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PVA Filament (desired goal)]

Polyvinyl alcohol (PVA; also referred to as: PVOH, PVAl) filament--the sacrificial support polymer filament used in 3D printing, how is that made? All the reactions I've seen that make PVA create a gel-like substance that could be used as a glue or perhaps a film. But it's not solid. (See image with beaker.)

PVA gel (what I currently know how to make)

The reactions I've seen use an alcohol (ethanol or methanol) and an alkaline catalyst (sodium hydroxide) which are combined with polyvinyl acetate. Here's the reaction that was used to make the beaker's gel PVA:

enter image description here

Another preparation can be seen in this video.

Is there some kind of coagulation/further reaction I must do to the gel to solidify its structure, or is the trick to do something during the first reaction, such as varying the temperature or pressure?

To clarify, I don't actually need/want it in the typical extruded filament form that would be needed for a 3D printer. A simple solid blob of the stuff would suffice. I'm very new to materials science and only a novice in chemistry, but I'd love any answers you wonderful folk could provide, even if they are dense scholarly articles. Thank you for your time!

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All the reactions I've seen that make PVA (also called PVOH, PVAl), create a gel-like substance that could be used as a glue or perhaps a film.

Yes, the reaction you describe is done in a solvent (water, ethanol, methanol, etc...) so that no acetate groups are unaccessable to reaction in a crystalline phase. A gel is formed because when poly(vinylacetate) is fully hydrolyzed, it is less soluble, typical white glue has about $12\%$ of the acetate groups unhydrolyzed to reduce crystallinity and keep solubility high. The polyvinyl alcohol in filament is just dried out solid PVA, whereas the gel has water in a polymer matrix. All they have to do is melt and extrude the dry PVA powder into filament.

I don't actually need/want it in the typical extruded filament form that would be needed for a 3D printer. A simple solid blob of the stuff would suffice.

Side note: you can buy PVA powder online with less mess than self synthesis or depending on your application, you might be able to just use dried out white glue.

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