To investigate the contributions of polymer relaxation phenomena to the mechanism of disperse dye adsorption on poly(ethylene terephthalate) fibres, a commercial grade dye was applied to poly(ethylene terephthalate) fabric at temperatures between 30°C and 130°C. Three regions of temperature‐dependent dyeing behaviour were identified, in which the promotional effect imparted by increasing dyeing temperature varied, depending on whether dyeing had been carried out at temperatures that were below, within or above the polymer's glass transition temperature, Tg, namely < 65°C, between 65°C and 110°C and between 110°C and 130°C, respectively. When experimentally determined colour strength data points (log 1/fk) were fitted to plots of polymer structural relaxation (log aT) calculated using the Williams, Landel and Ferry equation as a function of (T − Tg), three different levels of correspondence were achieved which paralleled the observed three regions of temperature‐dependent dye uptake. The adsorption of the commercial disperse dye on the poly(ethylene terephthalate) fibre therefore concurs with the free volume model of dye diffusion insofar as the diffusional behaviour of the dye is related to the relaxation time of the molecular motions occurring within the poly(ethylene terephthalate) polymer. The finding that the poly(ethylene terephthalate) substrate's glass transition extends over a broad range of temperature upto ~110°C explains why elevated dyeing temperatures in the region of 130/140°C must be used in High Temperature dyeing processes, and also, why ~75% of uptake of the commercial disperse dye on the poly(ethylene terephthalate) fabric occurs over the very narrow 20‐30°C critical temperature range between 110 and 130°C/140°C.

The marked temperature‐dependent uptake of a commercial disperse dye on poly(ethylene terephthalate) fabric achieved during an aqueous high temperature dyeing process is the likely amalgamation of at least two separate, but intrinsically inter‐related, thermally activated processes, namely, poly(ethylene terephthalate) structural relaxations, as articulated in terms of polymer chain segmental mobility and available free volume, in which glass transition adopts a principal role, as well as disperse dye aqueous solubility. Both polymer relaxation times and disperse dye solubility therefore assume crucially important roles in the mechanism of adsorption of disperse dyes on poly(ethylene terephthalate) fibres.

To further investigate the contribution of polymer relaxation times to the mechanism of disperse dye adsorption on poly(ethylene terephthalate) fibres, the temperature‐dependent uptake of Teratop Yellow HL‐G 150% on both cotton and polyamide 66 fabrics at temperatures between 30 and 130°C was compared with that on poly(ethylene terephthalate) fabric. Although uptake of the commercial grade dye on polyester fabric is governed by the thermally regulated, broad glass transition of the water‐saturated poly(ethylene terephthalate) substrate, as this was not observed for either cotton or nylon 66 fabrics, the respective cellulose or polyamide 66 polymer glass transition does not present a major thermal impediment to dye uptake over the wide range of dyeing temperatures used. This is because the onset and end‐set temperatures of the glass transition of the water‐plasticised poly(ethylene terephthalate) material reside within the range of dyeing temperatures employed, whereas those of the water‐plasticised cotton and polyamide materials occur below the lowest dyeing temperature examined (30°C). The thermal dependency of disperse dye solubility also likely makes a meaningful contribution to the temperature‐dependent dye uptake observed for each type of fibre.

In the absence of published information regarding the temperature dependency of water‐derived poly(ethylene terephthalate) fibre properties, the findings reported for the thermally regulated interactions between water and 100% amorphous poly(ethylene terephthalate) materials were interpreted from the perspective of the amorphous domains that reside within semi‐crystalline polyester textile fibres. This analysis suggests that the pronounced temperature dependent uptake of a commercial grade disperse dye on poly(ethylene terephthalate) fabric achieved during an aqueous dyeing process at temperatures between 30 and 130°C is the likely result of the combination of three separate, but inherently inter‐related, thermally activated phenomena, namely, polymer structural relaxation, in which polymer glass transition assumes a dominant role, dissolution of disperse dye in the aqueous dyebath, as well as various water–fibre interactions, in the guise of water sorption, water molecule diffusivity, water‐induced swelling and water‐induced plasticisation. Although thermally regulated macromolecular relaxation processes adopt the principal role in dye uptake, temperature dependent dye solubility and water‐derived fibre properties nevertheless likely provide crucially important supportive roles.

The temperature dependent uptake of a commercial disperse dye on cotton and polyamide 66 fabrics at dyeing temperatures between 30°C and 130°C adhered to the Williams–Landel–Ferry equation, insofar as, very good correspondence was observed between plots of experimentally determined colour strength data points (log1/fk) and the respective structural relaxation times of the cellulose and nylon 66 polymers (logaT data points), as a function of the parameter (T − Tg). Adsorption of the dye on both types of fibre therefore concurs with the fundamental precept of the free volume model of dye diffusion. Comparison of the adherence of the uptake of the commercial dye on cotton and polyamide 66 fabrics with that secured on polyester fabric revealed that despite the major chemical and physical differences between the three types of fibre, the same dyeing mechanism likely applies to each fibre type. The marked temperature dependent uptake of the commercial grade disperse dye each of the three types of substrate is the consequence of two, different, but inherently interconnected, thermally activated phenomena, namely the relaxation times of the molecular rearrangements occurring within the respective cellulose, nylon 66 or poly(ethylene terephthalate) macromolecule, in which polymer glass transition assumes the principal role, and the aqueous solubility of the commercial grade disperse dye.