Page 209 - Basic Principles of Textile Coloration

198 DYEING THEORY

It is common practice to determine the amount of dye in the fibre from the
initial quantity added to the bath, less that remaining in solution at equilibrium.
The latter is readily obtained by spectrophotometric analysis of the dye solution
(Chapter 24). A mass balance, however, is a necessary prerequisite to ensure that
there are no losses of dye from decomposition. This involves completely extracting
the dye from the fibre, or dissolving the dyed fibres and determining the dye in the
polymer solution. Again, the dye should not decompose during these processes.

11.1.1 Adsorption isotherms

An adsorption isotherm gives the concentration of a substance adsorbed on a solid
surface in relation to its concentration in the surrounding fluid when the system is
at equilibrium at a constant temperature. The graph representing a dyeing
adsorption isotherm has the adsorbed dye concentration (Cf in g kg–1 or
mol kg–1) plotted against the solution concentration (Cs in g l–1 or mol l–1).
Adsorption isotherms are useful for the information they provide on the dyeing
mechanism. There are three main types of dyeing adsorption isotherm, usually
referred to as the Nernst, Langmuir and Freundlich isotherms. Most dyeing
systems involving only adsorption are completely reversible. Equilibrium
isotherms, established by adsorption of dye from solution onto initially undyed
fibres, are identical to those obtained by desorption of dye from dyed fibres into an
initially blank dyebath.

The Nernst isotherm is the simplest and is given by the equation:

Cf = kCs (1)

where k a constant. This is also the equation describing the distribution or
partition of a solute between two immiscible solvents. The graph of Cf against Cs is
linear up to the point corresponding to the dye saturating the fibre and the water.
The dyeing of many synthetic fibres with disperse dyes follows this type of
isotherm (Figure 11.1). The fibre, in which the dye is soluble, extracts the disperse
dye from the aqueous bath, in which it is only slightly soluble.

The Langmuir isotherm applies to adsorption on specific sites in the solid, of
which there are often only a limited number. Such a situation exists in the dyeing
of nylon with simple acid dyes by an ion exchange mechanism. The counter ion
associated with an alkylammonium ion group in the nylon, under weakly acidic
conditions, is exchanged for a dye anion (Scheme 4.4). The Langmuir adsorption