The PET Melt-Cycle Bound: How Many Bottle-to-Bottle Lives a Polymer Chain Survives, and Whether Restoring It Beats the Cascade

A plastic bottle cannot be melted back into a bottle indefinitely, and the reason is arithmetic before it is economics. This paper models the loss of intrinsic viscosity (IV) of polyethylene terephthalate (PET) at each melt reprocessing cycle, together with contaminant accumulation, and derives how many bottle-to-bottle cycles the material survives before it falls below bottle grade and must cascade to strapping or fibre. SIMULATED, NOT MEASURED. Starting from IV 0.84 dL/g with a bottle-grade threshold of 0.72 dL/g, well-dried feedstock (degradation factor 0.045 per cycle) allows 3 full bottle cycles; typical drying (0.075 per cycle) allows 2; poorly dried feedstock (0.11 per cycle) allows only 1. Contamination, modelled at 15 ppm added per cycle with 30 per cent removal per cycle, approaches a steady state of 50.0 ppm and is not the binding limit in this model — chain scission is. Restoring cascaded PET by solid-state polymerisation from IV 0.62 to 0.80 dL/g costs 1.091 MJ/kg (0.3029 kWh/kg, 0.1212 kg CO₂ per kg at the stated grid factor), which is 0.0156 of the 70 MJ/kg assumed embodied energy of virgin PET. On energy and carbon, restoration wins decisively over both the cascade-plus-virgin-top-up and virgin replacement; the cascade wins only where food-contact approval, colour or plant access, not energy, decides. The honest headline is short lives, cheap restoration: bottle-to-bottle recycling is a 2–3 cycle system unless IV is restored, and restoring it is energetically inexpensive.