Plaster of Paris and lime mortar are widespread, cheap, rigid materials that can be easily shaped, especially before they harden. But they don’t harden that much. What if we could harden them further, once they were shaped, or otherwise strengthen them?
In all of what follows, it’s worth keeping in mind that the material produced can be formed either as a solid or, sometimes more easily, as a foam. Solid foams can permit faster permeation of liquid reagents, permitting the reaction throughout the whole material of a reagent that would otherwise only be able to reach the surface, and can also have superior mechanical properties in some applications.
The simplest way to alter such objects’ material properties is to coat them with a liquid or gel which then adheres to them. For example, portland-cement mortar, calcium-aluminate mortar, magnesium-phosphate mortar, shellac, wax, sodium silicate, paint, or glued paper. Often a shell of a hard, dense, or tensilely-reinforced material around a lightweight, rigid core provides better tradeoffs of strength and weight, and sometimes even better absolute resilience to impacts, than either material could alone.
The material in my note on globoflexia goes into considerably more detail about this family of construction, as well as the note in Dercuano about sandwich panels.
Plaster is fairly porous, lime a bit less so unless you find some way to foam it. You can make plaster even more porous by the expedient of making it with more water. These porous substances can have their pores infiltrated with other substances, such as polymerizing resins; vacuum or high pressure may be a useful way to make this infiltration more complete.
Other useful infiltration materials might include thermoplastics, paraffin wax, molten sulfur, and reagents for replacement reactions.
As I mentioned in Dercuano, there are many anions that precipitate as water-insoluble solids (chart) when confronted with polyvalent cations such as calcium, magnesium, iron, copper, zinc, titanium, manganese, boron, or aluminum. Anions with such behavior include phosphate, carbonate, alginate, silicate, sulfide, and also usually hydroxide and occasionally oxalate or sulfate (with barium or calcium).
In the note there on “Likely-feasible non-flux-deposition powder-bed 3-D printing processes”, I suggested using binder jetting to exploit these reactions to instantly cement powders. But a possibly even more interesting possibility is using such reactions to change the properties of an already-existing object made from, for example, plaster of Paris or lime. For example, tadelakt is made by precipitating calcium stearate (etc.) in a lime surface from soluble stearates (etc.) such as that of sodium or potassium, then burnishing the surface; thus lime is waterproofed.
It might be reasonable to use other semi-soluble or semi-solid sources of polyvalent cations as well, such as gelatinous aluminum hydroxide, or iron metal in the case of phosphate conversion coating.
There are lots of phosphates, many water-insoluble, hard, and refractory, even without getting into pyrophosphates, metaphosphates, and polyphosphates. A wide variety of phosphate minerals exist in nature.
I’ve gone into some details on possible combinations in the note mentioned above. Perhaps you could, for example, apply a solution of diammonium phosphate, monoammonium phosphate, or trisodium phosphate to an object made of plaster of Paris, calcium hydroxide, or calcium carbonate, and thus get a harder object made partly or wholly of calcium phosphate. The ammonium-carbonate combinations seem particularly appealing, since it can be thermally decomposed to fairly harmless materials. Phosphoric acid probably would not work on plaster of Paris, and although it reacts with calcite (same source), I’m not sure it strengthens the material in the process.
One thing that does not work is ordinary hardware-store aqueous phosphoric acid at room temperature and pressure; after a couple of days no change was observable, and the plaster crumbled just as easily as before. This is in retrospect completely obvious: commercial phosphoric acid is prepared by precisely this reaction, in reverse. I’ve now gradually added enough baking soda to mostly convert the phosphoric acid into some kind of gel; we’ll see if the phosphate of soda presumably now dominating the scene is any more effective at phosphating the calcium.
Gelatinous aluminum hydroxide is another appealing target for this kind of phosphate replacement reaction, since it is so easily molded; perhaps it would yield extremely insoluble and refractory aluminum phosphate (whether berlinite or in some other form, most likely an amorphous one), along with either caustic soda or easily-boiled-off aqueous ammonia. Maybe some such reaction would be useful for preventing neutral-electrolyte aluminum-air batteries from getting clogged up with slime.
Although as a mineral its Mohs hardness is 6, magnesia or periclase is a cheap “crushable ceramic” commonly used for electrical insulation of heating elements due to its high thermal conductivity, and experiments have been done reacting it in this way with monoammonium phosphate; they explain:
Phosphate cements possess mechanical and chemical properties that are superior to those of ordinary hydraulic (Portland) cements, … The reaction between a reactive form of magnesia and acid ammonium phosphate is very rapid and exothermic, and the materials cannot be practically used as such. Thus, the use of calcined or deadburned magnesia is suggested.
