Dye Diffusion and Free-Volume Theory
topic
Disperse dye diffusion into PET is governed by free-volume theory: above Tg, polymer chain mobility creates transient free volume for dye molecule migration. Diffusion coefficient D follows Arrhenius equation: D = D₀exp(−Ea/RT), Ea typically 80–150 kJ/mol for disperse dyes in PET. Fick's second law describes concentration–depth profile. Half-dyeing time t½ = 0.0669r²/D (for cylinder of radius r). Rate-limiting step: diffusion within fibre (not adsorption).
Role
Dye diffusion theory quantitatively explains why polyester requires elevated temperature for dyeing, the effect of carriers on rate, and the relationship between fibre structure (crystallinity, amorphous orientation) and dyeability. It is the theoretical core of polyester dyeing science.
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