There actually are some things that can be done to certain plastics to make them more clear. One material in particular is polypropylene (PP). 20-25 years ago, PP could only be found as a translucent material: think about older Tupperware that was thick, white, and durable. This is because standard PP is a semicrystalline material with crystals of a size that is comparable to the wavelength of visible light (400-700nm).
Chemists found that by introducing certain additives, they could make PP create smaller crystalline areas that were no longer near the same size as the wavelength of visible light, thus rendering the PP more clear. There are also more of these smaller crystals, making the PP stronger, increasing its performance and allowing it to compete in more demanding applications.
They were so successful in tweaking the clarity of PP that by 2010 it was stealing business from more expensive clear plastics like polystyrene and polycarbonate.
Other plastics can be made clearer by introducing an additional comonomer. (Think of the chemical structure of a plastic as a string of beads. If all the beads are the same, then strings next to each other can pack efficiently and form crystal areas. Now imagine that you randomly replace a few of the beads with larger beads: the strings of beads no longer can line up straight in large areas and crystallize.) As with PP above, the end result is smaller crystals and a clearer plastic.
TL;DR: adding certain stuff to certain specific plastics can make them clear, or at least clearer.
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