claimed the intrinsic reaction was implemented in a very small reaction volume (2.5 ml), with a minimized gas flow rate. If the flow is further increased, both performance and reproducibility would dramatically decrease. This demonstrates that the technology is far from being applicable for large-scale industrial production.\n4. Many of the responses to the reviewers’ previous concerns remain rather superficial. For instance, in the previous comment 6, the reviewer asked for a detailed comparison between the batch and continuous systems. However, Table R2 provides no quantitative performance comparison and presents the information solely in the form of textual statements.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Response letter to reviewers' comments\nManuscript ID: # NCOMMS-25-58387B\nReviewers' comments:\nReviewer #1 (Remarks to the Author):\nThe authors have fully addressed my comments. Therefore, from my perspective, I see no reason not\nto publish the paper in its current form in Nature Communications. The work is interesting and it will\nbe of considerable import to the community in my view.\nResponse: We sincerely thank Reviewer #1 for their positive evaluation of the revised manuscript.\nWe are grateful for their careful review and for confirming that all comments have been fully\naddressed.\nReviewer #2 (Remarks to the Author):\nRegarding the revised manuscript entitled “Efficient Nitrogen Fixation via Non-Equilibrium\nThermodynamics Induced by Acoustic Cavitation”, the reviewer appreciates the authors’ efforts to\nimprove the manuscript quality. However, the reviewer still considers the level of innovation to be\ninsufficient, and technology lacks convincing prospects for practical application.\nResponse: We thank the Reviewer #2 for their continued engagement with the revised manuscript\nand for recognising the improvements made. We have reframed the manuscript and emphasised the\nmechanic insights into the mechanism for sonochemical nitrogen fixation, which represents the\ndistinct advancement of this work. The detailed response to all the comments is listed below.\n1. In the authors’ explanation of the innovation of their work on Page 9, although the authors claimed\nthe physical origin of the transient high-temperature state is different between their work and the\npreviously reported literatures, these distinctions cannot be regarded as significant conceptual\ninnovation or advancement sufficient to meet the standards of Nat. Commun.\nResponse: We appreciate the reviewer’s high standard for conceptual novelty. We respectfully clarify\nthat the innovation of this work does not lie in the mere observation of transient high temperatures,\nbut in resolving how and where nitrogen activation occurs under cavitation conditions, and why\nacoustic cavitation is uniquely suited to nitrogen chemistry from a thermodynamic and kinetic\nperspective.\nPrevious literature has largely interpreted sonochemical nitrogen fixation through indirect aqueous\nradical pathways or by analogy to combustion chemistry, without in depth experimental and\ntheoretical investigation. Our study provides the convergent experimental and modelling evidence\nthat nitrogen fixation proceeds predominantly through non-equilibrium activation-quenching\nchemistry inside collapsing bubbles. The coexistence of oxidative and reductive pathways within a\nsingle collapse event arises from rapid quenching and efficient product transfer into the liquid phase,\ndistinguishing this mechanism fundamentally from steady-state reaction systems. This mechanistic\nresolution, supported by isotopic labelling, gas-composition-dependent selectivity, single-bubble\nmodelling, and energy scaling, is not a marginal physical distinction but a foundational clarification\nthat resolves a long-standing ambiguity in sonochemistry. We therefore believe this mechanistic\nresolution constitutes a foundational conceptual advance.