This is music to my ears, since of course instantly setting cements are precisely what I most want for 3-D printing. Also, they mention that struvite, the very soft ammonium magnesium phosphate that I feared would be formed from such reactions, does in fact form, but decomposes to monomagnesium hydrogen phosphate at 55° by losing its water and ammonia!
To retard the setting and permit molding, and in particular to avoid increases in temperature that would be fatal to their waste-immobilization purpose, they include boric acid as a setting retardant. They also included sodium tripolyphosphate, to increase strength and reduce porosity, sand, and grinding dust (probably mostly aluminum oxide and steel, with significant amounts of fiberglass); the monoammonium phosphate:water:magnesia relationship seems to have been 3:2:4, probably by weight.
They report final compressive strengths in the 20–40 range (MPa, I assume), and tensile strengths in the 1–2.5 MPa range.
Another 2011 paper explains:
Magnesium phosphate cements (MPCs) have been extensively used as fast setting repair cements in civil engineering. They have properties that are also relevant to biomedical applications, such as fast setting, early strength acquisition and adhesive properties. However, there are some aspects that should be improved before they can be used in the human body, namely their highly exothermic setting reaction and the release of potentially harmful ammonia or ammonium ions...
They also used borate (as sodium borate) as a retardant, and also used larger grains of phosphate salt. They reported that monosodium phosphate rather than phosphates of ammonium gave an amorphous result instead.
Very interestingly, this also mentions “apatitic calcium phosphate cements”, which have been investigated by the same authors and others as possible bone cements.
Yet another paper, this one in 2015, reports on 3-D printing:
Strontium ions (Sr²⁺) are known to prevent osteoporosis and also encourage bone formation. Such twin requirements have motivated researchers to develop Sr-substituted biomaterials for orthopaedic applications. …developing Sr-substituted Mg₃(PO₄)₂-based biodegradable scaffolds. … powder printing, followed by high temperature sintering and/or chemical conversion…. strength properties of 36.7 MPa (compression), 24.2 MPa (bending) and 10.7 MPa (tension) were measured.
They were using powdered trimagnesium diphosphate with strontium replacing varying amounts of magnesium (up to ⅓), sintering it, crushing it, 3-D printing it with a bit of hydroxypropylmethylcellulose, depowdering it, sintering it again, and then soaking it in diammonium phosphate to post-harden it.
See also below about zinc phosphate dental cement.
Phosphate conversion coating coats steel with water-insoluble phosphates of these three metals by taking advantage of their solubility in acid, such as (of course) phosphoric acid.
Ferric phosphate is what protects the Iron Pillar of Delhi, and also some of my girlfriend’s kitchen pans, from rusting, despite its porosity. It can be achieved using nothing more than phosphoric acid. Wikipedia leads me to believe that it should be orange to brown, but mixing hardware-store phosphoric acid “converter” with powdered orange rust gives a black insoluble compound instead, and so too is the coating on the pans produced by boiling Coca-Cola in them.
Zinc phosphate is sometimes deposited on steel in the same way; the steel reduces the hydrogen ions at its surface, precipitating zinc phosphate out of solution. It’s also used together with magnesium phosphate as a dental cement; zinc oxide and magnesia are mixed with phosphoric acid on a glass plate to allow them to cool, giving a pot life of a few minutes. Wikipedia explains:
Zinc phosphate dental cement is one of the oldest and widely used dental cements. It is commonly used for luting permanent metal and zirconium dioxide restorations and as a base for dental restorations. Zinc phosphate cement is used for cementation of inlays, crowns, bridges, and orthodontic appliances and occasionally as a temporary restoration.
It is prepared by mixing zinc oxide and magnesium oxide powders with a liquid consisting principally of phosphoric acid, water, and buffers. It is the standard cement to measure against. It has the longest track record of use in dentistry. It is still commonly used; however, resin-modified glass ionomer cements are more convenient and stronger when used in a dental setting.
Manganous phosphate is used similarly for metal protective coatings. Natural paragenetic combinations with iron phosphate include triplite (Mohs 5–5.5), triploidite (Mohs 4.5–5), and purpurite (Mohs 4–5, without iron). Another score of other minerals include manganese and phosphate.
All three of these relatively hard phosphates, or families of phosphates, can reasonably be formed by reacting phosphoric acid with the respective oxides, which are easy to prepare and acquire, and relatively inert (except, of course, for the heptoxide of manganese.) I suspect that other soluble phosphate salts would also work as phosphate donors. Most of the oxides are soft materials that are easy to shape and even cast, though solid pyrolusite (dioxide of manganese) is 6–6.5. In the form of fine powders with a little binder, the materials might be more easily shaped before being bonded with a phosphate donor.
