I was digging into old e-mails, and stumbled on a saved draft about black phosphorus, dating from several years ago. After the 2010 Nobel prize to graphene, the attention around two-dimensional materials, either single-layered, multi-layered, or grown on a bulk support, had rapidly increased, with a variety of prospective applications in many technological fields. Black phosphorus (BP) was known since 1914, as an unstable and strongly toxic material. It had been synthesized by Percy W. Bridgman, the pioneer of high-pressures (I will soon dedicate a Sunday letter to Bridgman, a mostly interesting character between physics and philosophy), by compressing ordinary white phosphorus under 12 atm at 200 °C. This irreversibly turns the transparent, P4 molecular flakes into a dark shiny solid, with a large increase in density by about 50%. The BP crystal structure was identified in 1935 to be a trigonal, graphite-like assembly of monolayers held together by Van der Waals forces. Rediscovered exactly one century later in 2014, the corrugated (puckered) two-dimensional lattice of monolayers obtained by scotch-peeling black phosphorus, or phosphorene, attracted wide attention because of its tunable bandgap (between 0.3 and 2 eV as a function of the number of monolayers), and demonstrated quite more interesting properties compared to other 2D competitors, e.g. graphene or silicene, such as quantum confinement perpendicular to the layer plane, lack of dangling bonds, enhanced surface area, a thermoelectric ZT larger than 2, and strong interaction with light. Minuscule variations of the lattice structure are sufficient to bring about new properties: this week’s Advanced Functional Materials reports a study done at the Soleil synchrotron facility in Saclay, where “blue” phosphorene monolayers (slightly different from the black allotrope) display Dirac cones like graphene. 

As a theorist, however, my interest inevitably tends to linger around some useless curiosities. The A7 trigonal layered structure, with each atom coordinated to three others in a nearly-tetrahedral pyramid, is widely adopted by group-V elements, arsenic, antimony, bismuth. Curiosity number 1: phosphorus is slightly off the mark, since its characteristic BP structure only shows up under pressure, and the “pyramid” is so much distorted to end up in a double-layer, with two of the neighbors coplanar, and the third shifted almost vertically up or down. Curiosity number 2: a “black arsenic” can also be made crystallize in that same BP structure, by cooling arsenic vapor at 100-220 °C, or by heating amorphous-As at 100-175 °C; because of the breaking of the trigonal symmetry, both black phosphorus and black arsenic are wide band-gap semiconductors, while group-V elements are generally metallic in character. Curiosity number 3: nitrogen (the lightest of the group-V elements) is the exception. Atomic nitrogen forms diatomic N2 molecules held together by a very strong triple bond, which at 946 kJ/mol is the second-strongest bond among all molecules (only the triple bond C≡O is slightly stronger). To transform N2 molecules into BP-structured nitrogen, a huge energy would be required to convert the N≡N triple bond, into a weak (160 kJ/mol) N─N single bond. This requires extreme conditions to be applied and is very difficult to achieve. However, once BP “black nitrogen” would form, with a mass density 16% higher than silicon, it would release the same huge ~800 kJ/mol upon transforming back to N2, making it a (theoretically) powerful high-density energy storage material. Yet, I fail to see how a battery could be made out of this.

But let us go back to phosphorus, an element of key importance to any life form. I dedicated a nice chapter of my book The Physics of Living Systems to ecological equilibria, from which I take inspiration for the following discussion. A bio-geochemical cycle is a way to look at how living organisms incorporate, store, and eventually get rid of, the chemical elements necessary for their survival and reproduction. The inorganic nutrients in the environment enter into the atmosphere, oceans and rocks, and are cycled through the trophic levels (where species are ranked according to “which eats which”). Each chemical element has its own unique cycle, but all of the cycles have some things in common. A reservoir is a spot in the cycle where a particular element is held in large quantities for long periods of time; in an exchange pool, on the other hand, that element is held for only a short residence time. For example, oceans are a reservoir for water, but clouds are exchange pools. In this respect, animal and vegetal species in an ecosystem are biovectors, in that they (involuntarily) serve the function of moving the elements from one level to the next in the cycle. They also act as transformers. For instance, the trees of the tropical rain forest bring water up from the forest floor, to be evaporated into the atmosphere and make new clouds. Likewise, coral endosymbionts take carbon from the water and turn it into limestone rock. Needless to say, the energy for most of the transportation of chemicals from one place to another is provided by the Sun (with a minor participation of the geothermic heat). For your physicists’ pleasure, bio-geochemical cycles can be nicely modelled by systems of coupled rate equations, this is what animal or plant ecologists do all the time.