\nTo more clearly present the advancement of this work, we have revised both the Introduction and\nConclusions (pages 3 and 13).\n2. In Table R1, it is apparent that the authors selectively highlight the limitations of other methods\nregardless of their strengths, which is not an objective practice from a scientific perspective.\nResponse: We appreciate the reviewer’s concern regarding objectivity. Our intention in Table R1 was\nnot to selectively emphasise the limitations of other nitrogen fixation approaches, but rather to provide\na transparent comparison of product selectivity, and yield metrics, which are evaluated differently\nacross methods and are therefore inherently difficult to compare directly.\nTo address this concern, we have substantially revised Table R1. The updated table now focuses\nprimarily on quantitative metrics, including reported or literature-derived yields and selectivity, rather\nthan qualitative assessments. Where exact values are unavailable, we explicitly state when estimates\nare used and provide appropriate references. In addition, the “challenges” column has been removed\nand the challenges only for the presented ultrasound technology is discussed. We believe this revised\npresentation offers a more balanced and objective comparison while still enabling readers to clearly\nassess how different nitrogen fixation strategies differ in mechanism, selectivity, and practical\nconstraints.\nWe now include the revised table (Table R1, Supplementary Table 3) in the Supplementary\ninformation and revised manuscript accordingly (page11).\nTable R1 (new Supplementary Table 3.) Comparison between nitrogen-fixation approaches (In\naddition to Haber-Bosch, other methods are aqueous solutions based)\nProcess Reaction Typical conditions Selectivity Yields Reference\n400–500 °C, 150–300 ≈100% selectivity\nHaber–Bosch Reduction to Tonne-scale continuous\n(industrial) NH3 a\nfr\nt\no\nm\nm\n, F\nfo\\e\ns\\c\ns\\a\nil\nt a\\s\nl\no\ny\nu\ns\r\nts\\c\n,\ne\nH\ns\n2 (\nN\non\nH\nv\n3\ne\n)\n,\n1\n5\n%\nper-pass production 1,2\nElectrocatalytic Ambient condition, 1–20% selectivity\nReduction to ~102–105 μmol h−1\nN\n(a\n2\nq u\nre\ne\nd\no\nu\nu\nc\ns\nt\n)\ni on NH3 t\nc\nr\na\na\nt\nn\na\ns\nly\nit\ns\ni\nt\no\ns\nn metal (\ne\ne\nff\ns\ni\nt\nc\nim\nie\na\nn\nt\nc\ne\ny\nd\nt\n)\nfrom faradic gcat −1 3-5\nPhotocatalytic N2\nReduction to\nAmbient condition,\n1–10% (dominated by\nr\n(a\ne\nd\nu\nu\nc\neo\nti\nu\no\ns\nn\n)\nNH3\ns\np\ne\nh\nm\not\ni\no\nc\nc\no\nn\nt\nd\na\nu\nc\nt\ns\nt\nr\n+ light\nH2 production)\n~1–103 μmol h−1 gcat −1 6\nAmbient condition,\nPlasma reduction\nnon-thermal plasma\n(\np\nh\ng\ny\nla\na\nb\ns\nr\nm\n-\ni\np\nd\na\nh\n)\n-\na\nl\ns\niq\ne\nu\no\nid\nr R\nN\ne\nH\nd\n3\nu ction to\na h c y t d iv ro a g ti e n n g s N ou 2 r + c e (H2 or\n<\nH\n2\n2\n0\n,\n%\nO3\n(\na\nn\ni\nd\nx e\nH\nd\nw\n2\ni\n)\nth NOx ~\ngc\n1\na\n0\nt −\n2\n1\n– 103 μmol h−1\n7,8\nH2O)\nBall milling with\nMechanochemical Reduction to Up to 99% (rarely\nN2 reduction NH3\nc\nH\na\n2\nt\n/\nH\n2O\nsts under N2 and\nreported)\n≈250 μmol h−1 gcat −1 9,10\nSonochemical\nAmbient conditions,\nreaction (N2-H2 Reduction to\nhigh-intensity\n<80% (estimated from 1.11 μmol h−1, 0.18\nThis work\nmixtures, NH3\nultrasound\ndetectable products) mol kWh−1\naqueous)\nOxidation to\nElectric arc at >3000 K,\nBirkeland–Eyde\nNOx and\nrapid quenching,\nNo specific data (newly ~60 MWh per tonne\n11,12\nconversion\natmospheric air\nreported data 84% NO2) HNO3\nto HNO3\nElectrochemical Oxidation to Ambient conditions, <30% selectivity\nOxidation of N2 nitrite/nitrate catalyst/radical (estimated from faradic ~10–103 μmol h−1 gcat −1 13,14\n(aqueous) in solution pathways efficiency)\nPlasma oxidation\nOxidation to Ambient conditions,\n(gas-phase or 20–99% (mixture of\nplasma-liquid\nn\nin\nit\ns\nra\no\nt\nl\ne\nu\nt\nn\nio\nit\nn\nri te p\no\nl\nr\na\no\ns\nn\nm\nwa\na\nd\nt\ni\ne\nr\nc h\nin\na\nt\nr\ne\ng\nr\ne\nf a\ni\nc\nn\ne\na ir\nNO2 −, NO3 −, H2O2)\n~10−1–105 mgNOx h−1 15-17\nhybrid)\nSonochemical\nOxidation to Ambient conditions,\noxidation system 40-70% (mixture of 27.7 μmol h−1, ~0.67\nnitrate/nitrite high-intensity This work\n(air/air–Ar\nin solution ultrasound\nNO2 −, NO3 −, H2O2) mol kWh−1\nmixtures)\nReferences for Table R1\n1. Humphreys, J., Lan, R. & Tao, S. Development and recent progress on ammonia synthesis\ncatalysts for Haber–Bosch process. Adv. Energ. Sust. Res. 2, 2000043 (2021).