There’s lots of ways, more or less convenient. If you have lots of analytical equipment you might try differential scanning calorimetry to see at what energies the crystalline organizations of the polymers disappear. If you had an infrared spectroscope you could look for specific chemical bonds. If you have two dinky little bits of fiber and whatever’s in the kitchen drawer, there may still be ways.
We do have another problem to deal with. Many polymers are “filled”, or mixed with powders to extend the expensive polymer or to impart other properties like opacity or flame retardancy. I think this is less common with fibers, though, in part because fillers can lower tensile strength. But I gotta say that you can make all sorts of experiments turn out differently by adding the right filler.
First you could check the density. Polyethylene and polypropylene will be lighter than water. IIRC polyester (Dacron) will be sort of similar to water, as would polycarbonate (Lexan), and I think polyacetal (Delrin), and nylon. Polyvinylchloride would be denser than water, as would polytetrafluoroethylene (PTFE)and perfluoroalkoxy (PFA) and fluorinated ethylene propylene (FEP) (all Teflons) and PEEK. You can check densities that are less or greater than water by floating the fibers in saltwater, vinegar, isopropanol, mineral oil, hexane, etc etc.
Then you could check the melting point. I’m going from hazy memory here but polyethylene would melt at the lowest temperature, then polypropylene, then acrylic, then PFA, then FEP, then PTFE. This is less certain, but I think that nylon and some of the others decompose rather than melting.
You could check whether the fibers are “oriented” (stretched while molten to orient the polymer molecules along the length of the fiber, making it stronger). Practically all polymer fibers are, almost certainly if they are used for weaving or sewing. Oriented polymers shrink along the orientation direction when you melt them.
You might check the index of refraction (the factor by which they slow the passage of light, relative to a vacuum). PTFE is about 1.3, and I don’t think many polymers get up to 1.5 or so. You can make mixtures such as water and glycerine, or different brine concentrations, to get different indices of refraction. When you dip the fiber into a solution having the same index of refraction, you won’t be able to see its edges anymore - if it’s transparent and colorless, you won’t be able to see it at all. Weird.
The last little thing I can think of is to check the critical surface tension of the fibers. This is the same sort of issue that keeps oil and water from mixing. Briefly, any liquid has a surface tension, which is a retractive force acting throughout its surface (the molecules at the surface have to concentrate their interactions into the plane of the surface because there’s no liquid molecules above them to pal around with). Any solid will be easily wet by a liquid whose surface tension is lower than some critical value, and that’s the critical surface tension of that solid. I think polyethylene and polypropylene have a critical surface tension like 20 N/m whereas nylon is more like 35 or 40. FEP would be maybe 15, some silicones as low as 5 or 10, glass 75, and metals are in the hundreds.
So there’s lots of things to try. I think if you find something that distinguishes the two you should look up that property for both and see if you can get a clear answer that way.
You can also check the
You could check the flammability