Fertilizer from air plasma

What a strange feature of our world that the nitrogen-nitrogen triple bond is so strong, almost 1 MJ/mol. Virtually every molecular machine in every organism on the planet is built on a backbone of single nitrogen atoms, while virtually all environmental nitrogen is bound as N₂. That sets up a dynamic where the cleavage of the N≡N bond to bioavailable N is a limiting step for virtually all life on earth.

For biology, splitting nitrogen is a tall order, the province mostly of unusual microbes (diazotrophs) who harbor one version or another of the jaws-like enzyme nitrogenase. Nitrogenase can split N≡N only by reducing it to NH₃, which is challenging to orchestrate biochemically—it ends up costing 8 ATP per N (or ~400kJ/mol NH₃), plus the metabolic cost of the hydrogen. That makes dinitrogen cleavage relatively rare in nature and keeps bioavailable nitrogen scarce^[1].  

So when we want to accelerate the growth of plants, we need to supplement N. That is, of course, the story of synthetic nitrogen fertilizers, which everyone knows at least in outline: how manure and guano used to be a strategic assets, how we used to blast nitrogen in giant energy guzzling electric arcs to try to break it apart until noble Bosch and self-loathing Haber invented their process to reduce dinitrogen with hydrogen to ammonia, a process which now supports over 50% of food production—and therefore is life support for about 4.5 billion people today.^[2] 

Here's the strange thing. Despite Haber-Bosch’s prevalence, it’s arguably solving a harder problem than it needs to. We spend ~1% of world energy to make the hydrogen to feed Haber Bosch, so we can then reduce N₂ to NH₃. But organisms don’t need reduced N. For the most part, all they need is bioavailable N.

Nitrogen can also be oxidized out of the N₂ state (to nitric oxide, as well as nitrates^[3] etc.). We do this at huge scale now in the Ostwald process—taking about 10% of the world’s NH₃ (recently reduced at great expense) and then oxidizing it so we can make nitrate fertilizers. But that loop (of reduction and then oxidation) is a big waste of free energy. From first principles, there’s no reason the oxidation couldn’t have started directly from N₂.

In fact, from a thermodynamic standpoint oxidizing N₂ to bioavailable nitrogen oxides should be an easier task than making the hydrogen and reducing N₂ with it. Far easier; nitrogen oxidation would happen spontaneously in air and water if not for kinetic limitations imposed by the ultra-strong N≡N triple bond.^[4]

From this perspective, the use of hydrogen in Haber-Bosch is clearly a waste of energy: in Haber-Bosch, about 0.4 MJ of otherwise useful hydrogen energy is supplied per mol N, yet the formation of nitric oxide at STP only requires <0.1 MJ per mol N. A more direct approach would be to cut out ammonia synthesis entirely and produce nitric oxide from the N₂ and O₂ found in cheap, abundant air.

To chemists back in the era of guano islands, this looked like the most direct path. The Birkeland-Eyde process (1903, a decade before Haber-Bosch) attempted to crack N₂ to NO in air using an arc discharge, which created a thermal plasma at several thousand degrees Kelvin. Yet at those temperatures the desired product, NO, is quite unstable; even with rapid quenching to ~1000 C to suppress reverse reactions, Birkeland-Eyde only achieved percent-scale conversion to NO. The net result was poor energy efficiency: even recovering some of the heat in the quenching process, Birkeland-Eyde required an energy input around 2.4-3.1 MJ/mol NO—about 30 times more than the formation energy at standard temperature and pressure.

Could we do better with a non-equilibrium plasma? After all, the key problem with Birkeland-Eyde is the mismatch in bond energies between NO and N₂; conditions that dissociate N₂ invariably also dissociate NO. The key to higher conversions might be getting the N₂ molecules vibrationally “hot” so that they’ll crack while keeping the NO molecules vibrationally “cold”. The analogous technique in the optical context is like a “molecular harp” – shining a light at the right frequency to pluck at the vibrational modes of some molecules but not others.^[5] In the plasma context, this technique isn’t as far-fetched as it might sound. Back in 1980, a group of Soviet scientists claimed to have done it with N₂ and O₂.^[6] Specifically, they claimed that by coupling microwaves into a plasma via its electron cyclotron resonance, excited electrons would preferentially transfer energy to the N₂ molecular vibration, rather than rotations and translations. Crucially, energy flows preferentially into the N₂ vibrational frequency, but not the NO vibrational frequency. N₂ at high vibrational temperature would then crack into atomic N and subsequently react with O₂ to form NO. By pumping energy mainly into the vibrational modes of the reactants, their process supposedly required a very low energy input of 0.3 MJ/mol NO, and yielded ~15% conversion of reactants to products (mostly NO). This impressive energy input figure is only 3x the thermodynamic minimum, is 10x more efficient than Birkeland-Eyde, and handily beats the best fully “green” ammonia-based schemes, which require 0.6 MJ/mol NO [4]. It’s not out of the question that a refined version of this process could compete against the incumbent Haber-Bosch + Ostwald route from N₂ to nitrogen oxides.

