Short answer yes. Plastic is something called a polymer, which means its many (like thousands) of the same molecule all chemically bonded together. When its recycled the object is melted down, and each time this basically weakens the bonds, so it becomes easier and easier for it to degrade.
The problem if you’re asking thinking that we can just recycle everything 7 or 8 times and it will quickly degrade – you might speed up the process but it will still take many years for that weakened plastic to degrade fully and we’re making and using new plastic it still far outpaces that.
Latest Answers