Suppose you have made a lightweight model of something out of aluminum foil or thin aluminum mesh, for example by origami or stamping or bending, and you’d like to solidify that geometry. But the aluminum foil is very lightweight and flimsy (see Aluminum foil, typically 10 μm) and so it can’t withstand much force at all without deforming dramatically.
Extending this to thinner metal sheets such as gold leaf would be desirable but seems much more challenging.
One approach to this is cathodic deposition, whether of metals or of other minerals; see Fast electrolytic mineral accretion (seacrete) for digital fabrication?. That file covers many candidate approaches to cathodic deposition of nonmetals. But there are some other approaches I want to explore.
Another thing you can do is to coat the foil with waterglass, for example by spraying. I think this is sort of the opposite of spray drying: as in spray drying, you want very fine droplets, under 10 μm, so that they don’t collapse the aluminum with their weight, but you probably need the air to be sufficiently humid that the fine droplets do not dry before they can stick to the aluminum, where they are smoothed out by the surface tension of the solution and the hydrophilicity of the surface. (You may need to functionalize the surface to be more hydrophilic first.) With sufficiently outrageous pressure, you should be able to atomize even a fairly concentrated waterglass solution (≈30%) through a small orifice.
By this means you ought to be able to deposit an additional 10 μm or so of waterglass on the surface of the aluminum to stiffen it; upon exposing the object to dry, hot air, such a thin film should be able to dry fairly quickly. The resulting silica gel might be 5 μm thick on both sides of the foil, doubling its thickness. Silica xerogel is not very stiff, with a Young’s modulus in the neighborhood of E = 3 GPa (compare to aluminum’s E = 70–90 GPa).
If the surface is sprayed in the same way, either before or after the silicate, with a solution of a salt containing polyvalent cations that will not displace aluminum in the metal, with anions that will not decompose to oxidize the aluminum (such as the acetate or formate of magnesium, calcium, manganese(II), zinc, copper, or iron, especially ferrous but even ferric; or the acetate, sulfate, nitrate, iodide, or chloride of aluminum or magnesium; or the nitrate or iodide of calcium) it should immediately render the silicate insoluble upon contact, in the same way as in Keim’s process for mineral painting (Keimfarben), but much more rapidly because of the thinness of the layer and because of carrying out the whole process at an elevated temperature.
In addition, some of the resulting silicate compounds might be stiffer than a simple silica xerogel; some silicates of aluminum and magnesium are notable for their outstanding quartz-like hardness. I think aluminum and magnesium are also more advantageous in this respect because there is no danger that they will displace the aluminum metal, so they afford a wider choice of salts than zinc, copper, or iron, and because they contain more valence electrons per mass; I fear that the acetate, sulfate, nitrate, iodide, or chloride of zinc, copper, or iron might corrode the aluminum, though I think they normally are not sufficiently aggressive to corrode it in the time available.
(In general, lower alkalinity waterglasses will not only be able to solidify with smaller additions of polyvalent cations, but will also produce stiffer materials, because the silicate network tends to provide most of the mineral’s strength.)
Alternative ways to rapidly solidify waterglass include carbonic acid gas, and alcohols such as methanol or ethanol, but these last are reputed to produce a rubbery effect which would be counterproductive in this context.
As an alternative to waterglass in this process, sources of soluble phosphate can be used, such as phosphoric acid and the soluble monobasic, dibasic, or tribasic phosphates of sodium, potassium, or azanium. These can be reacted with polyvalent cations in the same way as the soluble silicates to form insoluble mineral phosphates, some of which are competitive in hardness with the silicates. In many cases the reactions are not as calm as the corresponding silicate reactions.
Sufficient quantities of phosphoric acid can convert aluminum foil into the water-soluble acidic monoaluminum tri(dihydrogen)phosphate, though normally this reaction takes hours, while the more usual 1:1 aluminum phosphate is aggressively insoluble. Another possible disadvantage of phosphoric acid is that it would be much harder to dry out. I don’t think the other phosphates are aggressive enough to attack aluminum foil.