Many of the key elements needed for life survival (carbon, oxygen, nitrogen) are directly and plentiful available in gaseous form, while other crucial elements such as sodium and potassium are easily found as soluble salts. Hence their cycles do not pose issues of availability or sequestering, at least in principle. These elements will indeed go through several chemical changes, notably oxidation and reduction, which can sometimes slow down the corresponding cycle, however they eventually will be completely recycled. The phosphorous cycle is the simplest, from the chemical point of view, but it has a peculiarity that makes it both special and critical. Isaac Asimov famously called it “the bottleneck of life”. For biological purposes, the only interesting form is the inorganic phosphate oxide, PO4. In fact, white phosphorus is very easily oxidized to PO4, and it normally appears as an uninviting yellowish cake, a bit like rotten butter. Phosphate oxide is a heavy, non-volatile molecule, which is always either incorporated into an organism, or dissolved in water, or sequestered in a rock where it combines with calcium, silicon, magnesium and other species. When a phosphate rock is exposed to water, especially at a slightly acidic pH, the rock is weathered out, and phosphate slowly goes back into solution. Phosphorus is an important constituent of cell membranes, of DNA, RNA, and ATP/ADP. Animals obtain all their phosphorous from the food they eat, also using it as a component of bones, teeth or shells. When animals and plants die or expel waste, their reserve of phosphate can be returned to the soil or water by the action of the bacterial decomposers; there, it can be taken up by another plant and used again. This cycle will continue, but with a substantial amount getting progressively lost to the sea by environmental weathering. Actually, it is not a chance that about 85% of all the biomass thrives in the sea and only 15% lives on the Earth’s surface. Eventually PO4 or its organic-transformed forms (phospate esters, phosphites etc.), being much heavier than water, will settle on the ocean floor and become part of the sedimentary rocks that, some million years later, will come back to the surface. It is such long time that practically makes phosphorus a non-renewable resource, at least on human time scale.

Liebig’s law, or the law of the minimum, is a principle developed in agricultural science by Carl Sprengel (1828) and later popularised by the German chemist Justus von Liebig, often considered the founding father of organic chemistry. The principle states that population growth (as in insects, mushrooms, men…) is not controlled by the total amount of resources available, but by the single, most scarce resource. This acts as a limiting factor for growth, and could be either a whole resource (e.g. bread, or gasoline) or just one chemical element. The very example of the latter is phosphorus, an element for which no known natural or synthetic input can stand in. Various soils contain between 0.2-0.8% phosphorus, about half of it easily available in organic form, but a typical plant like the Alfalfa (luzerne, for the French out there) can thrive in a soil containing even ∼0.1% phosphorus. However, the plant’s living structure contains about 0.7% phosphorus. Such a large concentration of one chemical element (0.7/0.1 = 7) is quite special, since all other elements for the plant are below or close to 1 in their need/supply ratio. This means that the plant must get rid of their excess. On the contrary, whenever the concentration ratio for any substance is greater than 1, it means that that particular substance – to be extracted from the environment – could be a limiting factor in the multiplication of living things. To survive, the organism must collect it, rather than get rid of it, and this element can turn into a bottleneck to survival, if not readily available. When comparing concentration ratios for animal tissues, for example with respect to seawater, values well above 1 are found for carbon (2,000), nitrogen (19,000), iron (3,500); some other elements have values higher than 1, such as silicon and calcium (both ~17), and potassium (~6). We animals use a lot of energy to accumulate all the chemicals necessary to build up our complex bodies. However, concentrating such elements is not difficult in principle, since they are biologically available in various forms. The problem is, again, phosphorus. Animals can eat plants and other animals, to get phosphorus from food (most likely as orthophosphate H2PO4); however, when inorganic phosphorus is locked in a grain of sand it is not readily usable, while plants constantly need their supply from the soil, in order to become food for higher trophic levels. All the useful phosphorus a plant can eat is actually recycled from dead organic matter waste by various decomposers, worms and bacteria. For plants, phosphorus availability is the bottleneck. And such it is for us, who occupy higher trophic levels.

