Transparent plastics are clear because they aren’t crystalline, either because that’s their natural way to be or because they are carefully made that way in manufacturing. There are two major ways solid materials exist: as crystals or as glasses. Crystalline materials have their atoms and molecules perfectly ordered in a packed structure, like stacking golf balls in a box. Glassy materials don’t have that order, their molecules make big messy piles like a plate of spaghetti. Glassy materials don’t scatter light, so they look clear. Crystalline materials do scatter light, so they look opaque.
Plastics are very versatile. Some of them tend to crystallize some or a lot in the solid state, while others remain totally glassy. Glassy plastics are naturally transparent. A good example of this is the polyester that makes plastic soda bottles. Other plastics form little crystals embedded in a mesh of glassy material, which makes them opaque. A good example of this is high-density polyethylene, a common plastic used to make things like milk jugs and molded plastic items.
Even more crystalline plastics can be made transparent, though the use of added chemicals and/or the way they are processed. Certain chemicals, called “plasticizers”, stop the plastic molecules from ordering into crystals, and can make a normally opaque plastic clear. You can also do it just by cooling melted plastic really, really fast when you are shaping it. If the plastic is cooled very quickly, it freezes the molecules in place and doesn’t give crystals a chance to form. The lack of crystals makes the plastic transparent.
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