Other possible cation-donating solids include the hydroxides (more or less equivalent to the oxides, if we’re talking about aqueous reactions) and the chloride of zinc.
Boron phosphate is a somewhat refractory material, subliming above 1400°, and water-insoluble in its crystalline form. However, both the reaction and the crystallization seem to be fairly slow at room temperature.
There is a very interesting monozirconium diphosphate but I suspect that zirconia will not yield it easily. You could surely deposit zirconium nitrate on an inert surface, wash it with aqueous lye to produce mostly insoluble zirconium hydroxide, and react that with phosphoric acid; there might be easier routes.
Copper? Titanium?
Perhaps you can convert plaster of Paris to the harder lime, once shaped, by one of the following approaches:
I’m not confident that any of these will work. Hot CO₂ works to convert the sulfide of calcium into calcium carbonate, releasing sulphuretted hydrogen, but you cannot convert plaster of Paris into the sulfide as far as I know. Heating the plaster past 1400° in air will outgas vitriol, leaving behind lime, which is so much smaller that it tends to fall apart. Perhaps heating it to a somewhat lower temperature in a CO₂ atmosphere, particularly under high pressure, would work better; and perhaps it would help if something else were removing vitriol from the gas chamber.
A process that would more likely work: carbothermically reduce the sulfate to the sulfide, perhaps with carbon plasma, carbon monoxide, or ethylene, rather than solid carbon, and then blasting the sulfide with hot carbonic acid gas to liberate sulphuretted hydrogen and produce the carbonate.
This is not the kind of tranquil process of painting on some kind of conversion liquid that I was hoping for.
Lots of other polyvalent cation donor materials can productively form insoluble carbonates, though. Barium, copper, iron, lead, manganese, nickel, and zinc, for example.
I haven’t seen a whole lot about alginates except for the usual dental-mold and spherification stuff, using soluble sodium alginate and insoluble calcium alginate. I imagine that most candidate polyvalent cations would work to coagulate the stuff. In particular, though, washing lime or plaster of Paris with a solution of sodium alginate ought to give you a waterproof surface, similar to tadelakt.
Presumably washing the surface of lime or plaster of Paris with soluble silicates such as those of sodium or potassium would strengthen and waterproof the surface, and perhaps also improve its refractory properties. By applying these solutions to an open-cell foam, perhaps the change could be usefully obtained throughout the material.
As with phosphates, the possibilities of aluminum anions here are tantalizing: can you mold something out of gelatinous aluminum hydroxide, then harden it with sodium silicate? But the silicates of aluminum are enormously varied, ranging from kaolin and zeolites to mullite.
One form of natural magnesium silicate, with a 3:4 Mg:Si ratio, is talc, itself very easily carved, even with thumbnails, before being fired to hardness. Synthetic magnesium silicate, for example as a food additive or a plastic filler, is routinely precipitated in amorphous form by mixing sodium silicate with the nitrate, chloride, or sulfate of magnesium.
Another form of natural magnesium silicate, with a 2:1 Mg:Si ratio, is forsterite olivine, including the gemstone peridot. Olivine is a spectrum between forsterite and the silicates of iron (fayalite) and manganese (tephroite). Forsterite is just as hard as quartz and considerably more refractory; forsterite melts at 1890°, fayalite at merely 1205°, and tephroite at only 1345°.
So you could imagine that a sufficiently small amount of silicate added to a concentrated source of somewhat soluble magnesium, such as magnesia, would produce forsterite, or an amorphous polymorph thereof. The carbonate of magnesium (magnesite, Mohs 3.5–4.5) is some four times as soluble as the oxide, and the fluoride (sellaite, Mohs 5–6) a little less soluble than the oxide.
Boric acid can form insoluble, hard, and sometimes refractory borates of many polyvalent cations, as well as the water-soluble borax; worth mentioning are chambersite: Mohs 7 (manganese); boracite: Mohs 7–7.5 (magnesium); suanite: Mohs 5.5 (also magnesium); and hilgardite: Mohs 5 (calcium and chloride). Other borate minerals are known.
Really though I suspect that the most promising thing to do with borates is to burn them into boria or to somehow convert them into boron nitride. Ammonium borate seems like the ticket:
- 10.9% soluble by weight at room temperature
- stable to about 230°F (110°C), at which point it loses all but two moles of water. If heated sufficiently, it releases the balance of its hydration water and decomposes to boric oxide and ammonia.
