The
hydrophilic fibres such as cotton, wool, silk etc swell in the aqueous dyeing
solutions yielding an open water filled structure. The water filled channels or
pores provide a route for the dye to reach its adsorption site. This pore model
presents the fibres as a network of interconnecting channels or pores through
which the dye diffuses. The dye diffuses more rapidly through never-dried
cotton or wet spun fibres than dried fibres. eg: as spun acrylic tow before
drying can be dyed with in a few seconds at 50˚C, but it takes several minutes
at 100˚C once the fibre is dried before dyeing.
Instead
hydrophobic fibres such as Polyester do not take up large quantities of water.
The dye must therefore find a path through the polymer structure itself. This
is the case in dry dyeing systems such as thermofixation or sublimation dye
transfer process. Such a diffusion process is explained by a free volume model
of diffusion.
Free Volume Model
In a free volume model it is assumed that the
thermal motion of atoms generate a volume associated with molecules that is not
occupied by the constituent atoms. This volume increases with increasing
temperature. Free volume is assumed to be the difference between the total
volume and occupied volume.
 |
| Fig. Specific Volume vs Temperature Curve |
In dyeing system the dye molecules are visualised as
moving through the fibre in a series of jumps from one location to another
where they can be accommodate. This movement of dye molecules depend on the
development of free volume due to segmental mobility. Therefore the dyeing
properties are related with the segmental mobility due to free volume.
Below a certain temperature the polymer chains are frozen into
a position and the only motion they undergo are thermal vibrations. But with
increase in temperature the thermal motion increases and provides sufficient
energy for bond rotation in polymer chain. At this point a whole segment in the
polymer chain moves and displaces its position until hindered by other polymer
molecules. Once the segment has moved the space is free to be occupied by
another segment or diffusion of dye and the process is repeated throughout the
whole polymer structure. The temperature above which there is markedly increase
in free volume is called the glass transition temperature (Tg).
Thus the influence of
temperature on diffusion is represented by Williams, Landel and Ferry
(WLF) equation.
where DT is the
diffusion coefficient at temperature T or Tg and aT is the shift factor of WLF
equation, where
Where A and B are constants. The shift factor
represents the fraction by which the property is changed in going from Tg to
the ambient temperature T shown in Fig. These constants A and B represent the
critical free volume needed to permit a segmental jump and the free volume at a
given temperature. A large number of polymers have been found to confirm with
WLF equation over the temperature range from Tg to Tg + 120˚C.
 |
| Fig. Curve for Diffusion and Shift Factor w.r.t (T-Tg) |
This WLF equation successfully expresses the
relationship between the diffusion coefficient and temperature or the
difference in the dyeing temperature and glass transition temperature i.e. (T-Tg).
The rate of diffusion is a direct function of the
difference (T-Tg), where T is the dyeing temperature.
The greater the value of (T-Tg), the more rapid is
the diffusion of dye shown in fig. Thus a reduction in Tg would have the same
effect as an increase in the temperature of dyeing.
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