Correlation between apparent solubility and dye exhaustion in carrier‐assisted dyeing of disperse dyeable polyester under normal pressure

Conventional dyeing of poly(ethylene terephthalate) (PET) typically necessitates energy‐intensive high‐temperature processes at approximately 130°C. In contrast, disperse dyeable polyester under normal pressure, modified with flexible ether‐bond segments, exhibits a significantly reduced crystallinity of 26.83% compared to 48.04% for PET, offering intrinsic potential for atmospheric‐pressure dyeing. This study establishes a mechanism‐guided strategy to overcome the trade‐off between solubility‐limited uptake and thermal migration risks. Microscopic mechanism elucidation via low‐field nuclear magnetic resonance quantified a critical free volume expansion between 70 and 98°C, creating physical channels for dye diffusion. To bridge the aqueous solubility gap, environmentally friendly bio‐based carriers were evaluated. The investigation revealed a crucial ‘solubilisation‐transfer trade‐off’: while excessive dye‐carrier affinity sequesters dye molecules in the bath, an optimised carrier system (1 g/L 4‐propylguaiacol at pH 5) successfully balances dye solubilisation and interfacial transfer. This carrier‐assisted protocol achieved a 20%–30% increase in exhaustion, ultimately delivering a final dye uptake exceeding 95% with colour fastness ≥Grade 4. This work provides a validated, low‐carbon methodology that facilitates the sustainable commercialisation of next‐generation polyesters.