Cotton–Polyester Blends: A Second-Use Bound on Mechanical Recycling Cycles and Chemical Separation

Cotton–polyester blends are the hardest common clothing fibre to use a second time: the two fibres need different recycling routes, and the standard route for each damages the other. This paper models both routes and derives a bound for each. For mechanical recycling (shredding and re-spinning), fibre length is modelled with a retention factor of 0.62 per cycle for cotton and 0.78 per cycle for polyester, starting from 28 mm cotton staple and 38 mm polyester. Pure cotton falls from 28.0 mm to 17.4 mm in a single shredding cycle and to 10.8 mm in two, so it supports one recycled generation at coarse ring-spinning length (16 mm) and none at medium count (20 mm). A 50/50 blend falls from a 33.0 mm blend mean to 23.5 mm after one cycle and 16.9 mm after two, supporting one medium-count generation, two coarse generations and three open-end generations before it is fit only for nonwoven use. For chemical separation, two routes are costed per kilogram of 50/50 blend at stated prices: selective dissolution of the cotton costs $3.13 per kg of feed and recovers $0.75 of product value, a loss of $2.38 per kg; depolymerisation of the polyester costs $3.54 per kg and recovers $0.77, a loss of $2.77 per kg. Mechanical processing itself also loses money on a standalone basis at the stated prices, by $0.58 per kg, and pays only if a gate fee, extended-producer-responsibility payment or avoided disposal payment of at least that size is present. The energy bound does not kill chemical separation — separation uses 3.2 to 4.1 kWh per kg against about 7.2 kWh per kg embodied in virgin blend fibre — solvent loss, capital cost and yield loss do. The honest conclusion, printed at full size, is that neither chemical separation route pays per kilogram at the stated prices, and that blend second use should be organised as a short mechanical cascade into coarse yarn, then nonwoven and insulation uses, rather than as fibre-to-fibre separation. SIMULATED, NOT MEASURED: all lengths, yields and costs are model outputs at stated parameters.