How can a mixture of unknown plastics be separated?

Yeah, that's not a trivial question.  Ideally, it's a lot simpler never to let them become unknown in the first place.  Because of this, places keen on recycling plastic try to avoid this scenario entirely, using systems like the plastic identification code: Plastic recycling

Failing that, if there's some other sort of label attached, you could call up whoever made the product and ask them what it is.

Assuming that you can't just look at a label or a number stamped into your not-so-unknown-after-all plastics, you have to get more clever about it.  You could narrow down the list of suspects by taking density measurements.  You could measure over which parts of the spectrum the plastic absorbs light.  Refractive index measurements might be helpful.  Testing its hardness and Elastic modulus might be informative.

If you REALLY need to know what kind of plastic is sitting in front of you, you could attempt to dissolve it in various solvents, checking to see which solvents actually succeed at this (which might tell you a lot).  Once you've done that, you have the option of doing Multiangle light scattering to get a sense of the average polymer size and overall distribution of sizes in your samples.

By the time you've found someone who knows what that is and has the equipment needed to do it, you should then simply ask that person how THEY think you should proceed.  Most likely, you are now standing next to a polymers expert who can glance at what you've discovered so far and take it from there.  Good luck!
Components of a mixture of materials can be separated using the differences in their densities. This method can be used to separate unknowns polymers in a mixture.
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