The azanium phosphates are particularly interesting here because the azanium can be driven off by heating, leaving the anhydrous acid if this is done before adding the other reagent; the monobasic phosphate decomposes around 200°. In the case where the salt contributing the polyvalent cations is a muriate, fluoride, iodide, or formate, the heating step can remove the azanium-salt byproduct entirely after combining the two solutions, leaving only the desired mineral. Of these, the azanium muriate gas is probably the least objectionable.
Pyrophosphates or metaphosphates are likely alternatives to orthophosphates here; as with lower-alkalinity soluble silicates, these longer-chain phosphates may require smaller amounts of polyvalent cations and produce stiffer materials. If this effect exists, it would be much weaker than with the silicate systems.
Getting sprayed drops of the right size onto the aluminum is probably best done by producing the spray in a chamber with a slight updraft which will carry the smaller drops to the workpiece, while allowing larger drops to fall and be recycled. In the cases other than waterglass/carbonic acid, it would be best to use one such chamber for each liquid so that they do not react in the spray chamber and can be recycled safely.
Micron-sized filler particles, such as clay, talc, mica, silica (as in sol-silicate paint), or nanotubes (whether of carbon, BCN, boron nitride, halloysite, or some other material) could further enhance the stiffness of the resulting material and reduce the quantity of polyvalent cations required. These could be mixed into either of the two solutions.
As the object gets thicker layer by layer, it will become stiffer in proportion to the square of its thickness, so after a while it will be possible to deposit thicker layers.
A possible alternative approach is to form your original shape out of not one but two layers of aluminum foil which are stuck together with drops of dried waterglass before being formed. Upon heating the formed shape, the waterglass softens, and the substantial amount of water locked inside its gel structure bubbles out, forming a foam, which pushes the two sheets of aluminum some distance apart. If the waterglass layer is continuous before foaming, this will badly distort the shape and quite likely rip the aluminum foil, but if adequate space is present laterally between the drops, they will have space to expand without damaging the foil or distorting the shape much, while still forming a continuous foam network and doing most of their expansion perpendicular to the surface. Once cooled, the resulting sandwich panel is potentially substantially more rigid than the original easily-formable material.
According to a preliminary test on a much larger scale (see Material observations, section 02021-08-20) waterglass foamed by heating commonly expands in volume by about a factor of 10; so a layer of 10-μm-thick waterglass drops that is half waterglass drops and half air might expand 5× in thickness to 50 μm, making the total sandwich panel 70 μm and, I think, 9× its original rigidity ((60/20)²). If you can manage full density, no spaces between drops, without ripping the foil, you can get to 100 μm and 30× the original rigidity ((110/20)²).
By placing the waterglass drops along a pattern of crisscrossing lines, rather than uniformly distributed over the whole plane, it may be possible to use less total material at the expense of less increase in thickness and thus in rigidity.
If instead of a sandwich between two layers of foil we deposit the drops of waterglass on a wire mesh, they are more likely to chip off, but they will tend to distort the form less when heated, forming a solid foam piece.
If instead of waterglass we use drops of dried phosphates of azanium, heating will drive off azanium instead of water, melting the resulting phosphoric acid and allowing it to foam up with the azanium gas. A slow-acting source of polyvalent cations, inert to phosphates of azanium at room temperature but reactive with warm anhydrous phosphoric acid, can be mixed in with the phosphates. Oxides of zinc, copper, aluminum, iron, or magnesium would probably work well for this with the grain size and grain surface structure adjusted to get the right level of reactivity.
In either case, including a small amount of a polyvalent cation in the waterglass or phosphate solution before drying, but not enough to precipitate on its own, might enable it to gel at a higher water content, thus providing a greater foaming structure.
Borax is another material that foams up at temperatures below the melting point of aluminum, because like waterglass it softens up and water is driven out, but it’s not as easy to precipitate a water-insoluble material from. It might be possible to convert it into hydroboracite (CaMgB₆O₁₁·6H₂O) by reacting it with both calcium and magnesium ions, but this is far from the enthusiasm with which the phosphate and silicate systems form insoluble products, and even hydroboracite is not very hard.
Mixing pyrophosphates, orthophosphates, and metaphosphates together may be useful to encourage phosphates to form an amorphous gel (that can trap a lot of water) rather than crystals (which in a few cases can be quite hydrated, for example the decahydrates of di- and trisodium phosphate.)