(Though boric acid decomposes to boria at 300°.)
Generally the sulfides have the problem that they slowly decompose to produce sulphuretted hydrogen and sulfuric acid, given access to moist air. Carbothermic reduction of plaster of Paris produces calcium sulfide.
Toxic ammonium fluorosilicate is reasonably water-soluble, as are the fluorosilicates of copper, ferrous iron, lead, lithium, manganese, and magnesium, but the fluorosilicates of barium and calcium are much less so.
Oxalates of soda, potassa, and ammonium are fairly water-soluble, while oxalates of magnesium, silver, scandium, iron, and barium are practically insoluble, and the oxalates of lime, copper, and zinc are almost totally insoluble. WP says the oxalate of lime starts to decompose at 200°, though, so it’s not very heat-stable — but what it decomposes to is, I think, the carbonate. It looks like that’s right, but the temperature is around 500°, not 200°. The magnesium oxalate, similarly, decomposes to the carbonate between 420° and 620°.
To take a particular example, the oxalate of potassa (LD₅₀ 660 mg/kg orl-rat) dissolves 36.4 g/100 mℓ water at 20°, the sulfate of potassa 11.1 g, the oxalate of lime 670 μg, and the sulfate of lime 255 mg. This suggests that a solution of 10% potassium oxalate will eventually convert plaster of Paris into >99% insoluble oxalate of lime, which can then be gently heated to get limestone.
Bernd Jendrissek very graciously pointed out that a fluoride replacement reaction is commonly used to harden teeth and make them more acid-resistant by converting hydroxyapatite to fluoroapatite. The fluoride of calcium, fluorspar, is both harder and less water-soluble than either its sulfate or its carbonate, and so a double metathesis with a soluble fluoride salt such as sodium fluoride might plausibly work to harden plaster bodies. These salts are somewhat poisonous; NaF’s LD₅₀ is about 100 mg/kg, so it’s used as rat poison, but also in toothpaste and to treat osteoporosis.
Sodium monofluorophosphate, as used in some toothpastes, might be another alternative, doing the phosphate conversion and fluorination in a single step; its LD₅₀ is [about 500 mg/kg][40].
[40: https://en.wikipedia.org/wiki/Sodium_monofluorophosphate
There’s a fourth totally different approach to strengthening these quasi-refractory calcium compounds, one that doesn’t involve room-temperature gas-phase or aqueous reactions.
Both plaster of Paris and ordinary lime cement remain solid up to high temperatures — plaster of Paris decomposes to quicklime above 1400°, while fully carbonatated lime decomposes to quicklime starting much colder, above 825°, but then quicklime itself remains solid to 2613°. However, it may be in smaller pieces than the original shape, if the changes in volume were enough to crack the shape.
One possible approach to the problem is to incorporate inert needlelike material into the original plaster to bridge the gaps; mullite can be bought in crystals for this purpose for making pottery, or as polycrystalline fibers for foundry linings. At lower temperatures, wire of steel, copper, or stainless steel can work. Plant fibers, such as sisal, sawdust, or used yerba mate, char between 200° and 300°; but the charcoal can survive and continue to add significant strength up to much higher temperatures than the rest of the components, unless oxygen burns it out first.
Even ordinary quartz sand may help. Suppose your plaster mix is 90% quartz sand and 10% plaster of Paris binder, and when you heat the plaster enough to dehydrate it, the plaster shrinks by 0.2% linearly (0.6% in volume). But, since each linear dimension is only about 1.2% plaster binder across most of the perpendicular cross-sectional area, the linear shrinkage is only 0.0024% instead of 0.2%. This can make the difference between heat cracking the material and not.
(Quartz is not the ideal material because it dunts at 573°, expanding 0.45%. Many other tempers are used in pottery to improve this situation, crushed-brick grog being one of the most common.)
However, we can go further and actually use fillers that will actually react with the calcium compounds at high temperature. I saw this on a sciencemadness thread, but I don’t know who to credit: for example, you can incorporate an “inert” filler such as rutile, which at 1300° and above will stop being inert and combine with the quicklime to form calcium titanate (melting point 1975°). Even silica, particularly in an amorphous form such as infusorial earth, or as soluble silicates, might work for this; larnite melts at 2130°. And clays could provide both alumina and silica.
(Titanate also forms mineral salts with manganese, magnesium, barium, lead, zinc, iron, and half a dozen other metals. These are basically all insoluble, even the metatitanate of soda, but supposedly there’s a water-soluble triethanolamine titanate.)