Under equilibrium ecological conditions, animals excrete food residuals as pee and poo, and in this way all the chemical elements not retained in the organism are returned to the Earth’s soil, more or less around the very place from where they were extracted. It is estimated that biomass retains about 10 grams of phosphorus per kg of tissue (that’s an average between P-rich and P-poor tissues of any animal or plant, in higher animals 70-80% of it is found in bones), hence about 5 billion tons of phosphorus remain constantly concentrated in organic form, trapped in the Earth’s biomass. We humans represent about 0.1% of Earth’s biomass (definitely its most poisonous fraction), therefore we distract 5 million tons from the P count. Estimates of World’s P consumption in food are in the range of 2-3 million tons/year, which means that we recycle about half of the P mass in our body in a year, that is about 1 gram/day per person. This was not a problem in the ancient rural world, which knew no toilets, plumbing and sewers. But in our civilized world we get rid of our pee/poo by flushing it into the dark. And in this way tons after tons of precious, non-renewable phosphorus never return to the soil where they were found, but just run into the sea (a medium-size city like Lille and its surroundings produces about 700 tons – a pile 10m in diameter and 10m high – of human excrement PER DAY). Today there are options to recover phosphorus from the waste, however the cost is about 4 to 10 times that of a conventional fertilizer (not counting the heavy CO2 footprint of the process…). More futuristic options seek genetic modifications to create plants capable of breaking down phosphorus from the soil conglomerates.

Historically, farmers relied on natural organic phosphorus from the soil to grow crops, to which they added manure (both animal and human). Over time, however, soil degradation and population increase led to searching for external sources of phosphate fertilizers, such as bird-produced guano, and most importantly, rocks. Especially the latter has been a cheap and plentiful source (phosphate rock extraction doubled between 1970 and 2010, and it is today worth 15 times that in 1940), which contributed a dramatic increase in global crop yields, and saved millions of humans from starvation. While P is the 11-th most abundant element on the planet, however the sites where it is available in sufficient quantity and concentration, are relatively scarce. It is estimated that about 2 billion tons of P from the Earth crust are practically accessible and useable, about 70% of reserves being concentrated in a 300-km strip north of Marrakech, Morocco; another 15% spread among Maghreb, China and Russia; and smaller to negligible amounts elsewhere. As far as industrial production, China is the largest (85 Mtons in 2022), Morocco is second (40 Mtons), USA third (21 Mtons) although being only 13th in reserves. In all, we are – at best – safe for just about 2-3 centuries. Back in 1938, Franklin D. Roosevelt had already addressed the US Congress with a cautious alert about the strategic role phosphorus plays in a country’s economy. “The disposition of our phosphate deposits should be regarded as a national concern,” he said. “This nation [must] exercise foresight in the use of a great national resource heretofore almost unknown in our plans for the development.” Nearly nine decades on, the phrase “heretofore almost unknown” still echoes in discussions about phosphorus. Meanwhile, phosphate rock has emerged as a globally traded commodity linked to a diverse set of politically-charged debates, ranging from environmental degradation, to threats to human health, to food security and agricultural sovereignty.

Some thoughts for the next time you will flush your toilet.

Where your phosphorus ends

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