Page 215 - Basic Principles of Textile Coloration

204 DYEING THEORY

This value for the standard affinity indicates a favourable equilibrium for dyeing.

At equilibrium at 100 °C, the dye is almost 900 times more soluble in the

polyester than it is in water.

For ionic dyes, the affinity equation is more complex and involves the activities

of the individual ions and possibly a term for the fibre internal volume. For

example, the sodium salt of a trisulphonated dye in solution has an activity

approximated by:

as = [Dye3- ] [Na+ ]3 (11)

This is derived from:

Dye(SO3Na)3(s)+ H2O(l) øííí÷í Dye(SO3- )3(aq)+ 3Na+(aq) (12)

The affinity equation for the adsorption by cotton of a polyvalent direct dye anion
with a charge of –z per molecule is:

- Dm 0 = ln Ë Cf Û + z ln Ë Naf Û -(z +1) ln(V) (13)
ÍÌ Cs ÜÝ ÌÍ Nas ÜÝ
RT

where the symbols C and Na represent concentrations, rather than activities. V is
the internal volume of the cotton, usually given a value of 0.22 l kg–1. One can
see that the calculation of the dye’s affinity becomes quite involved.

The equation for the standard affinity shows that the dyeing equilibrium
constant decreases with increasing temperature if –Dm0 is positive. More dye
adsorbs at lower temperature, although reaching equilibrium at lower temperatures
takes longer. The standard affinity is the change in the chemical potential of the
dye when one mole is transferred from the standard state in solution to the
standard state in the fibre. It is therefore the standard molar free energy change for
dyeing.

-Dm0 = -DG0 = -DH0 + TDS0 = RT ln(K) (14)

The enthalpy of dyeing DH0 can be derived from the temperature dependence of
the standard affinity using the above free energy equation. A graph of ln(K) versus
1/T will be linear with a slope of –DH0/R. The data in Table 11.1 are derived from