\n2. Jennings, J. R. Catalytic ammonia synthesis: fundamentals and practice. (Springer Science &\nBusiness Media, 1991).\n3. Ren, Y. et al. Strategies to suppress hydrogen evolution for highly selective electrocatalytic\nnitrogen reduction: challenges and perspectives. Energ. Environ. Sci. 14, 1176–1193 (2021).\n4. Qing, G. et al. Recent advances and challenges of electrocatalytic N reduction to ammonia.\n5. Yang, B., Ding, W., Zhang, H. & Zhang, S. Recent progress in electrochemical synthesis of\nammonia from nitrogen: strategies to improve the catalytic activity and selectivity. Energ. Environ.\nSci. 14, 672–687 (2021).\n6. Tang, X. C. et al. Recent advances in photocatalytic nitrogen fixation based on two‐dimensional\nmaterials. ChemCatChem 16, e202401355 (2024).\n7. Sakakura, T., Murakami, N., Takatsuji, Y. & Haruyama, T. Nitrogen fixation in a plasma/liquid\ninterfacial reaction and its switching between reduction and oxidation. J. Phys. Chem. C 124, 9401–\n9408 (2020).\n8. Zhao, X. & Tian, Y. Sustainable nitrogen fixation by plasma-liquid interactions. Cell Rep. Phys.\nSci. 4, 101618 (2023).\n9. Han, G.-F. et al. Mechanochemistry for ammonia synthesis under mild conditions. Nat.\nNanotechnol. 16, 325–330 (2021).\n10. He, C. et al. Mechanochemical synthesis of ammonia employing H O as the proton source\n2\nunder room temperature and atmospheric pressure. ACS Sustain. Chem. Eng. 10, 746–755 (2022).\n11. Rouwenhorst, K. H., Jardali, F., Bogaerts, A. & Lefferts, L. From the Birkeland–Eyde process\ntowards energy-efficient plasma-based NO synthesis: a techno-economic analysis. Energ. Environ.\nx\nSci. 14, 2520–2534 (2021).\n12. Angineni, J., Reddy, P. M. K., Anga, S. & Somaiah, P. V. Nitrogen Fixation by Simple Gling Arc\nPlasma Reactor at Elevated Pressure for Synthesis of Aqueous Nitrogen Fertilizer. Plasma Process.\nPolym. 22, 2400209 (2025).\n13. Chen, S. et al. Direct electroconversion of air to nitric acid under mild conditions. Nat. Syn. 3,\n76–84 (2024).\n14. Wan, H., Bagger, A. & Rossmeisl, J. Limitations of electrochemical nitrogen oxidation toward\nnitrate. J. Phys. Chem. L 13, 8928–8934 (2022).\n15. Bradu, C., Kutasi, K., Magureanu, M., Puač, N. & Živković, S. Reactive nitrogen species in\nplasma-activated water: generation, chemistry and application in agriculture. J. Phys. D Appl. Phys.\n53, 223001 (2020).\n16. Bruggeman, P. J. et al. Plasma–liquid interactions: a review and roadmap. Plasma Sources Sci.\nT. 25, 053002 (2016).\n17. Gromov, M. et al. Electrification of fertilizer production via plasma-based nitrogen fixation: a\ntutorial on fundamentals. RSC Sustain. 3, 757–780 (2025).\n3. In response to comment 4, the authors claimed the intrinsic reaction was implemented in a very\nsmall reaction volume (2.5 ml), with a minimized gas flow rate. If the flow is further increased, both\nperformance and reproducibility would dramatically decrease. This demonstrates that the technology\nis far from being applicable for large-scale industrial production.