Fastness properties measurements
Washing and light fastness of the samples was carried out according to ISO 105-C06: 1994 (E) and ISO 105-B02: 1994 (E), respectively. For light fastness, the samples were tested using an air-cooled xenon arc lamp. For wash fastness, the degree of color change and staining were assessed according to ISO 105-A05: 1996 (E) and 105-A04: 1989 (E), respectively.
In this work, the color strength (K/S)λ of the samples was determined by using Kubelka-Munk equation (Eq. 1).
where Rλ is the reflection factor of the samples at wavelength λ. K and S are the absorption and scattering coefficients, respectively .
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The results obtained from the equilibrium dyeing of wool fibers with the madder and the curves fitted using Freundlich and Langmuir adsorption isotherm equations (Eqs. 4, 5) have been shown in Figs. 2 and 3, respectively. It can be noticed that the correlation coefficient obtained from fitting using Freundlich equation is 0.86 while for Langmuir 0.88. These correlation coefficients indicate that adsorption of the madder on wool follows Type Langmuir. However, the linear forms of adsorption isotherm equations (Eqs. 6, 7) are widely used to determine the constant values ( , , , ).
In this work, the correlation coefficient of the linear forms of adsorption isotherms also obtained and it was found that the correlation coefficient of the linear form of the Freundlich was significantly higher than that of the Langmuir (Figs. 4, 5). It seems that adsorption of the madder on wool at pH 7 is similar to direct dyes onto cellulosic fibers conform to Freundlich type of adsorption. Hydrogen bonding and van der Waals forces contribute in Freundlich adsorption. The Iranian madder, from Rubia tinctorum family , contains hydroxyl and carbonyl groups which can be attached with polymer chains in wool via hydrogen bonding. On the other hand, madder contains anthraquinonic skeleton dyes  which result in van der Waals forces between the madder and polymer chains in wool. The value α in Eq. 6 was also calculated 0.61 corresponding to 0.5 for the adsorption of anionic dyes on cellulosic fibers .
The Langmuir adsorption isotherm is frequently used for the adsorption of a solute on absorbant’s specific sites . Since the coloring matters existing in the madder have no electrical charge and chemical interaction and hence the Langmuir isotherm could not be used to describe the equilibrium state in wool dyeing.
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Effect of dyebath pH on adsorption of the madder on wool fibers
Wool fabrics were dyed at different pH 4.5, 7 and 9 using the extracted solutions from powdered madder (300% o.w.f.) at an L: R of 30:1. The results obtained have been shown in Fig. 6. It can be seen that adsorption of the madder onto wool fibers has considerably increased at acidic pH.
The hydrolysis of proteins in wool can be catalysed by acids and alkalis and damage to wool can be significantly increased in hot solutions, especially under alkaline conditions , therefore, pH 4.5 was applied for dyeing of wool fabrics. Farizadeh et al.  also found that K/S in wool fabrics dyed with madder increased with decreasing of pH and attributed it to Keto-enol tautomerism of carbonyl groups of madder in acidic media, leading to higher hydrogen bonding with carboxyl groups of wool fibers. In addition, the increase in absorbance of extracted Iranian-madder solutions  and the coloring components, purpurin and nordamncanthal, solutions in Indian madder [10, 24] proves that the...