Which type of dye you are using? 

I will assume that disperse dyes are the subject of the question since this is by far and away the most important dye class for polyester.  I shall also assume that the term polyester refers to polyethylene terephthalate (PET) which is the type of polyester most commonly dyed.  Nylon 6 fabric or yarn is typically exhaustion dyed at the boil for ~1hr.  However, PET fabric and yarn (without use of carriers) must generally be dyed under pressure at temperatures of up to 130C for 60-90min to achieve a commercially acceptable rate of dye diffusion and colour strength because the polymer is so hydrophobic and crystalline.  Consequently, if the same concentration of dye is applied to nylon 6 and PET by exhaustion dyeing at the boil for the same length of time, then the most likely outcome is much weaker coloration of PET, i.e. a lower K/S value, compared to nylon because the rate of dye diffusion into the former substrate will be much slower and so the concentration of dye within the substrate will be lower.

Hi Dr Tanveer and Dr Andy, The type is disperse dyes

Dear, Dr Andy;

in our case:

The dyeing bath was settled at 40- 60ºC by adding the calculated volumes of dispersing agent ( Ejanal , 1g /l ), acetic acid ( pH= 5 - 5.5 ), dye ( 2% ) and water, where liquor ratio was kept at 1:30 . Fabric sample (polyester or polyamide) was added to the bath and temperature was raised gradually to Aº C (98 ºC for polyamide and 130ºC for polyester, through 15 minutes). Dyeing was continued at AºC (98º C for polyamide and 130º C for polyester) for 60 minutes then the dyeing bath gradually cooled .On completion of dyeing, the fabric was taken out and washed in a solution containing 5 g/l detergent at 60°C for 15 min. Finally, the washed fabric sample was rinsed with water and dried at ambient conditions.

I agree with Andy Towns, Reason is the structural difference of the two polymers. PET being denser than Nylon 6. For comparison of structure/densities/Tgs check out the link.

http://www.polymerprocessing.com/polymers/PA6.html

http://www.polymerprocessing.com/polymers/PET.html

Syed