But there are two unfortunate caveats. The first is that nobody has reproduced the plasma results from 1980.^[7] In fact, none of the recent works appear to have improved on even the vastly higher ~2.4 MJ/mol NO achieved by the century-old Birkeland-Eyde process!^[8] The second caveat is that the 0.3 MJ/mol NO figure of merit from 1980 draws a very small control volume around the actual plasma chamber; the figure doesn’t include the energy cost of the liquid nitrogen cooling applied in that apparatus, nor the energy cost of recompression from the low-pressure plasma. The latter might be small, whereas the former (cooling) could be substantial, depending on the details.

What should we make of all this? The whole field of non-equilibrium plasma chemistry certainly has shades of cold fusion. Other Soviet publications in the 1980s claimed that they could split CO₂ into CO + O with 90% efficiency by similarly targeting specific vibrational modes in microwave plasma, another process that (if replicable) could contribute to an epochal shift in the chemical industry. But as with the plasma production of NO, the CO₂ splitting results have not been reproduced (the best modern efficiencies are still below 50% .^[7] ).

At the same time, it’s likely that relatively few faithful attempts have been made to recreate the plasma conditions for N₂ oxidation, at least for the case of NO production, because frankly the experiment looks pretty challenging. The apparatus was complicated by the need for a high magnetic field, high microwave frequency, and cooled reactor walls. Think a freakish combination of microwave oven, arc welder, MRI machine, and chemical reactor. The ratio of microwave electric field to pressure (10-100 Torr) had to be tuned appropriately to allow electrons to complete their cyclotron resonances in the applied field (1.2 T; cyclotron frequency 37 GHz) and reach adequate electron temperatures and ionization fractions, but also suppress intermolecular collisions which lead to vibrational-translational relaxation. (The whole scheme would be for nothing if the excited vibrational states are allowed to thermalize more broadly). The plasma conductivity, magnetic field, and microwave frequency had to be appropriately selected to achieve high (90%) microwave coupling to the cyclotron resonance, as opposed to reflection by or transmission through the plasma. All of this is guided by theory that is now explained in textbooks [4], but I wonder how much of it is correct. The experimental phase space is rather large—the Soviets used a 1:1 N₂:O₂ feed ratio, and 30W of microwave stimulation (claiming  90% microwave absorption in the plasma) either continuous wave or pulsed (300ns, 1000Hz, 30 kW peak). These knobs can presumably all turn in many ways, and it’s unclear if the researchers at the time (or even now) know what would be best.

Somebody should probably revisit both theory and experiment for non-equilibrium plasma production of NO. As demanding as they may be, the experiments would not be nearly as hard as e.g. controlling plasma currents in tokamaks for D-T fusion. It could be that the substantial (and thus far still unrewarded) progress in that field could be adapted to quickly disprove or improve on the 1980s work. If the results could be theoretically understood and reproduced, one could then try to optimize the setup. For instance, is the liquid nitrogen cooling really required to keep the reaction temperature low? (The gas temperature already supposedly reaches ~1000 K [4]. Could water or other cooling be used, or would this interact too strongly with microwaves?) Is it possible to achieve a high plasma efficiency at higher pressures by appropriately increasing microwave electric field to maintain electron temperature, increasing microwave frequency (e.g., with a gyrotron and a higher magnetic field) to yield smaller cyclotron orbits, and increasing flow rate to decrease residence time? The apparatus is complex and somewhat expensive, and likely doesn’t offer much room to improve on throughput, so I don’t have high hopes that this method would displace Haber-Bosch + Ostwald—but it’s hard to say this a priori, and the risk-adjusted return of this research could be very high compared to a lot of the energy R&D projects we undertake now. Alexander Fridman, one of the authors on the original 1980 plasma paper and author of a seminal textbook ^[9] is still a professor at Drexel; it might be interesting to learn what he thinks about all this.

This plot is doing a lot of apples to oranges. The biological values concatenate some rosy assumptions and seem to neglect proton costs, mettalocomplexes may be inefficient but capable of donating nitrogen to form amides or amino groups directly, etc. But it shows the huge promise—and huge error bars—in non-thermal plasma. Figure from Cherkasov et al., “A review of the existing and alternative methods for greener nitrogen fixation” .

For completeness, we might also consider purely thermal production of NO from air using temperatures of ~3000 C, as achieved in the Birkeland-Eyde plasma. After all, we know a lot more about high-temperature materials than we did in 1903, and we have more compelling ways to deliver high-temperature heat. Even so, the percent-scale conversion to NO (this figure seems to be the literature consensus for an equilibrium process) would be killer. We’d need amazing counterflow heat exchangers that recover nearly all of the input heat, since we’d be heating up ~100x more gas than stoichiometrically “necessary” for the reaction. To boot, these thermal approaches are already at equilibrium on the market for ideas, with a startup and a few research projects out there looking to “modularize” fertilizer production. While that might be an attractive vision for self-sufficiency or eutrophication reasons, economies of scale in fertilizer production are stark for a reason—true even if the underlying process weren’t an order of magnitude worse. So we consider thermal plasma fertilizer production likely DoA.

As often happens to our inquiries, on the sci-fi side here (nonequilibrium plasma) we have too much upstream scientific risk. On the ho-hum but practical side (thermal plasma) the reward would be small to nonexistent. So this is another topic that’s dead for our purposes.

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