## Synthesis of surfactants The details of synthesis

2.5. Pretreatment effect

Acrylic samples were first pretreated in surfactant solutions 2% (o.w.f) individually at 100 °C for 2 h and the samples were rinsed thoroughly and dried. The dye adsorption onto these pretreated samples was investigated in the same way as described in Section 2.4. This was to determine the ability of dye SB 415286 to replace the pre-adsorbed surfactant molecules onto the acrylic fiber.

In addition, the effect of the cationic surfactants on desorption of the cationic dye from pre-dyed fibers was determined. The dyed samples were placed in the surfactant solution 1% (o.w.f) and treated at 100 °C for 2 h. At the end of this procedure, the amount of desorbed dye into the dye-bath solution was determined using UV-Vis spectroscopy.

2.6. Empirical kinetic models

The empirical kinetic models can be used to estimate the dyeing rate constant which shows how fast the dye adsorption takes place. There are cytokinesis a number of empirical kinetic models for determination of the rate constant (k) such the zero order or parabolic equation (Eq. (2)), the first order or exponential equation (Eq. (3)), the Cegarra and Puente equation (Eq. (4)) and the modified Cegarra-Puente equation (Eq. (5)) [14] and [30].equation(2)dCtdt=kCt→Ct=ktequation(3)dCtdt=k(C−∞Ct)→ln1−CtC∞=−ktequation(4)ln1−Ct2C∞2=−ktequation(5)ln−ln1−Ct2C∞2=a×ln k+a×ln t