\nResponse: We appreciate the reviewer’s concern about the scalability. The present reactor geometry\n(2.5 mL focal volume) is not designed to represent an industrially optimised system. However, this\ndoes not undermine the relevance of the chemistry demonstrated. The purpose of the current\nconfiguration is to isolate and characterise the intrinsic non-equilibrium reaction mechanism under\nwell-defined cavitation conditions. The observation that excessive gas flow disrupts cavitation\nstability in a small-volume reactor is a known hydrodynamic limitation, not an intrinsic barrier to\nscale-up. In larger reactors, increased flow rates would be accompanied by proportionally larger\ncavitation-active volumes and appropriately designed acoustic fields, as is established in\nsonochemical reactor engineering.\nNevertheless, to ensure that the conclusions of the manuscript remain fully supported by experimental\nevidence, we have reframed the discussion to focus on mechanistic insight rather than scale-up claims.\nThe revised manuscript therefore emphasises the fundamental non-equilibrium chemistry governing\nnitrogen activation inside collapsing bubbles, which is independent of reactor size and represents the\nprimary contribution of this work.\nThe revisions can be found in page 11, where we clarify this work is based on small scale experiments\nand future research needs to be explored for practical applications. All other statements that could\nimply large‑scale applicability have been removed to avoid over‑interpretation.\n4. Many of the responses to the reviewers’ previous concerns remain rather superficial. For instance,\nin the previous comment 6, the reviewer asked for a detailed comparison between the batch and\ncontinuous systems. However, Table R2 provides no quantitative performance comparison and\npresents the information solely in the form of textual statements.\nResponse: We appreciate the reviewer’s continued attention to this point. In our previous response,\nwe clarified that several of the earlier comments extended beyond the scope of the present study due\nto the fundamentally different reaction system. Specifically, we clarified that the batch system is used\nexclusively as a mechanistic probe, whereas all performance metrics (rates, energy costs, stability)\nare derived from continuous-flow operation. A direct “batch vs continuous” performance comparison\nis not provided because batch operation is not proposed as a model to derive a performance.\nTo directly address the reviewer’s request, we have now added a quantitative comparison between\nbatch and continuous systems using identical acoustic conditions (820 kHz transducer, identical\nacoustic pressure, gas composition, and liquid volume). The comparison shows that, the continuous-\nflow system consistently delivers higher nitrogen fixation rates than the batch system for both air and\nN –H feed gases. The time linearity of product accumulation is significantly improved under\n2 2\ncontinuous flow, indicating more stable cavitation activity and sustained gas availability. Batch\nexperiments exhibit earlier deviation from linearity due to progressive gas depletion and\naccumulation effects, which limits their suitability for performance evaluation.\nTable R2 Comparison table summarising the differences between closed system and\ncontinuous flow system.\nFeature Closed System (Batch) Continuous Flow System\nPurpose Mechanistic investigation Practical operation & rate quantification\nGas Supply Static, pre-saturated Constant gas refresh, controlled composition\nCavitation Stability Limited, degas easily Stable due to continuous bubble seeding\nSuitability for Scale-Up Not suitable Suitable and preferred\nPerformance 0.41 μM/min for N2-H2, 0.45 μM/min for N2-H2,\n(nitrogen fixation rate) 1.38 μM/min for air 1.69 μM/min for air\nWe have included quantitative comparison in the revised manuscript (pages 7 and 8).\nReviewer #4 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part\nof the Nature Communications initiative to facilitate training in peer review and to provide\nappropriate recognition for Early Career Researchers who co-review manuscripts.\nResponse: We appreciate Reviewer #4's participation and their positive comment."}]

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